We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by sol...We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.展开更多
The fluid–structure interaction and aerodynamic shape optimization usually involve the moving or deforming boundaries, thus the dynamic mesh techniques are the key techniques to cope with such deformation. A novel dy...The fluid–structure interaction and aerodynamic shape optimization usually involve the moving or deforming boundaries, thus the dynamic mesh techniques are the key techniques to cope with such deformation. A novel dynamic mesh method was developed based on the Delaunay graph in this paper. According to the Delaunay graph, the mesh points were divided into groups. In each group, a factor ranging from 0 to 1 was calculated based on the area/volume ratio. By introducing a proper function for this factor, this method can control the mesh quality with high efficiency. Several test cases were compared with other dynamic mesh methods regarding mesh quality and CPU time, such as radial basis function method and Delaunay graph mapping method.展开更多
This work proposes a numerical investigation on the effects of damage on the structural response of Reinforced Concrete(RC)bridge structures commonly adopted in highway and railway networks.An effective three-dimensio...This work proposes a numerical investigation on the effects of damage on the structural response of Reinforced Concrete(RC)bridge structures commonly adopted in highway and railway networks.An effective three-dimensional FE-based numerical model is developed to analyze the bridge’s structural response under several damage scenarios,including the effects of moving vehicle loads.In particular,the longitudinal and transversal beams are modeled through solid finite elements,while horizontal slabs are made of shell elements.Damage phenomena are also incorporated in the numerical model according to a smeared approach consistent with Continuum Damage Mechanics(CDM).In such a context,the proposed method utilizes an advanced and efficient computational strategy for reproducing Vehicle-Bridge Interaction(VBI)effects based on a moving mesh technique consistent with the Arbitrary Lagrangian-Eulerian(ALE)formulation.The proposed model adopts a moving mesh interface for tracing the positions of the contact points between the vehicle’s wheels and the bridge slabs.Such modeling strategy avoids using extremely refined discretization for structural members,thus drastically reducing computational efforts.Vibrational analyses in terms of damage scenarios are presented to verify how the presence of damage affects the natural frequencies of the structural system.In addition,a comprehensive investigation regarding the response of the bridge under moving vehicles is developed,also providing results in terms of Dynamic Amplification Factor(DAFs)for typical design bridge variables.展开更多
We consider an iterative algorithm of mesh optimization for finite element solution,and give an improved moving mesh strategy that reduces rapidly the complexity and cost of solving variational problems.A numerical re...We consider an iterative algorithm of mesh optimization for finite element solution,and give an improved moving mesh strategy that reduces rapidly the complexity and cost of solving variational problems.A numerical result is presented for a 2-dimensional problem by the improved algorithm.展开更多
This paper applies a difference scheme to a singularly perturbed problem. The authors provide two algorithms on moving mesh methods by using Richardson extrapolation which can improve the accuracy of numerical solutio...This paper applies a difference scheme to a singularly perturbed problem. The authors provide two algorithms on moving mesh methods by using Richardson extrapolation which can improve the accuracy of numerical solution. In traditional algorithms of moving meshes, the initial mesh is a uniform mesh. The authors change it to Bakhvalov-Shishkin mesh, and prove that it improves efficiency by numerical experiments. Finally, the results of the two algorithms are analyzed.展开更多
This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)equations.The algorithm consists of two“independent”parts:the time evolution of th...This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)equations.The algorithm consists of two“independent”parts:the time evolution of the RHD equations and the(static)mesh iteration redistribution.In the first part,the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations.The second part is an iterative procedure.In each iteration,the mesh points are first redistributed,and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way.Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.展开更多
This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a pie...This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a piecewise linear function in time. Then, piecewise quadratic polynomial in space and an efficient method to discretize the memory term of the equation is designed using the moving mesh approach. In each time slice, a simple piecewise constant approximation of the integrand is used, and thus a quadrature is constructed for the memory term. The central finite difference scheme for space and the backward Euler scheme for time are used. The paper proves that the accumulation of the quadrature error is uniformly bounded and that the convergence of the method is second order in space and first order in time. Numerical experiments are carried out to confirm the theoretical predictions.展开更多
A high-order, well-balanced, positivity-preserving quasi-Lagrange movingmesh DG method is presented for the shallow water equations with non-flat bottomtopography. The well-balance property is crucial to the ability o...A high-order, well-balanced, positivity-preserving quasi-Lagrange movingmesh DG method is presented for the shallow water equations with non-flat bottomtopography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake ortsunami waves in the deep ocean. The method combines a quasi-Lagrange movingmesh DG method, a hydrostatic reconstruction technique, and a change of unknownvariables. The strategies in the use of slope limiting, positivity-preservation limiting,and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treatsmesh movement continuously in time and has the advantages that it does not need tointerpolate flow variables from the old mesh to the new one and places no constraintfor the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the wellbalance property, positivity preservation, and high-order accuracy of the method andits ability to adapt the mesh according to features in the flow and bottom topography.展开更多
This paper studies the convergence rates of a moving mesh implicit finite difference method with interpolation for partial differential equations （PDEs） with moving boundary arising in Asian option pricing. The movi...This paper studies the convergence rates of a moving mesh implicit finite difference method with interpolation for partial differential equations （PDEs） with moving boundary arising in Asian option pricing. The moving mesh scheme is based on Rnnacher timestepping approach whose idea is running the implicit Euler schemes in the initial few steps and continuing with Crank-Nicolson schemes. With graded meshes for time direction and moving meshes for space direction, the fully discretized scheme is constructed using quadratic interpolation between two consecutive time level for the PDEs with moving boundary. The second-order convergence rates in both time and space are proved and numerical examples are carried out to confirm the theoretical results.展开更多
The five-equation model of multi-component flows has been attracting much attention among researchers during the past twenty years for its potential in the study of the multi-component flows.In this paper,we employ a ...The five-equation model of multi-component flows has been attracting much attention among researchers during the past twenty years for its potential in the study of the multi-component flows.In this paper,we employ a second order finite volume method with minmod limiter in spatial discretization,which preserves local extrema of certain physical quantities and is thus capable of simulating challenging test problems without introducing non-physical oscillations.Moreover,to improve the numerical resolution of the solutions,the adaptive moving mesh strategy proposed in[Huazhong Tang,Tao Tang,Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws,SINUM,41:487-515,2003]is applied.Furthermore,the proposed method can be proved to be capable of preserving the velocity and pressure when they are initially constant,which is essential in material interface capturing.Finally,several classical numerical examples demonstrate the effectiveness and robustness of the proposed method.展开更多
In this paper, we present an adaptive moving mesh technique for solvingthe incompressible viscous flows using the vorticity stream-function formulation. Themoving mesh strategy is based on the approach proposed by Li ...In this paper, we present an adaptive moving mesh technique for solvingthe incompressible viscous flows using the vorticity stream-function formulation. Themoving mesh strategy is based on the approach proposed by Li et al. [J. Comput. Phys.,170 (2001), pp. 562–588] to separate the mesh-moving and evolving PDE at each timestep. The Navier-Stokes equations are solved in the vorticity stream-function form bya finite-volume method in space, and the mesh-moving part is realized by solving theEuler-Lagrange equations to minimize a certain variation in conjunction with a moresophisticated monitor function. A conservative interpolation is used to redistributethe numerical solutions on the new meshes. This paper discusses the implementationof the periodic boundary conditions, where the physical domain is allowed to deformwith time while the computational domain remains fixed and regular throughout. Numericalresults demonstrate the accuracy and effectiveness of the proposed algorithm.展开更多
This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tu...This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tubes proposed by Luo et al. using Prandtl＇s mixing-length theory. Our algorithm is formed by an outer iterative algorithm for handling the optimal control condition and an inner adaptive mesh redistribution algorithm for solving the singular governing equations. We discretize the nonlinear problem by using a upwinding approach, and the resulting nonlinear equations are solved by using the Newton- Raphson method. The mesh is generated and the grid points are moved by using the arc-length equidistribution principle. The numerical results demonstrate that proposed algorithm is effective in capturing the boundary layers associated with the turbulent model.展开更多
Examines the moving mesh methods for solving one-dimensional time dependent partial differential equations. Introduction of the differential-algebraic formulations based on geometrical variables; Investigation of the ...Examines the moving mesh methods for solving one-dimensional time dependent partial differential equations. Introduction of the differential-algebraic formulations based on geometrical variables; Investigation of the well-posedness of the numerical approach; Discussion of some detailed numerical procedures.展开更多
In recent years,Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences.To further improve their effectiven...In recent years,Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences.To further improve their effectiveness,we recently developed a new adaptive Fourier-spectral semi-implicit method(AFSIM)for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm.In this paper,we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous,anisotropic elasticity.Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes.It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.展开更多
Adaptive moving mesh research usually focuses either on analytical deriva-tions for prescribed solutions or on pragmatic solvers with challenging physical appli-cations. In the latter case, the monitor functions that ...Adaptive moving mesh research usually focuses either on analytical deriva-tions for prescribed solutions or on pragmatic solvers with challenging physical appli-cations. In the latter case, the monitor functions that steer mesh adaptation are oftendefined in an ad-hoc way. In this paper we generalize our previously used moni-tor function to a balanced sum of any number of monitor components. This avoidsthe trial-and-error parameter fine-tuning that is often used in monitor functions. Thekey reason for the new balancing method is that the ratio between the maximum andaverage value of a monitor component should ideally be equal for all components.Vorticity as a monitor component is a good motivating example for this. Entropy alsoturns out to be a very informative monitor component. We incorporate the monitorfunction in an adaptive moving mesh higher-order finite volume solver with HLLCfluxes, which is suitable for nonlinear hyperbolic systems of conservation laws. Whenapplied to compressible gas flow it produces very sharp results for shocks and otherdiscontinuities. Moreover, it captures small instabilities (Richtmyer-Meshkov, Kelvin-Helmholtz). Thus showing the rich nature of the example problems and the effective-ness of the new monitor balancing.展开更多
The paper introduces the gas-kinetic scheme for three-dimensional(3D)flow simulation.First,under a unified coordinate transformation,the 3D gaskinetic BGK equation is transformed into a computational space with arbitr...The paper introduces the gas-kinetic scheme for three-dimensional(3D)flow simulation.First,under a unified coordinate transformation,the 3D gaskinetic BGK equation is transformed into a computational space with arbitrary mesh moving velocity.Second,based on the Chapman-Enskog expansion of the kinetic equation,a local solution of gas distribution function is constructed and used in a finite volume scheme.As a result,a Navier-Stokes flow solver is developed for the low speed flow computation with dynamical mesh movement.Several test cases are used to validate the 3D gas-kinetic method.The first example is a 3D cavity flow with up-moving boundary at Reynolds number 3200,where the periodic solutions are compared with the experimental measurements.Then,the flow evolution inside a rotating 3D cavity is simulated with the moving mesh method,where the solution differences between 2D and 3D simulation are explicitly presented.Finally,the scheme is applied to the falling plate study,where the unsteady plate tumbling motion inside water tank has been studied and compared with the experimental measurements.展开更多
In this paper, we present an adaptive moving mesh algorithm for meshesof unstructured polyhedra in three space dimensions. The algorithm automaticallyadjusts the size of the elements with time and position in the phys...In this paper, we present an adaptive moving mesh algorithm for meshesof unstructured polyhedra in three space dimensions. The algorithm automaticallyadjusts the size of the elements with time and position in the physical domain to resolvethe relevant scales in multiscale physical systems while minimizing computationalcosts. The algorithm is a generalization of the moving mesh methods basedon harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To make 3D moving mesh simulations possible,the key is to develop an efficient mesh redistribution procedure so that this part willcost as little as possible comparing with the solution evolution part. Since the meshredistribution procedure normally requires to solve large size matrix equations, wewill describe a procedure to decouple the matrix equation to a much simpler blocktridiagonaltype which can be efficiently solved by a particularly designed multi-gridmethod. To demonstrate the performance of the proposed 3D moving mesh strategy,the algorithm is implemented in finite element simulations of fluid-fluid interface interactionsin multiphase flows. To demonstrate the main ideas, we consider the formationof drops by using an energetic variational phase field model which describesthe motion of mixtures of two incompressible fluids. Numerical results on two- andthree-dimensional simulations will be presented.展开更多
The Doi-Hess equation that describes the evolution of an orientational dis-tribution function is capable of predicting several rheological features of nematic poly-mers.Since the orientational distribution function be...The Doi-Hess equation that describes the evolution of an orientational dis-tribution function is capable of predicting several rheological features of nematic poly-mers.Since the orientational distribution function becomes sharply peaked as poten-tial intensity increases,powerful numerical methods become necessary in the relevant numerical simulations.In this paper,a numerical scheme based on the moving grid techniques will be designed to solve the orientational distribution functions with high potential intensities.Numerical experiments are carried out to demonstrate the effec-tiveness and robustness of the proposed scheme.展开更多
This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions.With some criteria,the domain is dynamically decomposed into three parts:kinetic regions where fl...This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions.With some criteria,the domain is dynamically decomposed into three parts:kinetic regions where fluids are far from equilibrium,hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition.The Boltzmann-BGK equation is solved in kinetic regions,while Euler equations in hydrodynamic regions and both equations in buffer regions.By a well defined monitor function,our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions.In each moving mesh step,the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion.In such a framework,the evolution of the hybrid model and the moving mesh procedure can be implemented independently,therefore keep the advantages of both approaches.Numerical examples are presented to demonstrate the efficiency of the method.展开更多
The typical elements in a numerical simulation of fluid flow using moving meshes are a time integration scheme,a rezone method in which a new mesh is defined,and a remapping(conservative interpolation)in which a solut...The typical elements in a numerical simulation of fluid flow using moving meshes are a time integration scheme,a rezone method in which a new mesh is defined,and a remapping(conservative interpolation)in which a solution is transferred to the new mesh.The objective of the rezone method is to move the computational mesh to improve the robustness,accuracy and eventually efficiency of the simulation.In this paper,we consider the onedimensional viscous Burgers’equation and describe a new rezone strategy which minimizes the L2 norm of error and maintains mesh smoothness.The efficiency of the proposed method is demonstrated with numerical examples.展开更多
基金The work of A.Kurganov was supported in part by the National Natural Science Foundation of China grant 11771201by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.
基金partially funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions of ChinaNational Natural Science Foundation of China (No. 11432007)Natural Science Foundation of Jiangsu Province of China (No. BK20140805)
文摘The fluid–structure interaction and aerodynamic shape optimization usually involve the moving or deforming boundaries, thus the dynamic mesh techniques are the key techniques to cope with such deformation. A novel dynamic mesh method was developed based on the Delaunay graph in this paper. According to the Delaunay graph, the mesh points were divided into groups. In each group, a factor ranging from 0 to 1 was calculated based on the area/volume ratio. By introducing a proper function for this factor, this method can control the mesh quality with high efficiency. Several test cases were compared with other dynamic mesh methods regarding mesh quality and CPU time, such as radial basis function method and Delaunay graph mapping method.
基金supported by Ministry of University and Research(MUR)through the Research Grant“PRIN 2020 No.2020EBLPLS”“Programma Operativo Nazionale(PON)2014-2020”.
文摘This work proposes a numerical investigation on the effects of damage on the structural response of Reinforced Concrete(RC)bridge structures commonly adopted in highway and railway networks.An effective three-dimensional FE-based numerical model is developed to analyze the bridge’s structural response under several damage scenarios,including the effects of moving vehicle loads.In particular,the longitudinal and transversal beams are modeled through solid finite elements,while horizontal slabs are made of shell elements.Damage phenomena are also incorporated in the numerical model according to a smeared approach consistent with Continuum Damage Mechanics(CDM).In such a context,the proposed method utilizes an advanced and efficient computational strategy for reproducing Vehicle-Bridge Interaction(VBI)effects based on a moving mesh technique consistent with the Arbitrary Lagrangian-Eulerian(ALE)formulation.The proposed model adopts a moving mesh interface for tracing the positions of the contact points between the vehicle’s wheels and the bridge slabs.Such modeling strategy avoids using extremely refined discretization for structural members,thus drastically reducing computational efforts.Vibrational analyses in terms of damage scenarios are presented to verify how the presence of damage affects the natural frequencies of the structural system.In addition,a comprehensive investigation regarding the response of the bridge under moving vehicles is developed,also providing results in terms of Dynamic Amplification Factor(DAFs)for typical design bridge variables.
基金Supported by the National Natural Science Foundation of China(No.19771062)
文摘We consider an iterative algorithm of mesh optimization for finite element solution,and give an improved moving mesh strategy that reduces rapidly the complexity and cost of solving variational problems.A numerical result is presented for a 2-dimensional problem by the improved algorithm.
基金This work is supported by the Foundation for Talent Introduction of Guangdong Provincial University, Guang- dong Province Universities and Colleges Pearl River Scholar Funded Scheme （2008）, and the National Natural Science Foundation of China under Grant No. 10971074.
文摘This paper applies a difference scheme to a singularly perturbed problem. The authors provide two algorithms on moving mesh methods by using Richardson extrapolation which can improve the accuracy of numerical solution. In traditional algorithms of moving meshes, the initial mesh is a uniform mesh. The authors change it to Bakhvalov-Shishkin mesh, and prove that it improves efficiency by numerical experiments. Finally, the results of the two algorithms are analyzed.
基金supported by the National Natural Science Foundation of China(No.10925101,10828101)the Program for New Century Excellent Talents in University(NCET-07-0022)and the Doctoral Program of Education Ministry of China(No.20070001036).
文摘This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)equations.The algorithm consists of two“independent”parts:the time evolution of the RHD equations and the(static)mesh iteration redistribution.In the first part,the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations.The second part is an iterative procedure.In each iteration,the mesh points are first redistributed,and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way.Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.
基金partly supported by SRF for ROCS, SEMsupported by a grant from the "project 211 (phase Ⅲ)" of the Southwestern University of Finance and Economics
文摘This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a piecewise linear function in time. Then, piecewise quadratic polynomial in space and an efficient method to discretize the memory term of the equation is designed using the moving mesh approach. In each time slice, a simple piecewise constant approximation of the integrand is used, and thus a quadrature is constructed for the memory term. The central finite difference scheme for space and the backward Euler scheme for time are used. The paper proves that the accumulation of the quadrature error is uniformly bounded and that the convergence of the method is second order in space and first order in time. Numerical experiments are carried out to confirm the theoretical predictions.
基金J.Qiu is supported partly by National Natural Science Foundation(China)grant 12071392.
文摘A high-order, well-balanced, positivity-preserving quasi-Lagrange movingmesh DG method is presented for the shallow water equations with non-flat bottomtopography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake ortsunami waves in the deep ocean. The method combines a quasi-Lagrange movingmesh DG method, a hydrostatic reconstruction technique, and a change of unknownvariables. The strategies in the use of slope limiting, positivity-preservation limiting,and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treatsmesh movement continuously in time and has the advantages that it does not need tointerpolate flow variables from the old mesh to the new one and places no constraintfor the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the wellbalance property, positivity preservation, and high-order accuracy of the method andits ability to adapt the mesh according to features in the flow and bottom topography.
文摘This paper studies the convergence rates of a moving mesh implicit finite difference method with interpolation for partial differential equations （PDEs） with moving boundary arising in Asian option pricing. The moving mesh scheme is based on Rnnacher timestepping approach whose idea is running the implicit Euler schemes in the initial few steps and continuing with Crank-Nicolson schemes. With graded meshes for time direction and moving meshes for space direction, the fully discretized scheme is constructed using quadratic interpolation between two consecutive time level for the PDEs with moving boundary. The second-order convergence rates in both time and space are proved and numerical examples are carried out to confirm the theoretical results.
基金The research of Yaguang Gu is funded by China Postdoctoral Science Foundation(2021M703040)The research of Dongmi Luo is supported by the National Natural Science Foundation of China(12101063)+3 种基金The research of Zhen Gao is supported by the National Natural Science Foundation of China(11871443)Shandong Provincial Qingchuang Science and Technology Project(2019KJI002)Fundamental Research Funds for the Central Universities(202042004)The research of Yibing Chen is supported by National Key Project(GJXM92579).
文摘The five-equation model of multi-component flows has been attracting much attention among researchers during the past twenty years for its potential in the study of the multi-component flows.In this paper,we employ a second order finite volume method with minmod limiter in spatial discretization,which preserves local extrema of certain physical quantities and is thus capable of simulating challenging test problems without introducing non-physical oscillations.Moreover,to improve the numerical resolution of the solutions,the adaptive moving mesh strategy proposed in[Huazhong Tang,Tao Tang,Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws,SINUM,41:487-515,2003]is applied.Furthermore,the proposed method can be proved to be capable of preserving the velocity and pressure when they are initially constant,which is essential in material interface capturing.Finally,several classical numerical examples demonstrate the effectiveness and robustness of the proposed method.
文摘In this paper, we present an adaptive moving mesh technique for solvingthe incompressible viscous flows using the vorticity stream-function formulation. Themoving mesh strategy is based on the approach proposed by Li et al. [J. Comput. Phys.,170 (2001), pp. 562–588] to separate the mesh-moving and evolving PDE at each timestep. The Navier-Stokes equations are solved in the vorticity stream-function form bya finite-volume method in space, and the mesh-moving part is realized by solving theEuler-Lagrange equations to minimize a certain variation in conjunction with a moresophisticated monitor function. A conservative interpolation is used to redistributethe numerical solutions on the new meshes. This paper discusses the implementationof the periodic boundary conditions, where the physical domain is allowed to deformwith time while the computational domain remains fixed and regular throughout. Numericalresults demonstrate the accuracy and effectiveness of the proposed algorithm.
基金supported by NSFC Outstanding Youth Scientist Grant 10625106 and NSFC grant 10671163the National Basic Research Program of China under the grant 2005CB3217(01,03)+1 种基金Scientific Research Fund of Hunan Provincial Education DepartmentSpecial thanks go to Guangdong Provincial"Zhujiang Scholar Award Project"
文摘This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tubes proposed by Luo et al. using Prandtl＇s mixing-length theory. Our algorithm is formed by an outer iterative algorithm for handling the optimal control condition and an inner adaptive mesh redistribution algorithm for solving the singular governing equations. We discretize the nonlinear problem by using a upwinding approach, and the resulting nonlinear equations are solved by using the Newton- Raphson method. The mesh is generated and the grid points are moved by using the arc-length equidistribution principle. The numerical results demonstrate that proposed algorithm is effective in capturing the boundary layers associated with the turbulent model.
基金This research was supported by Hong Kong Baptist University, Hong Kong Research Grants Council,Special Funds for Major State B
文摘Examines the moving mesh methods for solving one-dimensional time dependent partial differential equations. Introduction of the differential-algebraic formulations based on geometrical variables; Investigation of the well-posedness of the numerical approach; Discussion of some detailed numerical procedures.
基金This work has been supported by the National Science Foundation Information Technol-ogy Research Project(NSF-ITR)through Grant DMR-0205232The work of Qiang Du is also supported by NSF-DMS 0712744.
文摘In recent years,Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences.To further improve their effectiveness,we recently developed a new adaptive Fourier-spectral semi-implicit method(AFSIM)for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm.In this paper,we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous,anisotropic elasticity.Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes.It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.
基金The first author performs his research in the project‘Adaptive moving mesh methods for higher-dimensional nonlinear hyperbolic conservation laws’,funded by the Netherlands Organisation for Scientific Research(NWO)under project number 613.002.055.
文摘Adaptive moving mesh research usually focuses either on analytical deriva-tions for prescribed solutions or on pragmatic solvers with challenging physical appli-cations. In the latter case, the monitor functions that steer mesh adaptation are oftendefined in an ad-hoc way. In this paper we generalize our previously used moni-tor function to a balanced sum of any number of monitor components. This avoidsthe trial-and-error parameter fine-tuning that is often used in monitor functions. Thekey reason for the new balancing method is that the ratio between the maximum andaverage value of a monitor component should ideally be equal for all components.Vorticity as a monitor component is a good motivating example for this. Entropy alsoturns out to be a very informative monitor component. We incorporate the monitorfunction in an adaptive moving mesh higher-order finite volume solver with HLLCfluxes, which is suitable for nonlinear hyperbolic systems of conservation laws. Whenapplied to compressible gas flow it produces very sharp results for shocks and otherdiscontinuities. Moreover, it captures small instabilities (Richtmyer-Meshkov, Kelvin-Helmholtz). Thus showing the rich nature of the example problems and the effective-ness of the new monitor balancing.
基金supported by grants from the National Natural Science Foundation of China(Project No.10772033)K.Xu was supported by Hong Kong Research Grant Council 621709.
文摘The paper introduces the gas-kinetic scheme for three-dimensional(3D)flow simulation.First,under a unified coordinate transformation,the 3D gaskinetic BGK equation is transformed into a computational space with arbitrary mesh moving velocity.Second,based on the Chapman-Enskog expansion of the kinetic equation,a local solution of gas distribution function is constructed and used in a finite volume scheme.As a result,a Navier-Stokes flow solver is developed for the low speed flow computation with dynamical mesh movement.Several test cases are used to validate the 3D gas-kinetic method.The first example is a 3D cavity flow with up-moving boundary at Reynolds number 3200,where the periodic solutions are compared with the experimental measurements.Then,the flow evolution inside a rotating 3D cavity is simulated with the moving mesh method,where the solution differences between 2D and 3D simulation are explicitly presented.Finally,the scheme is applied to the falling plate study,where the unsteady plate tumbling motion inside water tank has been studied and compared with the experimental measurements.
基金the Joint Applied Mathematics Research Institute of Peking University and Hong Kong Baptist University.Li was also partially supported by the National Basic Research Program of China under the grant 2005CB321701The research of Tang was supported by CERG Grants of Hong Kong Research Grant Council,FRG grants of Hong Kong Baptist University,and NSAF Grant#10476032 of National Science Foundation of China.He was supported in part by the Chinese Academy of Sciences while visiting its Institute of Computational Mathematics.
文摘In this paper, we present an adaptive moving mesh algorithm for meshesof unstructured polyhedra in three space dimensions. The algorithm automaticallyadjusts the size of the elements with time and position in the physical domain to resolvethe relevant scales in multiscale physical systems while minimizing computationalcosts. The algorithm is a generalization of the moving mesh methods basedon harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To make 3D moving mesh simulations possible,the key is to develop an efficient mesh redistribution procedure so that this part willcost as little as possible comparing with the solution evolution part. Since the meshredistribution procedure normally requires to solve large size matrix equations, wewill describe a procedure to decouple the matrix equation to a much simpler blocktridiagonaltype which can be efficiently solved by a particularly designed multi-gridmethod. To demonstrate the performance of the proposed 3D moving mesh strategy,the algorithm is implemented in finite element simulations of fluid-fluid interface interactionsin multiphase flows. To demonstrate the main ideas, we consider the formationof drops by using an energetic variational phase field model which describesthe motion of mixtures of two incompressible fluids. Numerical results on two- andthree-dimensional simulations will be presented.
基金special funds for Major State Research Projects 2005CB1704National Science Foundation of China for Distinguished Young Scholars 10225103.
文摘The Doi-Hess equation that describes the evolution of an orientational dis-tribution function is capable of predicting several rheological features of nematic poly-mers.Since the orientational distribution function becomes sharply peaked as poten-tial intensity increases,powerful numerical methods become necessary in the relevant numerical simulations.In this paper,a numerical scheme based on the moving grid techniques will be designed to solve the orientational distribution functions with high potential intensities.Numerical experiments are carried out to demonstrate the effec-tiveness and robustness of the proposed scheme.
基金This work was partially supported by a grant of key program from the National Natural Science Foundation of China(No.10731060,10801120)National Basic Research Program of China(2011CB309704)Chinese Universities Scientific Fund No.2010QNA3019.
文摘This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions.With some criteria,the domain is dynamically decomposed into three parts:kinetic regions where fluids are far from equilibrium,hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition.The Boltzmann-BGK equation is solved in kinetic regions,while Euler equations in hydrodynamic regions and both equations in buffer regions.By a well defined monitor function,our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions.In each moving mesh step,the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion.In such a framework,the evolution of the hybrid model and the moving mesh procedure can be implemented independently,therefore keep the advantages of both approaches.Numerical examples are presented to demonstrate the efficiency of the method.
文摘The typical elements in a numerical simulation of fluid flow using moving meshes are a time integration scheme,a rezone method in which a new mesh is defined,and a remapping(conservative interpolation)in which a solution is transferred to the new mesh.The objective of the rezone method is to move the computational mesh to improve the robustness,accuracy and eventually efficiency of the simulation.In this paper,we consider the onedimensional viscous Burgers’equation and describe a new rezone strategy which minimizes the L2 norm of error and maintains mesh smoothness.The efficiency of the proposed method is demonstrated with numerical examples.
