A multi-phase field model is established to simulate the growth competition and evolution behavior between seaweed and columnar dendrites during directional solidification.According to the effects of surface tension a...A multi-phase field model is established to simulate the growth competition and evolution behavior between seaweed and columnar dendrites during directional solidification.According to the effects of surface tension and interfacial energy,we quantitatively analyze the influences of factors such as inclination angles,pulling velocity,and anisotropic strength on twin growth.The results demonstrate that the pulling velocity and anisotropic strength have an important influence on the morphology and evolution of the seaweed and dendritic growth.The low pulling velocity and anisotropic strength are both key parameters for maintaining the stable morphology of seaweed during competitive growth in a bicrystal,showing that the lateral branching behavior is the root of the dendrites that can ultimately dominate the growth.And it is clarified that the lateral branching behavior and lateral blocking are the root causes of the final dominant growth of dendrites.With the increase of anisotropy strength,the seaweed is eliminated fastest in case 1,the seaweed is transformed into degenerate dendritic morphology,and eliminates the seaweed by promoting the generation and lateral growth of the lateral branches of the dendrites.The increase of pulling velocity is to increase the undercooling of favorable oriented grain and accelerate the growth rate of dendrites,thus producing more new primary dendrites for lateral expansion and accelerating the elimination rate of unfavorable oriented grain.展开更多
With the multi-phase field model,the unidirectional solidification with constant velocity growth and variable velocity growth of the CBr_(4)-C_(2)Cl_(6)eutectic alloy is simulated in three dimensions.The simulated res...With the multi-phase field model,the unidirectional solidification with constant velocity growth and variable velocity growth of the CBr_(4)-C_(2)Cl_(6)eutectic alloy is simulated in three dimensions.The simulated results with constant velocity growth show that with the increase of pulling velocity,the morphology of the CBr_(4)-C_(2)Cl_(6)alloy evolves in the sequence of lamellar merging-lamellar-rod transition-stable lamellar growth-oscillating growth-lamellar branching.A morphology selection map is established with different pulling velocities,which is confirmed to be correct by the velocity change process.It is shown that all of the morphology transitions,the average interface growth velocity and average interface undercooling show a hysteresis effect against the instant of velocity change.The relationship between the interface average undercooling and interface average growth velocity is consistent with the theoretical value.展开更多
As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency...As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔE_(ST))of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔE_(ST)would be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S_(1)state energy(E(S_(1))),T_(1)state ener-gy(E(T_(1))),andΔE_(ST)using three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S_(1)),E(T_(1)),andΔE_(ST)for 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S_(1)state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T_(1)state energy.TheΔE_(ST)derived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔE_(ST)of MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.展开更多
This work establishes a temperature-controlled sequence function, and a new multi-phase-field model, for liquid- solid-solid multi-phase transformation by coupling the liquid-solid phase transformation model with the ...This work establishes a temperature-controlled sequence function, and a new multi-phase-field model, for liquid- solid-solid multi-phase transformation by coupling the liquid-solid phase transformation model with the solid-solid phase transformation model. Taking an Fe-C alloy as an example, the continuous evolution of a multi-phase transformation is simulated by using this new model. In addition, the growth of grains affected by the grain orientation of the parent phase （generated in liquid-solid phase transformation） in the solid-solid phase transformation is studied. The results show that the morphology of ferrite grains which nucleate at the boundaries of the austenite grains is influenced by the orientation of the parent austenite grains. The growth rate of ferrite grains which nucleate at small-angle austenite grain boundaries is faster than those that nucleate at large-angle austenite grain boundaries. The difference of the growth rate of ferrites grains in different parent phase that nucleate at large-angle austenite grain boundaries, on both sides of the boundaries, is greater than that of ferrites nucleating at small-angle austenite grain boundaries.展开更多
In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as...In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.展开更多
The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.Howeve...The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.展开更多
A graphics-processing-unit(GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection condit...A graphics-processing-unit(GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection conditions by coupling a multi-phase field model and a lattice Boltzmann model.The elimination mechanism in the evolution process is analyzed for the three conformational schemes constituting converging bi-crystals under pure diffusion and forced convection conditions,respectively,expanding the research of the competitive growth of columnar dendrites under melt convection conditions.The results show that the elimination mechanism for the competitive growth of converging bi-crystals of all three configurations under pure diffusion conditions follows the conventional Walton-Chalmers model.When there is forced convection with lateral flow in the liquid phase,the anomalous elimination phenomenon of unfavorable dendrites eliminating favorable dendrites occurs in the grain boundaries.In particular,the anomalous elimination phenomenon is relatively strong in conformation 1 and conformation 2 when the orientation angle of unfavorable dendrites is small,and relatively weak in conformation 3.Moreover,the presence of convection increases the tip growth rate of both favorable and unfavorable dendrites in the grain boundary.In addition,the parallelization of the multi-phase-field-lattice Boltzmann model is achieved by designing the parallel computation of the model on the GPU platform concerning the computerunified-device-architecture parallel technique,and the results show that the parallel computation of this model based on the GPU has absolute advantages,and the parallel acceleration is more obvious as the computation area increases.展开更多
The multi-phase field model of grain competitive growth during directional solidification of alloy is established.Solving multi-phase field models for thin interface layer thickness conditions,the grain boundary evolu...The multi-phase field model of grain competitive growth during directional solidification of alloy is established.Solving multi-phase field models for thin interface layer thickness conditions,the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt%camphor model alloy bi-crystals are investigated.The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed.The obtained results are shown below.In the competitive growth of convergent bi-crystals,when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large,the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite,blocking the unfavorably oriented dendrite,and the grain boundary is along the growth direction of the favorably oriented dendrite.When the pulling speed becomes small,the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite,eliminating the favorably oriented dendrite.In the process of competitive growth of divergent bi-crystal,when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small,the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains,and as the orientation angle of unfavorably oriented dendrites becomes larger,the unfavorably oriented grains are more likely to have stable secondary dendritic arms,which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space,but the grain boundary direction is still parallel to favorably oriented dendrites.In addition,the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes,this blocking of the tertiary dendritic arms has a random nature,which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.展开更多
The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase fiel...The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase field method was utilized to simulate the impact of displacement velocity,the water-gas viscosity ratio,and the density ratio on the flow behavior of two-phase fluids in porous media.The effectiveness of displacement was evaluated by analyzing CO_(2)saturation levels.The results indicate that the saturation of CO_(2)in porous media increased as the displacement velocity increased.When the displacement velocity exceeded 0.01 m/s,there was a corresponding increase in CO_(2)saturation.Conversely,when the displacement velocity was below this threshold,the impact on CO_(2)saturation was minimal.An“inflection point,”M3,was present in the viscosity ratio.When the viscosity of CO_(2)is less than 8.937×10^(-5)Pa·s(viscosity ratio below M3),variations in the viscosity of CO_(2)had little impact on its saturation.Conversely,when the viscosity of CO_(2)exceeded 8.937×10^(-5)Pa·s(viscosity ratio greater than M3),saturation increased with an increase in the viscosity ratio.In terms of the density ratio,the saturation of CO_(2)increased monotonically with an increase in the density ratio.Similarly,increasing density ratios resulted in a monotonic increase in CO_(2)saturation,though this trend was less pronounced in numerical simulations.Analysis results of displacement within dead-end pores using pressure and velocity diagrams reveal eddy currents as contributing factors.Finally,the impact of pore throat structure on the formation of dominant channels was examined.展开更多
Path planning for recovery is studied on the engineering background of double unmanned surface vehicles(USVs)towing oil booms for oil spill recovery.Given the influence of obstacles on the sea,the improved artificial ...Path planning for recovery is studied on the engineering background of double unmanned surface vehicles(USVs)towing oil booms for oil spill recovery.Given the influence of obstacles on the sea,the improved artificial potential field(APF)method is used for path planning.For addressing the two problems of unreachable target and local minimum in the APF,three improved algorithms are proposed by combining the motion performance constraints of the double USV system.These algorithms are then combined as the final APF-123 algorithm for oil spill recovery.Multiple sets of simulation tests are designed according to the flaws of the APF and the process of oil spill recovery.Results show that the proposed algorithms can ensure the system’s safety in tracking oil spills in a complex environment,and the speed is increased by more than 40%compared with the APF method.展开更多
The formation water sample in oil and gas fields may be polluted in processes of testing, trial production, collection, storage, transportation and analysis, making the properties of formation water not be reflected t...The formation water sample in oil and gas fields may be polluted in processes of testing, trial production, collection, storage, transportation and analysis, making the properties of formation water not be reflected truly. This paper discusses identification methods and the data credibility evaluation method for formation water in oil and gas fields of petroliferous basins within China. The results of the study show that: (1) the identification methods of formation water include the basic methods of single factors such as physical characteristics, water composition characteristics, water type characteristics, and characteristic coefficients, as well as the comprehensive evaluation method of data credibility proposed on this basis, which mainly relies on the correlation analysis sodium chloride coefficient and desulfurization coefficient and combines geological background evaluation;(2) The basic identifying methods for formation water enable the preliminary identification of hydrochemical data and the preliminary screening of data on site, the proposed comprehensive method realizes the evaluation by classifying the CaCl2-type water into types A-I to A-VI and the NaHCO3-type water into types B-I to B-IV, so that researchers can make in-depth evaluation on the credibility of hydrochemical data and analysis of influencing factors;(3) When the basic methods are used to identify the formation water, the formation water containing anions such as CO_(3)^(2-), OH- and NO_(3)^(-), or the formation water with the sodium chloride coefficient and desulphurization coefficient not matching the geological setting, are all invaded with surface water or polluted by working fluid;(4) When the comprehensive method is used, the data credibility of A-I, A-II, B-I and B-II formation water can be evaluated effectively and accurately only if the geological setting analysis in respect of the factors such as formation environment, sampling conditions, condensate water, acid fluid, leaching of ancient weathering crust, and ancient atmospheric fresh water, is combined, although such formation water is believed with high credibility.展开更多
This paper introduces a framework for modeling random fields,with a particular emphasis on analyzing anisotropic spatial variability.It establishes a clear connection between the correlation function and the Kriging v...This paper introduces a framework for modeling random fields,with a particular emphasis on analyzing anisotropic spatial variability.It establishes a clear connection between the correlation function and the Kriging variogram across various anisotropic modes,providing mathematical models to enhance our understanding of random fields.A new anisotropy index,called LSAI,is introduced to quantify anisotropy based on the autocorrelation length and the orientation of the principal axes within the variogram.An LSAI value closer to one indicates a lower degree of anisotropy.The present study examines how the degree of anisotropy varies with different autocorrelation lengths and angles between the principal axes,providing valuable insights into these relationships.To improve the accuracy of parameter probability distribution estimations,this study integrates limited field test data using a Bayesian inference approach.Additionally,the Markov chain Monte Carlo simulation method is employed to develop a conditional random field(CRF)for the deformation modulus.By incorporating data from field bearing plate tests,the posterior variance data for the deformation modulus are derived.This process facilitates the construction of a detailed and reliable CRF for the deformation modulus.展开更多
A phase-field model including magnetic field induced dendrite fragmentation was established and applied to the cases with different initial crystal nuclear positions for AA5754 aluminum alloy electromagnetic laser bea...A phase-field model including magnetic field induced dendrite fragmentation was established and applied to the cases with different initial crystal nuclear positions for AA5754 aluminum alloy electromagnetic laser beam welding.Compare the calculated results that include dendrite fragmentation caused by the thermal electromagnetic Lorentz force with the results that consider only the thermal electromagnetic Lorentz force,without fragmentation,at the characteristic time instants.Both in the early and late stages,the small fragmentation at the dendrite tip promotes the number of higher-order branches and their growth,especially in the direction perpendicular to the solidification.The later stage fragmentation has the possibility of breaking one grain into several,which verifies the possibility of grain refinement caused by dendrite fragmentation.The fracture surface caused by fragmentation also makes more solid-liquid interfaces and their growth.In addition,the cases with different initial nuclear positions were compared.The grain growth in the low-temperature zone can be inhibited by the equiaxed grains'fragmentation at the high-temperature area(179.8μm^(2) and 14.7% start at the center,115.4μm^(2) and 9.4% start at the high-temperature corner,134.3μm^(2) and 10.9%start at the low-temperature corner),which is another kind of grain refinement by the dendrite fragmentation.This kind of inhibition effect on grain growth in the low-temperature region will be enhanced with the increasing time interval between the two crystal nuclei’appearance(179.8μm^(2) and 14.7%when virtual grains appear at t=4.3803 s and t=4.3803 s,134.3μm^(2) and 10.9%at t=4.0977 s and t=3.9564 s,and 115.4μm^(2) and 9.4%at t=3.8151 s and t=3.5325 s).展开更多
Lithium metal batteries(LMBs)represent a promising solution for next-generation energy storage due to their high energy density,but the growth of lithium dendrites presents significant challenges to their performance ...Lithium metal batteries(LMBs)represent a promising solution for next-generation energy storage due to their high energy density,but the growth of lithium dendrites presents significant challenges to their performance and safety.This review provides a comprehensive overview of the mechanisms behind lithium dendrite formation and the role of in situ/operando observation and phase field simulation in understanding and mitigating this issue,The key driving factors of dendrite growth,such as lithium-ion flux heterogeneity,surface defects,and localized stress,are explored through advanced experimental techniques,which enable real-time visualization of dendrite nucleation and growth dynamics.Complementarily,phase field simulations provide insights into subsurface and temporal evolution of dendrites by modeling thermodynamic and kinetic processes,while machine learning techniques optimize simulation accuracy through data-driven parameter refinement.The integration of experimental observations with simulation models holds great potential in improving understanding and predictive capabilities.Despite ongoing progress,challenges remain in resolving technical limitations in observation techniques,improving computational efficiency,and fostering interdisciplinary collaboration.This review highlights the synergy between experimental and computational strategies in advancing the development of LMBs and calls for continued research to overcome existing hurdles and unlock the full potential of lithium metal anodes.展开更多
The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled wi...The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.展开更多
By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage du...By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage during the ageing process under 1 000 K were studied. And free energy, microstructures, compositions and volume fractions of pre-precipitation phase and equilibrium phase were analyzed. The simulation results indicate that nonstoichiometric Llo pre-precipitation phase formed first, and then would gradually transform into L12 equilibrium phase. It is discovered that the phase transformation process was closely related to free energy and interatomic potentials. Additionally, it is revealed that free energy of Llo pre-precipitation phase was higher and interatomic potential was smaller than that of L12 equilibrium phase. Therefore, it is concluded that Llo phase was unstable, and phase transformation would occur to L12 which was more stable.展开更多
A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting backg...A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.展开更多
We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method...We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method, involves complex operation, and its digital filtering algorithm requires a large number of calculations. To solve these problems, we proposed an improved discrete image method, where the following are realized： the real number of the electromagnetic field solution based on the Gaver-Stehfest algorithm for approximate inversion, the exponential approximation of the objective kernel function using the Prony method, the transient electromagnetic field according to discrete image theory, and closed-form solution of the approximate coefficients. To verify the method, we tentatively calculated the transient electromagnetic field in a homogeneous model and compared it with the results obtained from the Hankel transform digital filtering method. The results show that the method has considerable accuracy and good applicability. We then used this method to calculate the transient electromagnetic field generated by a ground magnetic dipole source in a typical geoelectric model and analyzed the horizontal component response of the induced magnetic field obtained from the ＂ground excitation-stratum measurement method. We reached the conclusion that the horizontal component response of a transient field is related to the geoelectric structure, observation time, spatial location, and others. The horizontal component response of the induced magnetic field reflects the eddy current field distribution and its vertical gradient variation. During the detection of abnormal objects, positions with a zero or comparatively large offset were selected for the drill- hole measurements or a comparatively long observation delay was adopted to reduce the influence of the ambient field on the survey results. The discrete image method and forward calculation results in this paper can be used as references for relevant research.展开更多
A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth m...A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.展开更多
The shape optimization is studied by adopting the domain integrated method which is based on the calculus of variations during the shape design sensitivity analysis. A new method of improving the efficiency of the de...The shape optimization is studied by adopting the domain integrated method which is based on the calculus of variations during the shape design sensitivity analysis. A new method of improving the efficiency of the design velocity field analysis and the quality of the finite element method (FEM) mesh is put forward. The sensitivity analysis which is based on the calculus of variations is used in the shape optimization. The design velocity field is solved by Herrmann method. An example shows that both the quality of the FEM mesh and the efficiency of the computing of the design velocity field are improved by Herrmann method. So the effect and the efficiency of the shape optimization are guaranteed. If using sensitivity analysis which is based on the calculus of variations in the shape optimization, the sensitivity analysis can be a relatively independent module. The efficiency of computing the design velocity field and the quality of mesh will be improved by using Herrmann method.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020,and 11364024)the Postdoctoral Science Foundation of China(Grant No.2014M560371)the Funds for Distinguished Young Scientists of Lanzhou University of Technology,China(Grant No.J201304)。
文摘A multi-phase field model is established to simulate the growth competition and evolution behavior between seaweed and columnar dendrites during directional solidification.According to the effects of surface tension and interfacial energy,we quantitatively analyze the influences of factors such as inclination angles,pulling velocity,and anisotropic strength on twin growth.The results demonstrate that the pulling velocity and anisotropic strength have an important influence on the morphology and evolution of the seaweed and dendritic growth.The low pulling velocity and anisotropic strength are both key parameters for maintaining the stable morphology of seaweed during competitive growth in a bicrystal,showing that the lateral branching behavior is the root of the dendrites that can ultimately dominate the growth.And it is clarified that the lateral branching behavior and lateral blocking are the root causes of the final dominant growth of dendrites.With the increase of anisotropy strength,the seaweed is eliminated fastest in case 1,the seaweed is transformed into degenerate dendritic morphology,and eliminates the seaweed by promoting the generation and lateral growth of the lateral branches of the dendrites.The increase of pulling velocity is to increase the undercooling of favorable oriented grain and accelerate the growth rate of dendrites,thus producing more new primary dendrites for lateral expansion and accelerating the elimination rate of unfavorable oriented grain.
基金supported by the National Natural Science Foundation of China(Grant No.51001082)the China Postdoctoral Science Foundation(Grant No.20090460654)Shanghai Science and Technology Commit-tee(Grant Nos.0752nm004 and 08DZ2201300)
文摘With the multi-phase field model,the unidirectional solidification with constant velocity growth and variable velocity growth of the CBr_(4)-C_(2)Cl_(6)eutectic alloy is simulated in three dimensions.The simulated results with constant velocity growth show that with the increase of pulling velocity,the morphology of the CBr_(4)-C_(2)Cl_(6)alloy evolves in the sequence of lamellar merging-lamellar-rod transition-stable lamellar growth-oscillating growth-lamellar branching.A morphology selection map is established with different pulling velocities,which is confirmed to be correct by the velocity change process.It is shown that all of the morphology transitions,the average interface growth velocity and average interface undercooling show a hysteresis effect against the instant of velocity change.The relationship between the interface average undercooling and interface average growth velocity is consistent with the theoretical value.
基金support provided by the National Natural Science Foundation of China(No.22273043).
文摘As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔE_(ST))of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔE_(ST)would be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S_(1)state energy(E(S_(1))),T_(1)state ener-gy(E(T_(1))),andΔE_(ST)using three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S_(1)),E(T_(1)),andΔE_(ST)for 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S_(1)state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T_(1)state energy.TheΔE_(ST)derived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔE_(ST)of MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.
基金supported by the National Natural Science Foundation of China(Grant Nos.51661020,11504149,and 11364024)
文摘This work establishes a temperature-controlled sequence function, and a new multi-phase-field model, for liquid- solid-solid multi-phase transformation by coupling the liquid-solid phase transformation model with the solid-solid phase transformation model. Taking an Fe-C alloy as an example, the continuous evolution of a multi-phase transformation is simulated by using this new model. In addition, the growth of grains affected by the grain orientation of the parent phase （generated in liquid-solid phase transformation） in the solid-solid phase transformation is studied. The results show that the morphology of ferrite grains which nucleate at the boundaries of the austenite grains is influenced by the orientation of the parent austenite grains. The growth rate of ferrite grains which nucleate at small-angle austenite grain boundaries is faster than those that nucleate at large-angle austenite grain boundaries. The difference of the growth rate of ferrites grains in different parent phase that nucleate at large-angle austenite grain boundaries, on both sides of the boundaries, is greater than that of ferrites nucleating at small-angle austenite grain boundaries.
文摘In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103 and 42174090)the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the MOST Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4).
文摘The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020,and 11364024)the Postdoctoral Science Foundation of China(Grant No.2014M560371)the Funds for Distinguished Young Scientists of Lanzhou University of Technology,China(Grant No.J201304).
文摘A graphics-processing-unit(GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection conditions by coupling a multi-phase field model and a lattice Boltzmann model.The elimination mechanism in the evolution process is analyzed for the three conformational schemes constituting converging bi-crystals under pure diffusion and forced convection conditions,respectively,expanding the research of the competitive growth of columnar dendrites under melt convection conditions.The results show that the elimination mechanism for the competitive growth of converging bi-crystals of all three configurations under pure diffusion conditions follows the conventional Walton-Chalmers model.When there is forced convection with lateral flow in the liquid phase,the anomalous elimination phenomenon of unfavorable dendrites eliminating favorable dendrites occurs in the grain boundaries.In particular,the anomalous elimination phenomenon is relatively strong in conformation 1 and conformation 2 when the orientation angle of unfavorable dendrites is small,and relatively weak in conformation 3.Moreover,the presence of convection increases the tip growth rate of both favorable and unfavorable dendrites in the grain boundary.In addition,the parallelization of the multi-phase-field-lattice Boltzmann model is achieved by designing the parallel computation of the model on the GPU platform concerning the computerunified-device-architecture parallel technique,and the results show that the parallel computation of this model based on the GPU has absolute advantages,and the parallel acceleration is more obvious as the computation area increases.
基金supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020,and 11504149)the Postdoctoral Science Foundation of China(Grant No.2014M560371)the Funds for Distinguished Young Scientists of Lanzhou University of Technology,China(Grant No.J201304)。
文摘The multi-phase field model of grain competitive growth during directional solidification of alloy is established.Solving multi-phase field models for thin interface layer thickness conditions,the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt%camphor model alloy bi-crystals are investigated.The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed.The obtained results are shown below.In the competitive growth of convergent bi-crystals,when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large,the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite,blocking the unfavorably oriented dendrite,and the grain boundary is along the growth direction of the favorably oriented dendrite.When the pulling speed becomes small,the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite,eliminating the favorably oriented dendrite.In the process of competitive growth of divergent bi-crystal,when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small,the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains,and as the orientation angle of unfavorably oriented dendrites becomes larger,the unfavorably oriented grains are more likely to have stable secondary dendritic arms,which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space,but the grain boundary direction is still parallel to favorably oriented dendrites.In addition,the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes,this blocking of the tertiary dendritic arms has a random nature,which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.
基金National Science Foundation of China,Grant/Award Number:5227090113Shenzhen Science and Technology Program,Grant/Award Numbers:KCXFZ20230731093901003,KCXFZ20211020163816023The Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone,Grant/Award Number:HZQB-KCZYB-2020083。
文摘The two-phase flow in porous media is affected by multiple factors.In the present study,a two-dimensional numerical model of porous media was developed using the actual pore structure of the core sample.The phase field method was utilized to simulate the impact of displacement velocity,the water-gas viscosity ratio,and the density ratio on the flow behavior of two-phase fluids in porous media.The effectiveness of displacement was evaluated by analyzing CO_(2)saturation levels.The results indicate that the saturation of CO_(2)in porous media increased as the displacement velocity increased.When the displacement velocity exceeded 0.01 m/s,there was a corresponding increase in CO_(2)saturation.Conversely,when the displacement velocity was below this threshold,the impact on CO_(2)saturation was minimal.An“inflection point,”M3,was present in the viscosity ratio.When the viscosity of CO_(2)is less than 8.937×10^(-5)Pa·s(viscosity ratio below M3),variations in the viscosity of CO_(2)had little impact on its saturation.Conversely,when the viscosity of CO_(2)exceeded 8.937×10^(-5)Pa·s(viscosity ratio greater than M3),saturation increased with an increase in the viscosity ratio.In terms of the density ratio,the saturation of CO_(2)increased monotonically with an increase in the density ratio.Similarly,increasing density ratios resulted in a monotonic increase in CO_(2)saturation,though this trend was less pronounced in numerical simulations.Analysis results of displacement within dead-end pores using pressure and velocity diagrams reveal eddy currents as contributing factors.Finally,the impact of pore throat structure on the formation of dominant channels was examined.
基金Supported by the National Natural Science Foundation of China (Grant No. 52071097)Hainan Provincial Natural Science Foundation of China (Grant No. 522MS162)Research Fund from Science and Technology on Underwater Vehicle Technology Laboratory (Grant No. 2021JCJQ-SYSJJ-LB06910)。
文摘Path planning for recovery is studied on the engineering background of double unmanned surface vehicles(USVs)towing oil booms for oil spill recovery.Given the influence of obstacles on the sea,the improved artificial potential field(APF)method is used for path planning.For addressing the two problems of unreachable target and local minimum in the APF,three improved algorithms are proposed by combining the motion performance constraints of the double USV system.These algorithms are then combined as the final APF-123 algorithm for oil spill recovery.Multiple sets of simulation tests are designed according to the flaws of the APF and the process of oil spill recovery.Results show that the proposed algorithms can ensure the system’s safety in tracking oil spills in a complex environment,and the speed is increased by more than 40%compared with the APF method.
基金Supported by the PetroChina Science and Technology Project(2023ZZ0202)。
文摘The formation water sample in oil and gas fields may be polluted in processes of testing, trial production, collection, storage, transportation and analysis, making the properties of formation water not be reflected truly. This paper discusses identification methods and the data credibility evaluation method for formation water in oil and gas fields of petroliferous basins within China. The results of the study show that: (1) the identification methods of formation water include the basic methods of single factors such as physical characteristics, water composition characteristics, water type characteristics, and characteristic coefficients, as well as the comprehensive evaluation method of data credibility proposed on this basis, which mainly relies on the correlation analysis sodium chloride coefficient and desulfurization coefficient and combines geological background evaluation;(2) The basic identifying methods for formation water enable the preliminary identification of hydrochemical data and the preliminary screening of data on site, the proposed comprehensive method realizes the evaluation by classifying the CaCl2-type water into types A-I to A-VI and the NaHCO3-type water into types B-I to B-IV, so that researchers can make in-depth evaluation on the credibility of hydrochemical data and analysis of influencing factors;(3) When the basic methods are used to identify the formation water, the formation water containing anions such as CO_(3)^(2-), OH- and NO_(3)^(-), or the formation water with the sodium chloride coefficient and desulphurization coefficient not matching the geological setting, are all invaded with surface water or polluted by working fluid;(4) When the comprehensive method is used, the data credibility of A-I, A-II, B-I and B-II formation water can be evaluated effectively and accurately only if the geological setting analysis in respect of the factors such as formation environment, sampling conditions, condensate water, acid fluid, leaching of ancient weathering crust, and ancient atmospheric fresh water, is combined, although such formation water is believed with high credibility.
基金supported by the Doctoral Research Funds for Nanchang HangKong University,China(Grant No.EA202411211)support is gratefully acknowledged.
文摘This paper introduces a framework for modeling random fields,with a particular emphasis on analyzing anisotropic spatial variability.It establishes a clear connection between the correlation function and the Kriging variogram across various anisotropic modes,providing mathematical models to enhance our understanding of random fields.A new anisotropy index,called LSAI,is introduced to quantify anisotropy based on the autocorrelation length and the orientation of the principal axes within the variogram.An LSAI value closer to one indicates a lower degree of anisotropy.The present study examines how the degree of anisotropy varies with different autocorrelation lengths and angles between the principal axes,providing valuable insights into these relationships.To improve the accuracy of parameter probability distribution estimations,this study integrates limited field test data using a Bayesian inference approach.Additionally,the Markov chain Monte Carlo simulation method is employed to develop a conditional random field(CRF)for the deformation modulus.By incorporating data from field bearing plate tests,the posterior variance data for the deformation modulus are derived.This process facilitates the construction of a detailed and reliable CRF for the deformation modulus.
基金supported by the Alexander von Humboldt Foundation,and Deutsche Forschungsgemeinschaft(DFG,German Research Foundation,Project No.506270597 and No.466939224).
文摘A phase-field model including magnetic field induced dendrite fragmentation was established and applied to the cases with different initial crystal nuclear positions for AA5754 aluminum alloy electromagnetic laser beam welding.Compare the calculated results that include dendrite fragmentation caused by the thermal electromagnetic Lorentz force with the results that consider only the thermal electromagnetic Lorentz force,without fragmentation,at the characteristic time instants.Both in the early and late stages,the small fragmentation at the dendrite tip promotes the number of higher-order branches and their growth,especially in the direction perpendicular to the solidification.The later stage fragmentation has the possibility of breaking one grain into several,which verifies the possibility of grain refinement caused by dendrite fragmentation.The fracture surface caused by fragmentation also makes more solid-liquid interfaces and their growth.In addition,the cases with different initial nuclear positions were compared.The grain growth in the low-temperature zone can be inhibited by the equiaxed grains'fragmentation at the high-temperature area(179.8μm^(2) and 14.7% start at the center,115.4μm^(2) and 9.4% start at the high-temperature corner,134.3μm^(2) and 10.9%start at the low-temperature corner),which is another kind of grain refinement by the dendrite fragmentation.This kind of inhibition effect on grain growth in the low-temperature region will be enhanced with the increasing time interval between the two crystal nuclei’appearance(179.8μm^(2) and 14.7%when virtual grains appear at t=4.3803 s and t=4.3803 s,134.3μm^(2) and 10.9%at t=4.0977 s and t=3.9564 s,and 115.4μm^(2) and 9.4%at t=3.8151 s and t=3.5325 s).
基金the financial support of the National Natural Science Foundation of China(Nos.12172206 and 11972218)。
文摘Lithium metal batteries(LMBs)represent a promising solution for next-generation energy storage due to their high energy density,but the growth of lithium dendrites presents significant challenges to their performance and safety.This review provides a comprehensive overview of the mechanisms behind lithium dendrite formation and the role of in situ/operando observation and phase field simulation in understanding and mitigating this issue,The key driving factors of dendrite growth,such as lithium-ion flux heterogeneity,surface defects,and localized stress,are explored through advanced experimental techniques,which enable real-time visualization of dendrite nucleation and growth dynamics.Complementarily,phase field simulations provide insights into subsurface and temporal evolution of dendrites by modeling thermodynamic and kinetic processes,while machine learning techniques optimize simulation accuracy through data-driven parameter refinement.The integration of experimental observations with simulation models holds great potential in improving understanding and predictive capabilities.Despite ongoing progress,challenges remain in resolving technical limitations in observation techniques,improving computational efficiency,and fostering interdisciplinary collaboration.This review highlights the synergy between experimental and computational strategies in advancing the development of LMBs and calls for continued research to overcome existing hurdles and unlock the full potential of lithium metal anodes.
基金Project (10964004) supported by the National Natural Science Foundation of ChinaProject (20070731001) supported by Research Fund for the Doctoral Program of ChinaProject (096RJZA104) supported by the Natural Science Foundation of Gansu Province,China
文摘The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni-Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.
基金Projects(10902086, 50941020, 50875217) supported by the National Natural Science Foundation of China Projects(JC201005) supported by Basic Research Fund of Northwestern Polytechnical University, China Project supported by Graduate Starting Seed Fund and Doctoral Foundation of Northwestern Polytechnical University, China
文摘By utilizing phase field method combined with analysis on free energy and interatomic potentials, pre-precipitation phase formation and transformation process of Ni0.75Al0.05Fe0.2 alloy in early precipitation stage during the ageing process under 1 000 K were studied. And free energy, microstructures, compositions and volume fractions of pre-precipitation phase and equilibrium phase were analyzed. The simulation results indicate that nonstoichiometric Llo pre-precipitation phase formed first, and then would gradually transform into L12 equilibrium phase. It is discovered that the phase transformation process was closely related to free energy and interatomic potentials. Additionally, it is revealed that free energy of Llo pre-precipitation phase was higher and interatomic potential was smaller than that of L12 equilibrium phase. Therefore, it is concluded that Llo phase was unstable, and phase transformation would occur to L12 which was more stable.
文摘A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(No.41304082)the Young Scientists Fund of the Natural Science Foundation of Hebei Province(No.D2014403011)the Geological survey project of China Geological Survey(No.12120114090201)
文摘We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method, involves complex operation, and its digital filtering algorithm requires a large number of calculations. To solve these problems, we proposed an improved discrete image method, where the following are realized： the real number of the electromagnetic field solution based on the Gaver-Stehfest algorithm for approximate inversion, the exponential approximation of the objective kernel function using the Prony method, the transient electromagnetic field according to discrete image theory, and closed-form solution of the approximate coefficients. To verify the method, we tentatively calculated the transient electromagnetic field in a homogeneous model and compared it with the results obtained from the Hankel transform digital filtering method. The results show that the method has considerable accuracy and good applicability. We then used this method to calculate the transient electromagnetic field generated by a ground magnetic dipole source in a typical geoelectric model and analyzed the horizontal component response of the induced magnetic field obtained from the ＂ground excitation-stratum measurement method. We reached the conclusion that the horizontal component response of a transient field is related to the geoelectric structure, observation time, spatial location, and others. The horizontal component response of the induced magnetic field reflects the eddy current field distribution and its vertical gradient variation. During the detection of abnormal objects, positions with a zero or comparatively large offset were selected for the drill- hole measurements or a comparatively long observation delay was adopted to reduce the influence of the ambient field on the survey results. The discrete image method and forward calculation results in this paper can be used as references for relevant research.
基金Projects(11102164,11304243)supported by the National Natural Science Foundation of ChinaProject(2014JQ1039)supported by the Natural Science Foundation of Shannxi Province,China+1 种基金Project(3102016ZY027)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(13GH014602)supported by the Program of New Staff and Research Area Project of NWPU,China
文摘A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.
文摘The shape optimization is studied by adopting the domain integrated method which is based on the calculus of variations during the shape design sensitivity analysis. A new method of improving the efficiency of the design velocity field analysis and the quality of the finite element method (FEM) mesh is put forward. The sensitivity analysis which is based on the calculus of variations is used in the shape optimization. The design velocity field is solved by Herrmann method. An example shows that both the quality of the FEM mesh and the efficiency of the computing of the design velocity field are improved by Herrmann method. So the effect and the efficiency of the shape optimization are guaranteed. If using sensitivity analysis which is based on the calculus of variations in the shape optimization, the sensitivity analysis can be a relatively independent module. The efficiency of computing the design velocity field and the quality of mesh will be improved by using Herrmann method.
