An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in ...An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.展开更多
In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body...In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.展开更多
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources.The interface is repre...An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources.The interface is represented by the zero level set of a Lipschitz functionϕ(x,y).Our adaptive mesh refinement is done within a small tube of|ϕ(x,y)|δwith finer Cartesian meshes.The discrete linear system of equations is solved by a multigrid solver.The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically,therefore,reduce the size of the linear system of the equations.Numerical examples presented show the efficiency of the grid refinement strategy.展开更多
This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed...This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interlace method（IIM） divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two that the domain decomposition technique can placed around the discontinuity. The present reached, in spite of the enlarged computational discontinuous problems are tested to verify the present method. The results show reduce the error of the spectral IIM, especially when more collocation points are method is t：avorable for the reason that the same level of the accuracy can be domain.展开更多
The recently proposed interface propagation-based method has shown its advantages in obtaining the thermal conductivity of phase change materials during solid-liquid transition over conventional techniques. However, i...The recently proposed interface propagation-based method has shown its advantages in obtaining the thermal conductivity of phase change materials during solid-liquid transition over conventional techniques. However, in previous investigation, the analysis on the measurement error was qualitative and only focused on the total effects on the measurement without decoupling the influencing factors. This paper discusses the effects of influencing factors on the measurement results for the interface propagation-based method. Numerical simulations were performed to explore the influencing factors, namely model simplification, subcooling and natural convection, along with their impact on the measurement process and corresponding measurement results. The numerical solutions were provided in terms of moving curves of the solid-liquid interface and the predicted values of thermal conductivity. Results indicated that the impact of simplified model was strongly dependent on Stefan number of the melting process. The degree of subcooling would lead to underestimated values for thermal conductivity prediction. The natural convection would intensify the heat transfer rate in the liquid region, thereby overestimating the obtained results of thermal conductivity. Correlations and experimental guidelines are provided. The relative errors are limited in ±1.5%,±3%and ±2% corresponding to the impact of simplified model, subcooling and natural convection, respectively.展开更多
A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immerse...A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance, the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.展开更多
Many three-dimensional physical applications can be better analyzed and solved using the cylindrical coordinates.In this paper,the immersed interface method(IIM)tailored for Navier-Stokes equations involving interface...Many three-dimensional physical applications can be better analyzed and solved using the cylindrical coordinates.In this paper,the immersed interface method(IIM)tailored for Navier-Stokes equations involving interfaces under the cylindrical coordinates has been developed.Note that,while the IIM has been developed for Stokes equations in the cylindrical coordinates assuming the axis-symmetry in the literature,there is a gap in dealing with Navier-Stokes equations,where the non-linear term includes an additional component involving the coordinateφ,even if the geometry and force term are axis-symmetric.Solving the Navier-Stokes equations in cylindrical coordinates becomes challenging when dealing with interfaces that feature a discontinuous pressure and a non-smooth velocity,in addition to the pole singularity at r=0.In the newly developed algorithm,we have derived the jump conditions under the cylindrical coordinates.The numerical algorithm is based on a finite difference discretization on a uniform and staggered grid in the cylindrical coordinates.The finite difference scheme is standard away from the interface but is modified at grid points near and on the interface.As expected,the method is shown to be second-order accurate for the velocity.The developed new IIM is applied to the solution of some related fluid dynamic problems with interfaces.展开更多
Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the l...Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.展开更多
This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is ...This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid（VOF） method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.展开更多
The solid-liquid method was used to prepare the continuous casting of copper cladding aluminium by liquid aluminum alloy and solid copper, and the interfacial phase formation of Al-Cu bimetal at different pouring temp...The solid-liquid method was used to prepare the continuous casting of copper cladding aluminium by liquid aluminum alloy and solid copper, and the interfacial phase formation of Al-Cu bimetal at different pouring temperatures(700, 750, 800 oC) was investigated by means of metallograph, scanning electron microscopy(SEM) and energy dispersive spectrometry(EDS) methods. The results showed that the pouring temperature of aluminum melt had an important influence on the element diffusion of Cu from the solid Cu to Al alloy melt and the reactions between Al and Cu, as well as the morphology of the Al-Cu interface. When the pouring temperature was 800 oC, there were abundant Al-Cu intermetallic compounds(IMCs) near the interface. However, a lower pouring temperature(700 oC) resulted in the formation of cavities which was detrimental to the bonding and mechanical properties. Under the conditions in this study, the good metallurgical bonding of Al-Cu was achieved at a pouring temperature of 750 oC.展开更多
In order to study the failure process of an anchorage structure and the evolution law of the body＇s defor- mation field, anchor push-out tests were carried out based on digital speckle correlation methods （DSCM）. T...In order to study the failure process of an anchorage structure and the evolution law of the body＇s defor- mation field, anchor push-out tests were carried out based on digital speckle correlation methods （DSCM）. The stress distribution of the anchorage interface was investigated using the particle flow numerical simulation method. The results indicate that there are three stages in the deformation and fail- ure process of an anchorage structure： elastic bonding stage, a de-bonding stage and a failure stage. The stress distribution in the interface controls the stability of the structure. In the elastic bonding stage, the shear stress peak point of the interface is close to the loading end, and the displacement field gradually develops into a ＂V＂ shape, in the de-bonding stage, there is a shear stress plateau in the center of the anchorage section, and shear strain localization begins to form in the deformation field. In the failure stage, the bonding of the interface fails rapidly and the shear stress peak point moves to the anchorage free end. The anchorage structure moves integrally along the macro-cracl~ The de-bonding stage is a research focus in the deformation and failure process of an anchorage structure, and plays an important guiding role in roadway support design and prediction of the stability of the surrounding rock.展开更多
Knowledge on the interactions between engineered nanomaterials(ENMs) and biological systems is critical both for the assessment of biological effects of ENMs and for the rational design of ENM-based products. However,...Knowledge on the interactions between engineered nanomaterials(ENMs) and biological systems is critical both for the assessment of biological effects of ENMs and for the rational design of ENM-based products. However, probing the events that occur at the nano-bio interface remains extremely challenging due to their complex and dynamic nature. So far, the understanding of mechanisms underlying nano-bio interactions has been mainly limited by the lack of proper analytical techniques with sufficient sensitivity, selectivity and resolution for characterization of nano-bio interface events. Moreover, many classic bioanalytical methods are not suitable for direct measurement of nano-bio interface interactions. These have made establishing analytical methodologies for systematic and comprehensive study of nano-bio interface one of the most focused areas in nanobiology. In this review we have discussed some representative developments regarding analytical techniques for nano-bio interface characterization, including the improvements of traditional methods and the emergence of powerful new technologies. These developments have allowed ultrasensitive, real-time analysis of interactions between ENMs and biomolecules, transformations of ENMs in biological environment, and impacts of ENMs on living systems on molecular or cellular level.展开更多
The presence of Dirac delta function in differential equation can lead to a discontinuity,which may degrade the accuracy of related numerical methods.To improve the accuracy,a secondorder numerical method for elliptic...The presence of Dirac delta function in differential equation can lead to a discontinuity,which may degrade the accuracy of related numerical methods.To improve the accuracy,a secondorder numerical method for elliptic equations with singular sources is introduced by employing a local kernel flter.In this method,the discontinuous equation is convoluted with the kernel function to obtain a more regular one.Then the original equation is replaced by this fltered equation around the singular points,to obtain discrete numerical form.The unchanged equations at the other points are discretized by using a central difference scheme.1D and 2D examples are carried out to validate the correctness and accuracy of the present method.The results show that a second-order of accuracy can be obtained in the fltering framework with an appropriate integration rule.Furthermore,the present method does not need any jump condition,and also has extremely simple form that can be easily extended to high dimensional cases and complex geometry.展开更多
We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification.Here we focus on Stefan problems,and their quasi-static variants,with ...We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification.Here we focus on Stefan problems,and their quasi-static variants,with applications to crystal growth.New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.展开更多
The rigid body limit equilibrium method(LEM)and the nonlinear finite element method(NFEM)are often used in the analysis of anti-sliding stability of gravity dam.But LEM cannot reflect the process of progressive instab...The rigid body limit equilibrium method(LEM)and the nonlinear finite element method(NFEM)are often used in the analysis of anti-sliding stability of gravity dam.But LEM cannot reflect the process of progressive instability and mechanical mecha-nism on failure for rock mass while NFEM is difficult to use to solve the displacement discontinuity of weak structural plane.Combining the research with Xiangjiaba Hydropower Station project,the analysis of anti-sliding stability for segment 12#of the dam has been carried out using interface stress element method(ISEM).The results can reflect the most dangerous location,the scope and distribution of failure zone in weak structural plane,and present the process of progressive failure in dam foun-dation as well as the safety coefficient of possible sliding body.These achievements provide an important technical reference for dam foundation treatment measures.The computational results show that ISEM can naturally describe discontinuous de-formation of rock mass such as dislocation,openness and sliding.Besides,this method is characterized by good adaptability,convenient calculation and high compatibility,thus it is regarded as an effective way to make an analysis of anti-sliding stabil-ity of gravity dam.展开更多
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces.Since the solution has lo...A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces.Since the solution has low regularity across the interface,when applying finite difference discretization to this problem,an additional treatment accounting for the jump discontinuities must be employed.Here,we aim to elevate such an extra effort to ease our implementation by machine learning methodology.The key idea is to decompose the solution into singular and regular parts.The neural network learning machinery incorporating the given jump conditions finds the singular solution,while the standard five-point Laplacian discretization is used to obtain the regular solution with associated boundary conditions.Regardless of the interface geometry,these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation,making the hybrid method easy to implement and efficient.The two-and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives,and it is comparable with the traditional immersed interface method in the literature.As an application,we solve the Stokes equations with singular forces to demonstrate the robustness of the present method.展开更多
In this paper,a fairly simple 3D immersed interface method based on the CG-Uzawa type method and the level set representation of the interface is employed for solving three-dimensional Stokes flow with singular forces...In this paper,a fairly simple 3D immersed interface method based on the CG-Uzawa type method and the level set representation of the interface is employed for solving three-dimensional Stokes flow with singular forces along the interface.The method is to apply the Taylor’s expansions only along the normal direction and incorporate the jump conditions up to the second normal derivatives into the finite difference schemes.A second order geometric iteration algorithm is employed for computing orthogonal projections on the surface with third-order accuracy.The Stokes equations are discretized involving the correction terms on staggered grids and then solved by the conjugate gradient Uzawa type method.The major advantages of the present method are the special simplicity,the ability in handling the Dirichlet boundary conditions,and no need of the pressure boundary condition.The method can also preserve the volume conservation and the discrete divergence free condition very well.The numerical results show that the proposed method is second order accurate and efficient.展开更多
We propose a hybrid scheme combing the diffuse interface method and the material point method to simulate the complex interactions between the multiphase compressible flow and elastoplastic solid.The multiphase flow i...We propose a hybrid scheme combing the diffuse interface method and the material point method to simulate the complex interactions between the multiphase compressible flow and elastoplastic solid.The multiphase flow is modelled by the multi-component model and solved using a generalized Godunov method in the Eulerian grids,while the elastoplastic solid is solved by the classical material point method in a combination of Lagrangian particles and Eulerian background grids.In order to facilitate the simulation of fluid-solid interactions,the solid variables are further interpolated to the cell center and coexist with the fluid in the same cell.An instantaneous relaxation procedure of velocity and pressure is adopted to simulate the momentum and energy transfers between various materials,and to keep the system within a tightly coupled interaction.Several numerical examples,including shock tube problem,gasbubble problem,air blast,underwater explosion and high speed impact applications are presented to validate the numerical scheme.展开更多
In this paper,an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow.The tension is introduced as an augmented variable to satisfy the constraint of int...In this paper,an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow.The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility,and the resulting augmented system is solved by the GMRES method.In this work,the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation.The forces at the interface are calculated from the configuration of the interface and the computed augmented variable,and then applied to the fluid through the related jump conditions.The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method.The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow.Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously.These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.展开更多
基金supported by the National Natural Science Foundation of China(No.51174236)the National Basic Research Program of China(973 Program)(No.2011CB606306)the Opening Project of State Key Laboratory of Porous Metal Materials(No.PMM-SKL-4-2012)
文摘An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.
基金supported by the US ARO grants 49308-MA and 56349-MAthe US AFSOR grant FA9550-06-1-024+1 种基金he US NSF grant DMS-0911434the State Key Laboratory of Scientific and Engineering Computing of Chinese Academy of Sciences during a visit by Z.Li between July-August,2008.
文摘In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.
文摘An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources.The interface is represented by the zero level set of a Lipschitz functionϕ(x,y).Our adaptive mesh refinement is done within a small tube of|ϕ(x,y)|δwith finer Cartesian meshes.The discrete linear system of equations is solved by a multigrid solver.The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically,therefore,reduce the size of the linear system of the equations.Numerical examples presented show the efficiency of the grid refinement strategy.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金National Natural Science Foundation of China(51076006)
文摘This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interlace method（IIM） divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two that the domain decomposition technique can placed around the discontinuity. The present reached, in spite of the enlarged computational discontinuous problems are tested to verify the present method. The results show reduce the error of the spectral IIM, especially when more collocation points are method is t：avorable for the reason that the same level of the accuracy can be domain.
基金Project(51606224) supported by the National Natural Science Foundation of China
文摘The recently proposed interface propagation-based method has shown its advantages in obtaining the thermal conductivity of phase change materials during solid-liquid transition over conventional techniques. However, in previous investigation, the analysis on the measurement error was qualitative and only focused on the total effects on the measurement without decoupling the influencing factors. This paper discusses the effects of influencing factors on the measurement results for the interface propagation-based method. Numerical simulations were performed to explore the influencing factors, namely model simplification, subcooling and natural convection, along with their impact on the measurement process and corresponding measurement results. The numerical solutions were provided in terms of moving curves of the solid-liquid interface and the predicted values of thermal conductivity. Results indicated that the impact of simplified model was strongly dependent on Stefan number of the melting process. The degree of subcooling would lead to underestimated values for thermal conductivity prediction. The natural convection would intensify the heat transfer rate in the liquid region, thereby overestimating the obtained results of thermal conductivity. Correlations and experimental guidelines are provided. The relative errors are limited in ±1.5%,±3%and ±2% corresponding to the impact of simplified model, subcooling and natural convection, respectively.
文摘A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance, the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.
基金supported by Fundación Sáneca Grant 21728/EE/22(Este trabajo es resultado de la estancia financiada por la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia con cargo al Programa Regional de Movilidad,Colaboración Internacional e Intercambio de Conocimiento“Jiménez de la Espada”)B.Dong is partially supported by the National Natural Science Foundation of China Grant No.12261070+1 种基金Ningxia Key Research and Development Project of China Grant No.2022BSB03048Z.Li is partially supported by Simons Grant 633724 and by Fundación Séneca Grant 21760/IV/22(Este trabajo es resultado de la estancia financiada por la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia con cargo al Programa Regional de Movilidad,Colaboración Internacional Intercambio de Conocimiento“Jiménez de la Espada”).
文摘Many three-dimensional physical applications can be better analyzed and solved using the cylindrical coordinates.In this paper,the immersed interface method(IIM)tailored for Navier-Stokes equations involving interfaces under the cylindrical coordinates has been developed.Note that,while the IIM has been developed for Stokes equations in the cylindrical coordinates assuming the axis-symmetry in the literature,there is a gap in dealing with Navier-Stokes equations,where the non-linear term includes an additional component involving the coordinateφ,even if the geometry and force term are axis-symmetric.Solving the Navier-Stokes equations in cylindrical coordinates becomes challenging when dealing with interfaces that feature a discontinuous pressure and a non-smooth velocity,in addition to the pole singularity at r=0.In the newly developed algorithm,we have derived the jump conditions under the cylindrical coordinates.The numerical algorithm is based on a finite difference discretization on a uniform and staggered grid in the cylindrical coordinates.The finite difference scheme is standard away from the interface but is modified at grid points near and on the interface.As expected,the method is shown to be second-order accurate for the velocity.The developed new IIM is applied to the solution of some related fluid dynamic problems with interfaces.
文摘Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.
基金supported by the NSWC Carderock ILIR programby the US Office of Naval Research(Grant No.N000141-01-00-1-7)
文摘This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid（VOF） method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.
基金financially supported by the National Natural Science Foundation of China(Nos.51074031 and 51501027)the China Postdoctoral Science Foundation(No.2015M570246)the Fundamental Research Funds for the Central Universities of China[DUT15RC(3)065]
文摘The solid-liquid method was used to prepare the continuous casting of copper cladding aluminium by liquid aluminum alloy and solid copper, and the interfacial phase formation of Al-Cu bimetal at different pouring temperatures(700, 750, 800 oC) was investigated by means of metallograph, scanning electron microscopy(SEM) and energy dispersive spectrometry(EDS) methods. The results showed that the pouring temperature of aluminum melt had an important influence on the element diffusion of Cu from the solid Cu to Al alloy melt and the reactions between Al and Cu, as well as the morphology of the Al-Cu interface. When the pouring temperature was 800 oC, there were abundant Al-Cu intermetallic compounds(IMCs) near the interface. However, a lower pouring temperature(700 oC) resulted in the formation of cavities which was detrimental to the bonding and mechanical properties. Under the conditions in this study, the good metallurgical bonding of Al-Cu was achieved at a pouring temperature of 750 oC.
基金financially supported by the National Key Basic Research Program of China (No.2010CB226805)the National Natural Science Foundation of China (Nos.51474136 and 51474013)+1 种基金the Opening Project Fund of State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology (No.MDPC2013KF06)the Research Award Fund for the Excellent Youth of Shandong University of Science and Technology (No.2011KYJQ106)
文摘In order to study the failure process of an anchorage structure and the evolution law of the body＇s defor- mation field, anchor push-out tests were carried out based on digital speckle correlation methods （DSCM）. The stress distribution of the anchorage interface was investigated using the particle flow numerical simulation method. The results indicate that there are three stages in the deformation and fail- ure process of an anchorage structure： elastic bonding stage, a de-bonding stage and a failure stage. The stress distribution in the interface controls the stability of the structure. In the elastic bonding stage, the shear stress peak point of the interface is close to the loading end, and the displacement field gradually develops into a ＂V＂ shape, in the de-bonding stage, there is a shear stress plateau in the center of the anchorage section, and shear strain localization begins to form in the deformation field. In the failure stage, the bonding of the interface fails rapidly and the shear stress peak point moves to the anchorage free end. The anchorage structure moves integrally along the macro-cracl~ The de-bonding stage is a research focus in the deformation and failure process of an anchorage structure, and plays an important guiding role in roadway support design and prediction of the stability of the surrounding rock.
基金supported by the National Natural Science Foundation of China (21320102003, 31200752, 31661130152, 11435002)the National Distinguished Young Scientists Program (31325010)
文摘Knowledge on the interactions between engineered nanomaterials(ENMs) and biological systems is critical both for the assessment of biological effects of ENMs and for the rational design of ENM-based products. However, probing the events that occur at the nano-bio interface remains extremely challenging due to their complex and dynamic nature. So far, the understanding of mechanisms underlying nano-bio interactions has been mainly limited by the lack of proper analytical techniques with sufficient sensitivity, selectivity and resolution for characterization of nano-bio interface events. Moreover, many classic bioanalytical methods are not suitable for direct measurement of nano-bio interface interactions. These have made establishing analytical methodologies for systematic and comprehensive study of nano-bio interface one of the most focused areas in nanobiology. In this review we have discussed some representative developments regarding analytical techniques for nano-bio interface characterization, including the improvements of traditional methods and the emergence of powerful new technologies. These developments have allowed ultrasensitive, real-time analysis of interactions between ENMs and biomolecules, transformations of ENMs in biological environment, and impacts of ENMs on living systems on molecular or cellular level.
基金supported by the National Natural Science Foundation in China(Grant Nos.51076006,11202013)BUAA SJP ‘‘111’’ Program(Grant No.B08009)+1 种基金the National Basic Research Program of China(2012CB720200)the Open Research Fund of MOE Key Lab-oratory of High-speed Railway Engineering,Southwest Jiao-tong University and the European Community’s Seventh Framework Program(FP7/2007-2013)under Grant agreement 225967‘‘NextMuSE’’
文摘The presence of Dirac delta function in differential equation can lead to a discontinuity,which may degrade the accuracy of related numerical methods.To improve the accuracy,a secondorder numerical method for elliptic equations with singular sources is introduced by employing a local kernel flter.In this method,the discontinuous equation is convoluted with the kernel function to obtain a more regular one.Then the original equation is replaced by this fltered equation around the singular points,to obtain discrete numerical form.The unchanged equations at the other points are discretized by using a central difference scheme.1D and 2D examples are carried out to validate the correctness and accuracy of the present method.The results show that a second-order of accuracy can be obtained in the fltering framework with an appropriate integration rule.Furthermore,the present method does not need any jump condition,and also has extremely simple form that can be easily extended to high dimensional cases and complex geometry.
文摘We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification.Here we focus on Stefan problems,and their quasi-static variants,with applications to crystal growth.New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.
基金supported by the National Natural Science Foundation of China(Grant Nos.51179064,11132003 and 10972072)the National Science and Technology Supporting Plan(Grant No.2008BAB29B03)
文摘The rigid body limit equilibrium method(LEM)and the nonlinear finite element method(NFEM)are often used in the analysis of anti-sliding stability of gravity dam.But LEM cannot reflect the process of progressive instability and mechanical mecha-nism on failure for rock mass while NFEM is difficult to use to solve the displacement discontinuity of weak structural plane.Combining the research with Xiangjiaba Hydropower Station project,the analysis of anti-sliding stability for segment 12#of the dam has been carried out using interface stress element method(ISEM).The results can reflect the most dangerous location,the scope and distribution of failure zone in weak structural plane,and present the process of progressive failure in dam foun-dation as well as the safety coefficient of possible sliding body.These achievements provide an important technical reference for dam foundation treatment measures.The computational results show that ISEM can naturally describe discontinuous de-formation of rock mass such as dislocation,openness and sliding.Besides,this method is characterized by good adaptability,convenient calculation and high compatibility,thus it is regarded as an effective way to make an analysis of anti-sliding stabil-ity of gravity dam.
基金the supports by National Science and Technology Council,Taiwan,under the research grants 111-2115-M-008-009-MY3,111-2628-M-A49-008-MY4,111-2115-M-390-002,and 110-2115-M-A49-011-MY3,respectivelythe supports by National Center for Theoretical Sciences,Taiwan.
文摘A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces.Since the solution has low regularity across the interface,when applying finite difference discretization to this problem,an additional treatment accounting for the jump discontinuities must be employed.Here,we aim to elevate such an extra effort to ease our implementation by machine learning methodology.The key idea is to decompose the solution into singular and regular parts.The neural network learning machinery incorporating the given jump conditions finds the singular solution,while the standard five-point Laplacian discretization is used to obtain the regular solution with associated boundary conditions.Regardless of the interface geometry,these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation,making the hybrid method easy to implement and efficient.The two-and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives,and it is comparable with the traditional immersed interface method in the literature.As an application,we solve the Stokes equations with singular forces to demonstrate the robustness of the present method.
基金supported by the Special Project on High-performance Computing under the National Key R&D Program(No.2016YFB0200604)National Natural Science Foundation of China(11971502,11571385)Guangdong Natural Science Foundation(2017A030313017).
文摘In this paper,a fairly simple 3D immersed interface method based on the CG-Uzawa type method and the level set representation of the interface is employed for solving three-dimensional Stokes flow with singular forces along the interface.The method is to apply the Taylor’s expansions only along the normal direction and incorporate the jump conditions up to the second normal derivatives into the finite difference schemes.A second order geometric iteration algorithm is employed for computing orthogonal projections on the surface with third-order accuracy.The Stokes equations are discretized involving the correction terms on staggered grids and then solved by the conjugate gradient Uzawa type method.The major advantages of the present method are the special simplicity,the ability in handling the Dirichlet boundary conditions,and no need of the pressure boundary condition.The method can also preserve the volume conservation and the discrete divergence free condition very well.The numerical results show that the proposed method is second order accurate and efficient.
文摘We propose a hybrid scheme combing the diffuse interface method and the material point method to simulate the complex interactions between the multiphase compressible flow and elastoplastic solid.The multiphase flow is modelled by the multi-component model and solved using a generalized Godunov method in the Eulerian grids,while the elastoplastic solid is solved by the classical material point method in a combination of Lagrangian particles and Eulerian background grids.In order to facilitate the simulation of fluid-solid interactions,the solid variables are further interpolated to the cell center and coexist with the fluid in the same cell.An instantaneous relaxation procedure of velocity and pressure is adopted to simulate the momentum and energy transfers between various materials,and to keep the system within a tightly coupled interaction.Several numerical examples,including shock tube problem,gasbubble problem,air blast,underwater explosion and high speed impact applications are presented to validate the numerical scheme.
基金The authors would like to thank the referees for the valuable suggestions on the revision of the manuscript.The research of the first author was partially supported by Guangdong Provincial Government of China through the“Computational Science Innovative Research Team”program,the Sun Yat-sen University“Hundred Talents Program”(34000-3181201)the National Natural Science Foundation of China(No.11101446).
文摘In this paper,an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow.The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility,and the resulting augmented system is solved by the GMRES method.In this work,the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation.The forces at the interface are calculated from the configuration of the interface and the computed augmented variable,and then applied to the fluid through the related jump conditions.The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method.The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow.Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously.These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.
