An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To a...An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.展开更多
This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary condi...This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.展开更多
A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface i...A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.展开更多
The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdoma...The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.展开更多
The flow past a cylinder in a channel with the aspect ratio of 2 ： 1 for the upper convected Maxwell （UCM） fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-squar...The flow past a cylinder in a channel with the aspect ratio of 2 ： 1 for the upper convected Maxwell （UCM） fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.展开更多
The present article is concerned with the numerical solution of boundary integral e- quations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that ...The present article is concerned with the numerical solution of boundary integral e- quations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that is proportional to the solution＇s best N-term approximation. The focus of this article is on algorithmic issues which includes the crucial building blocks and details about the efficient implementation. By numerical examples for the Laplace equation and the Helmholtz equation, solved for different geome- tries and right-hand sides, we validate the feasibility and efficiency of the adaptive wavelet boundary element method.展开更多
One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.Hi...One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinement.展开更多
Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions,where the wave propagation is governed by the Helmholtz equation.The scattering problem is modeled as a boundary value problem over a...Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions,where the wave propagation is governed by the Helmholtz equation.The scattering problem is modeled as a boundary value problem over a bounded domain.Based on the Dirichlet-to-Neumann(DtN)operator,a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle.An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition.Numerical experiments are included to compare with the perfectly matched layer(PML)method to illustrate the competitive behavior of the proposed adaptive method.展开更多
常规边界元法(boundary element method,BEM)因形成的方程矩阵稠密非对称而难以应用于大规模问题,BEM矩阵的存储限制了BEM的工程应用。该文介绍了递阶矩阵(hierarchical matrix,H-matrix)的基本概念,并引入了一种新颖的H-matrix压缩技术...常规边界元法(boundary element method,BEM)因形成的方程矩阵稠密非对称而难以应用于大规模问题,BEM矩阵的存储限制了BEM的工程应用。该文介绍了递阶矩阵(hierarchical matrix,H-matrix)的基本概念,并引入了一种新颖的H-matrix压缩技术:自适应交叉逼近(adaptive cross approximation,ACA)。通过对普法BEM的节点根据拓扑结构重新分区和编号,可以将方程矩阵分解为若干具有递阶特性的子矩阵,应用自适应交叉逼近技术将这些子矩阵进行低秩分解可大大降低BEM矩阵对内存的消耗。为了对基于ACA技术的BEM内存消耗和有效性进行验证,建立了三维球形电极模型,通过与普通BEM比较,证实了该文方法可显著减小边界元法的内存使用,并验证了该方法的有效性。展开更多
基金Supported by the National Natural Science Foundation of China (10674109)the Doctorate Foundation of Northwestern Polytechnical University (CX200601)
文摘An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.
文摘This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.
基金supported by the Open Project of Key Laboratory of Aerospace EDLA,CASC(No.EDL19092208)。
文摘A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.
基金supported by the National Natural Science Foundation of China(Grant No.50579081)EPSRC UK(Grant No.EP/F00656X/1)+1 种基金the State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,China through an open Research (Grant No.2010A004)Zhang's one-year research visit to the University of Liv-erpool was funded by China Scholarship Council
文摘The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.
基金The project supported by the National Natural Science Foundation of China(50335010 and 20274041)the MOLDFLOW Comp.Australia.
文摘The flow past a cylinder in a channel with the aspect ratio of 2 ： 1 for the upper convected Maxwell （UCM） fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.
文摘The present article is concerned with the numerical solution of boundary integral e- quations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that is proportional to the solution＇s best N-term approximation. The focus of this article is on algorithmic issues which includes the crucial building blocks and details about the efficient implementation. By numerical examples for the Laplace equation and the Helmholtz equation, solved for different geome- tries and right-hand sides, we validate the feasibility and efficiency of the adaptive wavelet boundary element method.
文摘One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinement.
基金supported in part by the NSF grants DMS-0914595 and DMS1042958supported in part by China NSF under the grants 11031006 and 11171334+1 种基金by the Funds for Creative Research Groups of China(Grant No.11021101)by the National Magnetic Confinement Fusion Science Program(Grant No.2011GB105003).
文摘Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions,where the wave propagation is governed by the Helmholtz equation.The scattering problem is modeled as a boundary value problem over a bounded domain.Based on the Dirichlet-to-Neumann(DtN)operator,a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle.An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition.Numerical experiments are included to compare with the perfectly matched layer(PML)method to illustrate the competitive behavior of the proposed adaptive method.
