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A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection 被引量:31
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作者 Lin-Bo Zhang 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第1期65-89,共25页
Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement... Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp://lsec. cc. ac. cn/phg/), a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure. 展开更多
关键词 Adaptive refinement BISECTION tetrahedral mesh parallel algorithm MPI.
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Construction and analysis of the quadratic finite volume methods on tetrahedral meshes
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作者 Peng Yang Xiang Wang Yonghai Li 《Science China Mathematics》 SCIE CSCD 2023年第4期855-886,共32页
We construct and analyze a family of quadratic finite volume method(FVM)schemes over tetrahedral meshes.In order to prove the stability and the error estimate,we propose the minimum V-angle condition on tetrahedral me... We construct and analyze a family of quadratic finite volume method(FVM)schemes over tetrahedral meshes.In order to prove the stability and the error estimate,we propose the minimum V-angle condition on tetrahedral meshes,and the surface and volume orthogonal conditions on dual meshes.Through the technique of element analysis,the local stability is equivalent to a positive definiteness of a 9 × 9 element matrix,which is difficult to analyze directly or even numerically.With the help of the surface orthogonal condition and the congruent transformation,this element matrix is reduced into a block diagonal matrix,and then we carry out the stability result under the minimum V-angle condition.It is worth mentioning that the minimum V-angle condition of the tetrahedral case is very different from a simple extension of the minimum angle condition for triangular meshes,while it is also convenient to use in practice.Based on the stability,we prove the optimal H^(1) and L^(2) error estimates,respectively,where the orthogonal conditions play an important role in ensuring the optimal L^(2) convergence rate.Numerical experiments are presented to illustrate our theoretical results. 展开更多
关键词 finite volume method tetrahedral mesh orthogonal condition minimum V-angle condition stability and convergence
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Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes 被引量:6
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作者 Yong-Tao Zhang Chi-Wang Shu 《Communications in Computational Physics》 SCIE 2009年第2期836-848,共13页
We extend the weighted essentially non-oscillatory(WENO)schemes on two dimensional triangular meshes developed in[7]to three dimensions,and construct a third order finite volume WENO scheme on three dimensional tetrah... We extend the weighted essentially non-oscillatory(WENO)schemes on two dimensional triangular meshes developed in[7]to three dimensions,and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes.We use the Lax-Friedrichs monotone flux as building blocks,third order reconstructions made from combinations of linear polynomials which are constructed on diversified small stencils of a tetrahedral mesh,and non-linear weights using smoothness indicators based on the derivatives of these linear polynomials.Numerical examples are given to demonstrate stability and accuracy of the scheme. 展开更多
关键词 Weighted essentially non-oscillatory(WENO)schemes finite volume schemes highorder accuracy tetrahedral meshes
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Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes
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作者 Xiang Lai Zhiqiang Sheng Guangwei Yuan 《Communications in Computational Physics》 SCIE 2017年第1期162-181,共20页
We construct a nonlinear monotone finite volume scheme for threedimensional diffusion equation on tetrahedral meshes.Since it is crucial important to eliminate the vertex unknowns in the construction of the scheme,we ... We construct a nonlinear monotone finite volume scheme for threedimensional diffusion equation on tetrahedral meshes.Since it is crucial important to eliminate the vertex unknowns in the construction of the scheme,we present a new efficient eliminating method.The scheme has only cell-centered unknowns and can deal with discontinuous or tensor diffusion coefficient problems on distorted meshes rigorously.The numerical results illustrate that the resulting scheme can preserve positivity on distorted tetrahedral meshes,and also show that our scheme appears to be approximate second-order accuracy for solution. 展开更多
关键词 MONOTONICITY finite volume scheme diffusion equation tetrahedral meshes
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Open Volumetric Mesh-An Efficient Data Structure for Tetrahedral and Hexahedral Meshes
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作者 XIAN Chu-hua LI Gui-qing GAO Shu-ming 《Computer Aided Drafting,Design and Manufacturing》 2013年第3期23-27,共5页
This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalabil... This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalability by using hierarchical representa-tions of topological elements. The proposed data structure is array-based, and it is a compact representation of the half-edge data structure for volume elements and half-face data structure for volumetric meshes. This guarantees constant access time to the neighbors of the topological elements. In addition, an open-source implementation named Open Volumetric Mesh (OVM) of the pro-posed data structure is written in C++ using generic programming concepts. 展开更多
关键词 tetrahedral mesh hexahedral mesh geometry modeling data structure generic programming
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An h-Adaptivity DG Method on Locally Curved Tetrahedral Mesh for Solving Compressible Flows
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作者 AN Wei HUANG Zenghui LYU Hongqiang 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2020年第5期702-712,共11页
For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions w... For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex flows.However,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)methods.First,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be maintained.Second,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel computing.In this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the h-adaptivity.Furthermore,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel efficiency.Numerical results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields. 展开更多
关键词 h-adaptivity discontinuous Galerkin(DG)method curved mesh tetrahedral mesh compressible flows
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High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh
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作者 Fengxiang Zhao Xing Ji +1 位作者 Wei Shyy Kun Xu 《Advances in Aerodynamics》 EI 2023年第1期1-28,共28页
A general framework for the development of high-order compact schemes has been proposed recently.The core steps of the schemes are composed of the following.1).Based on a kinetic model equation,from a generalized init... A general framework for the development of high-order compact schemes has been proposed recently.The core steps of the schemes are composed of the following.1).Based on a kinetic model equation,from a generalized initial distribution of flow variables construct a time-accurate evolution solution of gas distribution function at a cell interface and obtain the corresponding flux function;2).Introduce the WENO-type weighting functions into the high-order time-derivative of the cell interface flux function in the multistage multi-derivative(MSMD)time stepping scheme to cope with the possible impingement of a shock wave on a cell interface within a time step,and update the cell-averaged conservative flow variables inside each control volume;3).Model the time evolution of the gas distribution function on both sides of a cell interface separately,take moments of the inner cell interface gas distribution function to get flow variables,and update the cell-averaged gradients of flow variables inside each control volume;4).Based on the cell-averaged flow variables and their gradients,develop compact initial data reconstruction to get initial condition of flow distributions at the beginning of next time step.A compact gas-kinetic scheme(GKS)up to sixth-order accuracy in space and fourth-order in time has been constructed on 2D unstructured mesh.In this paper,the compact GKS up to fourth-order accuracy on three-dimensional tetrahedral mesh will be further constructed with the focus on the WENO-type initial compact data reconstruction.Nonlinear weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock interactions.The fourth-order compact GKS uses a large time step with a CFL number 0.6 in the simulations from subsonic to hypersonic flow.A series of test cases are used to validate the scheme.The high-order compact GKS can be used in 3D applications with complex geometry. 展开更多
关键词 Compact scheme High-order GKS WENO reconstruction tetrahedral mesh
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Robust and Quality Boundary Constrained Tetrahedral Mesh Generation
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作者 Songhe Song Min Wan +2 位作者 Shengxi Wang Desheng Wang Zhengping Zou 《Communications in Computational Physics》 SCIE 2013年第10期1304-1321,共18页
A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique(AFT)and conforming Delaunay triangulation.Given a triangulated surface mesh,AFT is firstly applied to ... A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique(AFT)and conforming Delaunay triangulation.Given a triangulated surface mesh,AFT is firstly applied to mesh several layers of elements adjacent to the boundary.The rest of the domain is then meshed by the conforming Delaunay triangulation.The non-conformal interface between two parts of meshes are adjusted.Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality.Robustness and quality of the proposed method is shown.Convergence proof of each stage as well as the whole algorithm is provided.Various numerical examples are included as well as the quality of the meshes. 展开更多
关键词 Unstructured tetrahedral mesh Advancing Front Technique conforming Delaunay triangulation boundary constrained mesh refinement mesh optimization
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Unsteady analysis of six-DOF motion of a 6:1 prolate spheroid in viscous fluid
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作者 Ying Xiong Ying Xiong +1 位作者 Hui Guan ChuiJie Wu 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2017年第11期24-40,共17页
Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly... Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly challenging due to the extreme unsteady motions and high Re(Reynolds) numbers. The aim of this study is to perform a six-DOF motion simulation of a 6:1prolate spheroid that is falling in a fluid field. Prior to conducting the six-DOF simulation, some verification simulations were performed. First, a laminar flow past an inclined prolate spheroid at a Re number of 1000 and incidence angle of 45. with a tetrahedral mesh was simulated to verify the relevant targeted discrete method for an unstructured mesh. Second, to verify the LES(large eddy simulation) models and dependent parameters for the DDES(delayed detached eddy simulation), a turbulent flow past a sphere was performed at a subcritical Re number of 10000. Third, a steady maneuvering problem about a prolate spheroid pitching up from 0. to 30. incidence at a uniform angular velocity was established based on a dynamic tetrahedral mesh with changing topology and the ALE(arbitrary Lagrangian-Eulerian) method of fluid-structure coupling at a Re number of 4.2 × 10~6.Finally, two six-DOF motions of an inclined 6:1 prolate spheroid at an initial incidence of 45. were simulated at different Re numbers of 10000 and 4.2 × 10~6. 展开更多
关键词 unsteady six-DOF tetrahedral dynamic mesh discrete method DDES
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