This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target ...In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.展开更多
ADER-WAF methods were first introduced by researchers E.F. Toro and V.A. Titarev. The linear stability criterion for the model equation for the ADER-WAF schemes is CCFL≤1, where CCFLdenotes the Courant-Friedrichs-Lew...ADER-WAF methods were first introduced by researchers E.F. Toro and V.A. Titarev. The linear stability criterion for the model equation for the ADER-WAF schemes is CCFL≤1, where CCFLdenotes the Courant-Friedrichs-Lewy (CFL) coefficient. Toro and Titarev employed CCFL=0.95for their experiments. Nonetheless, we noted that the experiments conducted in this study with CCFL=0.95produced solutions exhibiting spurious oscillations, particularly in the high-order ADER-WAF schemes. The homogeneous one-dimensional (1D) non-linear Shallow Water Equations (SWEs) are the subject of these experiments, specifically the solution of the Riemann Problem (RP) associated with the SWEs. The investigation was conducted on four test problems to evaluate the ADER-WAF schemes of second, third, fourth, and fifth order of accuracy. Each test problem constitutes a RP characterized by different wave patterns in its solution. This research has two primary objectives. We begin by illustrating the procedure for implementing the ADER-WAF schemes for the SWEs, providing the required relations. Afterward, following comprehensive testing, we present the range for the CFL coefficient for each test that yields solutions with diminished or eliminated spurious oscillations.展开更多
Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under...Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under three different greening schemes in typical areas of the Guangzhou University campus.The results indicate that the outdoor thermal environment is significantly influenced by the underlying surface materials and vegetation.The temperature of brick-paved surface is 0.9℃higher than that of natural soil surfaces under tree shade.Numerical simulations further confirm that increasing vegetation coverage effectively reduces outdoor air temperature.When the greening rate increases to 40%,the outdoor average temperature decreases by 0.7℃and relative humidity increases by approximately 4%,while wind speed remains minimal change.The cooling effect of vegetation is found to extend vertically to an altitude of 13 m.As the greening rate increases from 15%to 40%,the Mean Radiant Temperature(MRT)decreases from 50.6℃to 28.9℃,which is lower than the average ambient temperature,indicating improved thermal conditions.The Physiological Equivalent Temperature(PET)decreases from 40.2℃to 30.0℃,with the proportion of the areas classified as″very hot″reducing by 36.8%,significantly improving thermal comfort across most areas.Therefore,changing the ground material and greening landscape design can effectively alter the outdoor wind and thermal environment of the campus,thereby enhancing the thermal comfort for the campus community.展开更多
To effectively select risk control schemes in uncertain environments,this paper has proposed an analysis and evaluation method based on the fuzzy comprehensive evaluation method.Firstly,enterprises have adopted the br...To effectively select risk control schemes in uncertain environments,this paper has proposed an analysis and evaluation method based on the fuzzy comprehensive evaluation method.Firstly,enterprises have adopted the brainstorming method and the Delphi method to identify risks in engineering projects,and organized the identified risks in the form of checklists to facilitate further analysis.Secondly,the fuzzy comprehensive evaluation theory was introduced to determine the comparison matrix of each risk factor and its weight.Furthermore,the top five risk factors in terms of weight ranking were taken as the evaluation factors for the selection of risk control plans.The plans were scored through the weighted scoring method,and the optimal risk control plan was determined based on the score.Finally,the feasibility of the proposed selection technology was verified through A research example of the risk control plan assessment for the construction project of Enterprise A.展开更多
The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These me...The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These methods allow to effectively suppress oscillations,including in velocity profiles,as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations.The methods can be applied both in explicit and implicit(method of separate sweeps)iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer,as well as in solving problems of magnetohydrodynamics and computational astrophysics.In order to avoid loss of solution accuracy on spatially non-uniform grids,in this work an algorithm of grid embeddings is developed,which is applied near transition points between cells of different sizes.The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes.Calculations are performed for the classical problem of decay of an arbitrary discontinuity(Sod’s problem)and the problem of propagation of two symmetric rarefaction waves in opposite directions(Einfeldt’s problem).In the case of using different methods for selecting the AAV,a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed.As a result of the comparative analysis,the applicability of these methods is shown in the spatially one-dimensional case(explicit and implicit iterative processes).The obtained results are compared with the data from the literature.The results coincide with analytical solutions with high accuracy,where the relative error does not exceed 0.1%,which demonstrates the effectiveness of the developed algorithms and methods.展开更多
International carbon tax issues such as carbon leakage and carbon neutralization have become major topics of social concern.Based on the practical experience of carbon tax system in individual countries,this paper int...International carbon tax issues such as carbon leakage and carbon neutralization have become major topics of social concern.Based on the practical experience of carbon tax system in individual countries,this paper integrates the existing research of international carbon tax scholars to the classification and comparative analysis of international carbon tax schemes.Using a literature review approach,this dissertation mainly applies the method of qualitative analysis to explain and compare the contents of four international carbon tax options.Through the analysis and evaluation of individual countries’carbon tax practice,the two-country model is verified.Through the method of comparative analysis,the schemes are evaluated from four dimensions and an assessment is made.The difference of carbon tax among countries makes the internal policies of countries adjust accordingly with the changes of international environment,which promotes the gradual convergence of carbon tax schemes.The results intend to provide reference to further study the issue on international carbon tax.展开更多
By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod func...By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.展开更多
A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can e...A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.展开更多
In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid colu...In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.展开更多
Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the...Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.展开更多
Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,c...Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,capturing extreme storm cases over complex terrain remains challenging.This study utilizes the Global–Regional Integrated Forecast System(GRIST)with variable resolution to simulate an eastward-propagating MCS event.The impact of three microphysics schemes,including two single-moment schemes(WSM6,Lin)and one double-moment scheme(Morrison),on the model sensitivity of MCS precipitation simulations is investigated.The results demonstrate that while all the schemes capture the spatial distribution and temporal variation of MCS precipitation,the Morrison scheme alleviates overestimated precipitation compared to the Lin and WSM6 schemes.The ascending motion gradually becomes weaker in the Morrison scheme during the MCS movement process.Compared to the runs with convection parameterization,the explicit-convection setup at 3.5-km resolution reduces disparities in atmospheric dynamics due to microphysics sensitivity in terms of vertical motions and horizontal kinetic energy at the high-wavenumber regimes.The explicit-convection setup more accurately captures the propagation of both main and secondary precipitation centers during the MCS development,diminishing the differences in both precipitation intensity and propagation features between the Morrison and two single-moment schemes.These findings underscore the importance of microphysics schemes for global nonhydrostatic modeling at the kilometer scale.The role of explicit convection for reducing model uncertainty is also outlined.展开更多
In this paper,the previously proposed second-order process-based modified Patankar Runge-Kutta schemes are extended to the third order of accuracy.Owing to the process-based implicit handling of reactive source terms,...In this paper,the previously proposed second-order process-based modified Patankar Runge-Kutta schemes are extended to the third order of accuracy.Owing to the process-based implicit handling of reactive source terms,the mass conservation,mole balance and energy conservation are kept simultaneously while the positivity for the density and pressure is preserved unconditionally even with stiff reaction networks.It is proved that the first-order truncation terms for the Patankar coefficients must be zero to achieve a prior third order of accuracy for most cases.A twostage Patankar procedure for each Runge-Kutta step is designed to eliminate the first-order truncation terms,accomplish the prior third order of accuracy and maximize the Courant number which the total variational diminishing property requires.With the same approach as the second-order schemes,the third-order ones are applied to Euler equations with chemical reactive source terms.Numerical studies including both 1D and 2D ordinary and partial differential equations are conducted to affirm both the prior order of accuracy and the positivity-preserving property for the density and pressure.展开更多
Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do ...Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.展开更多
We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH nume...We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.展开更多
In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two ...In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two nonlinear schemes and two linearized schemes are presented. All resulting schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities are used to highlight the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be also conducted. The numerical results show that the interaction behavior is elastic and the conserved quantities are conserved exactly, and this is a good indication of the reliability of the schemes which we derived. A comparison with some existing is presented as well.展开更多
The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipativ...The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were reported.The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations.The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do.Research progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.展开更多
The vertical structures of atmospheric temperature anomalies associated with El Nio are simulated with a spectrum atmospheric general circulation model developed by LASG/IAP （SAMIL）. Sensitivity of the model’s resp...The vertical structures of atmospheric temperature anomalies associated with El Nio are simulated with a spectrum atmospheric general circulation model developed by LASG/IAP （SAMIL）. Sensitivity of the model’s response to convection scheme is discussed. Two convection schemes, i.e., the revised Zhang and Macfarlane （RZM） and Tiedtke （TDK） convection schemes, are employed in two sets of AMIP-type （Atmospheric Model Intercomparison Project） SAMIL simulations, respectively. Despite some deficiencies in the upper troposphere, the canonical El Nio-related temperature anomalies characterized by a prevailing warming throughout the tropical troposphere are well reproduced in both simulations. The performance of the model in reproducing temperature anomalies in ＂atypical＂ El Nio events is sensitive to the convection scheme. When employing the RZM scheme, the warming center over the central-eastern tropical Pacific and the strong cooling in the western tropical Pacific at sea surface level are underestimated. The quadru-pole temperature anomalies in the middle and upper troposphere are also obscured. The result of employing the TDK scheme resembles the reanalysis and hence shows a better performance. The simulated largescale circulations associated with atypical El Nio events are also sensitive to the convection schemes. When employing the RZM scheme, SAMIL failed in capturing the classical Southern Oscillation pattern. In accordance with the unrealistic anomalous Walker circulation and the upper tropospheric zonal wind changes, the deficiencies of the precipitation simulation are also evident. These results demonstrate the importance of convection schemes in simulating the vertical structure of atmospheric temperature anomalies associated with El Nio and should serve as a useful reference for future improvement of SAMIL.展开更多
A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx...A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).展开更多
A deep foundation pit constructed for an underground transportation hub was excavated near the Yangtze River.Among the strata,there are two confined aquifers,between which lies an aquiclude that is partially missing.T...A deep foundation pit constructed for an underground transportation hub was excavated near the Yangtze River.Among the strata,there are two confined aquifers,between which lies an aquiclude that is partially missing.To guarantee the safety of pit excavation,the piezometric head of the upper confined aquifer,where the pit bottom is located,should be 1 m below the pit bottom,while that of the lower confined aquifer should be dewatered down to a safe water level to avoid uplift problem.The Yangtze River levee is notably close to the pit,and its deformation caused by dewatering should be controlled.A pumping test was performed to obtain the hydraulic conductivity of the upper confined aquifer.The average value of the hydraulic conductivity obtained from analytical calculation is 20.45 m/d,which is larger than the values from numerical simulation(horizontal hydraulic conductivity K_H=16 m/d and vertical hydraulic conductivity K_V=S m/d).The difference between K_H and K_V indicates the anisotropy of the aquifer.Two dewatering schemes were designed for the construction and simulated by the numerical models for comparison purposes.The results show that though the first scheme could meet the dewatering requirements,the largest accumulated settlement and differential settlement would be94.64 mm and 3.3‰,respectively,greatly exceeding the limited values.Meanwhile,the second scheme,in which the bottoms of the waterproof curtains in ramp B and the river side of ramp A are installed at a deeper elevation of-28 m above sea level,and 27 recharge wells are set along the levee,can control the deformation of the levee significantly.展开更多
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
基金supported by the National Natural Science Foundation of China(Grant No.11571181)by the Natural Science Foundation of Jiangsu Province(Grant No.BK20171454).
文摘In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.
文摘ADER-WAF methods were first introduced by researchers E.F. Toro and V.A. Titarev. The linear stability criterion for the model equation for the ADER-WAF schemes is CCFL≤1, where CCFLdenotes the Courant-Friedrichs-Lewy (CFL) coefficient. Toro and Titarev employed CCFL=0.95for their experiments. Nonetheless, we noted that the experiments conducted in this study with CCFL=0.95produced solutions exhibiting spurious oscillations, particularly in the high-order ADER-WAF schemes. The homogeneous one-dimensional (1D) non-linear Shallow Water Equations (SWEs) are the subject of these experiments, specifically the solution of the Riemann Problem (RP) associated with the SWEs. The investigation was conducted on four test problems to evaluate the ADER-WAF schemes of second, third, fourth, and fifth order of accuracy. Each test problem constitutes a RP characterized by different wave patterns in its solution. This research has two primary objectives. We begin by illustrating the procedure for implementing the ADER-WAF schemes for the SWEs, providing the required relations. Afterward, following comprehensive testing, we present the range for the CFL coefficient for each test that yields solutions with diminished or eliminated spurious oscillations.
基金Science and Technology Research Project of Guang-dong Meteorological Bureau(GRMC2022M21)Guangdong Basic and Applied Basic Research Foundation(2023A1515012240)Research Project of Guangzhou Meteor-ological Bureau(M202218)。
文摘Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under three different greening schemes in typical areas of the Guangzhou University campus.The results indicate that the outdoor thermal environment is significantly influenced by the underlying surface materials and vegetation.The temperature of brick-paved surface is 0.9℃higher than that of natural soil surfaces under tree shade.Numerical simulations further confirm that increasing vegetation coverage effectively reduces outdoor air temperature.When the greening rate increases to 40%,the outdoor average temperature decreases by 0.7℃and relative humidity increases by approximately 4%,while wind speed remains minimal change.The cooling effect of vegetation is found to extend vertically to an altitude of 13 m.As the greening rate increases from 15%to 40%,the Mean Radiant Temperature(MRT)decreases from 50.6℃to 28.9℃,which is lower than the average ambient temperature,indicating improved thermal conditions.The Physiological Equivalent Temperature(PET)decreases from 40.2℃to 30.0℃,with the proportion of the areas classified as″very hot″reducing by 36.8%,significantly improving thermal comfort across most areas.Therefore,changing the ground material and greening landscape design can effectively alter the outdoor wind and thermal environment of the campus,thereby enhancing the thermal comfort for the campus community.
文摘To effectively select risk control schemes in uncertain environments,this paper has proposed an analysis and evaluation method based on the fuzzy comprehensive evaluation method.Firstly,enterprises have adopted the brainstorming method and the Delphi method to identify risks in engineering projects,and organized the identified risks in the form of checklists to facilitate further analysis.Secondly,the fuzzy comprehensive evaluation theory was introduced to determine the comparison matrix of each risk factor and its weight.Furthermore,the top five risk factors in terms of weight ranking were taken as the evaluation factors for the selection of risk control plans.The plans were scored through the weighted scoring method,and the optimal risk control plan was determined based on the score.Finally,the feasibility of the proposed selection technology was verified through A research example of the risk control plan assessment for the construction project of Enterprise A.
基金carried out within the framework of the state assignment of KIAM RAS(No.125020701776-0).
文摘The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These methods allow to effectively suppress oscillations,including in velocity profiles,as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations.The methods can be applied both in explicit and implicit(method of separate sweeps)iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer,as well as in solving problems of magnetohydrodynamics and computational astrophysics.In order to avoid loss of solution accuracy on spatially non-uniform grids,in this work an algorithm of grid embeddings is developed,which is applied near transition points between cells of different sizes.The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes.Calculations are performed for the classical problem of decay of an arbitrary discontinuity(Sod’s problem)and the problem of propagation of two symmetric rarefaction waves in opposite directions(Einfeldt’s problem).In the case of using different methods for selecting the AAV,a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed.As a result of the comparative analysis,the applicability of these methods is shown in the spatially one-dimensional case(explicit and implicit iterative processes).The obtained results are compared with the data from the literature.The results coincide with analytical solutions with high accuracy,where the relative error does not exceed 0.1%,which demonstrates the effectiveness of the developed algorithms and methods.
文摘International carbon tax issues such as carbon leakage and carbon neutralization have become major topics of social concern.Based on the practical experience of carbon tax system in individual countries,this paper integrates the existing research of international carbon tax scholars to the classification and comparative analysis of international carbon tax schemes.Using a literature review approach,this dissertation mainly applies the method of qualitative analysis to explain and compare the contents of four international carbon tax options.Through the analysis and evaluation of individual countries’carbon tax practice,the two-country model is verified.Through the method of comparative analysis,the schemes are evaluated from four dimensions and an assessment is made.The difference of carbon tax among countries makes the internal policies of countries adjust accordingly with the changes of international environment,which promotes the gradual convergence of carbon tax schemes.The results intend to provide reference to further study the issue on international carbon tax.
基金The project supported by the National Natural Science Foundation of China (19582007) Partly by State Key Laboratory of Scientific/Engineering Computing
文摘By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.
基金Project supported by the National Natural Science Foundation of China (Nos. 10172015 and 90205010)
文摘A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.
基金supported by NSFC(No.41174118)one of the major state S&T special projects(No.2008ZX05020-004)+1 种基金a Postdoctoral Fellowship of China(No.2013M530106)China Scholarship Council(No.2010644006)
文摘In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.
基金Supported by the National Natural Defense Basic Scientific Research Program of China(A262006-1288)the Key Disciplines Program of Shanghai Municipal Commission of Education(J50501)~~
文摘Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.
基金supported by the National Natural Science Foundation of China(Grant No.42305169)the Basic Research Fund of CAMS(Grant No.2023Y001)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(Earth Lab)。
文摘Accurately simulating mesoscale convective systems(MCSs)is essential for predicting global precipitation patterns and extreme weather events.Despite the ability of advanced models to reproduce MCS climate statistics,capturing extreme storm cases over complex terrain remains challenging.This study utilizes the Global–Regional Integrated Forecast System(GRIST)with variable resolution to simulate an eastward-propagating MCS event.The impact of three microphysics schemes,including two single-moment schemes(WSM6,Lin)and one double-moment scheme(Morrison),on the model sensitivity of MCS precipitation simulations is investigated.The results demonstrate that while all the schemes capture the spatial distribution and temporal variation of MCS precipitation,the Morrison scheme alleviates overestimated precipitation compared to the Lin and WSM6 schemes.The ascending motion gradually becomes weaker in the Morrison scheme during the MCS movement process.Compared to the runs with convection parameterization,the explicit-convection setup at 3.5-km resolution reduces disparities in atmospheric dynamics due to microphysics sensitivity in terms of vertical motions and horizontal kinetic energy at the high-wavenumber regimes.The explicit-convection setup more accurately captures the propagation of both main and secondary precipitation centers during the MCS development,diminishing the differences in both precipitation intensity and propagation features between the Morrison and two single-moment schemes.These findings underscore the importance of microphysics schemes for global nonhydrostatic modeling at the kilometer scale.The role of explicit convection for reducing model uncertainty is also outlined.
基金This work was supported by the National Natural Science Foundation of China(No.12102211)the Science and Technology Innovation 2025 Major Project of Ningbo,China(No.2022Z213).
文摘In this paper,the previously proposed second-order process-based modified Patankar Runge-Kutta schemes are extended to the third order of accuracy.Owing to the process-based implicit handling of reactive source terms,the mass conservation,mole balance and energy conservation are kept simultaneously while the positivity for the density and pressure is preserved unconditionally even with stiff reaction networks.It is proved that the first-order truncation terms for the Patankar coefficients must be zero to achieve a prior third order of accuracy for most cases.A twostage Patankar procedure for each Runge-Kutta step is designed to eliminate the first-order truncation terms,accomplish the prior third order of accuracy and maximize the Courant number which the total variational diminishing property requires.With the same approach as the second-order schemes,the third-order ones are applied to Euler equations with chemical reactive source terms.Numerical studies including both 1D and 2D ordinary and partial differential equations are conducted to affirm both the prior order of accuracy and the positivity-preserving property for the density and pressure.
基金supported by Grant PID2020-117211GB-I00funded by MCIN/AEI/10.13039/501100011033+4 种基金by Grant CIAICO/2021/227funded by the Generalitat Valencianasupported by the Ministerio de Ciencia e Innovacion of Spain(Grant Ref.PID2021-125709OB-C21)funded by MCIN/AEI/10.13039/501100011033/FEDER,UEby the Generalitat Valenciana(CIAICO/2021/224).
文摘Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.
基金The work of B.S.Wang and W.S.Don was partially supported by the Ocean University of China through grant 201712011The work of A.Kurganov was supported in part by NSFC grants 11771201 and 1201101343by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.
文摘In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two nonlinear schemes and two linearized schemes are presented. All resulting schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities are used to highlight the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be also conducted. The numerical results show that the interaction behavior is elastic and the conserved quantities are conserved exactly, and this is a good indication of the reliability of the schemes which we derived. A comparison with some existing is presented as well.
基金The project supported by the National Natural Science Foundation of China(90205027)
文摘The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were reported.The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations.The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do.Research progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.
基金supported by the National Natural Science Foundation of China (40890054, 40821092, 90711004)R&D Spe-cial Fund for Public Welfare Industry (meteorol-ogy)(GYHY200706010)National Key Technologies R&D Program (2007BAC29B03)
文摘The vertical structures of atmospheric temperature anomalies associated with El Nio are simulated with a spectrum atmospheric general circulation model developed by LASG/IAP （SAMIL）. Sensitivity of the model’s response to convection scheme is discussed. Two convection schemes, i.e., the revised Zhang and Macfarlane （RZM） and Tiedtke （TDK） convection schemes, are employed in two sets of AMIP-type （Atmospheric Model Intercomparison Project） SAMIL simulations, respectively. Despite some deficiencies in the upper troposphere, the canonical El Nio-related temperature anomalies characterized by a prevailing warming throughout the tropical troposphere are well reproduced in both simulations. The performance of the model in reproducing temperature anomalies in ＂atypical＂ El Nio events is sensitive to the convection scheme. When employing the RZM scheme, the warming center over the central-eastern tropical Pacific and the strong cooling in the western tropical Pacific at sea surface level are underestimated. The quadru-pole temperature anomalies in the middle and upper troposphere are also obscured. The result of employing the TDK scheme resembles the reanalysis and hence shows a better performance. The simulated largescale circulations associated with atypical El Nio events are also sensitive to the convection schemes. When employing the RZM scheme, SAMIL failed in capturing the classical Southern Oscillation pattern. In accordance with the unrealistic anomalous Walker circulation and the upper tropospheric zonal wind changes, the deficiencies of the precipitation simulation are also evident. These results demonstrate the importance of convection schemes in simulating the vertical structure of atmospheric temperature anomalies associated with El Nio and should serve as a useful reference for future improvement of SAMIL.
文摘A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).
基金financially supported by the doctoral fund of the Ministry of Education of Chinathe Nature Science Foundation of Jiangsu Province,China(Grant Nos.20130091110020 and BE2015675)
文摘A deep foundation pit constructed for an underground transportation hub was excavated near the Yangtze River.Among the strata,there are two confined aquifers,between which lies an aquiclude that is partially missing.To guarantee the safety of pit excavation,the piezometric head of the upper confined aquifer,where the pit bottom is located,should be 1 m below the pit bottom,while that of the lower confined aquifer should be dewatered down to a safe water level to avoid uplift problem.The Yangtze River levee is notably close to the pit,and its deformation caused by dewatering should be controlled.A pumping test was performed to obtain the hydraulic conductivity of the upper confined aquifer.The average value of the hydraulic conductivity obtained from analytical calculation is 20.45 m/d,which is larger than the values from numerical simulation(horizontal hydraulic conductivity K_H=16 m/d and vertical hydraulic conductivity K_V=S m/d).The difference between K_H and K_V indicates the anisotropy of the aquifer.Two dewatering schemes were designed for the construction and simulated by the numerical models for comparison purposes.The results show that though the first scheme could meet the dewatering requirements,the largest accumulated settlement and differential settlement would be94.64 mm and 3.3‰,respectively,greatly exceeding the limited values.Meanwhile,the second scheme,in which the bottoms of the waterproof curtains in ramp B and the river side of ramp A are installed at a deeper elevation of-28 m above sea level,and 27 recharge wells are set along the levee,can control the deformation of the levee significantly.
