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High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

Advances in Aerodynamics 2023年第1期5卷 1-28页

作者： Fengxiang Zhao Xing Ji Wei Shyy Kun Xu Department of Mechanical and Aerospace Engineering Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina Shaanxi Provincial Key Laboratory of Environment and Control for Flight Vehicles Xi’an Jiaotong UniversityXi’anChina Center for Ocean Research in Hong Kong and Macao(CORE) Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina Shenzhen Research Institute Hong Kong University of Science and TechnologyShenzhenChina

A general framework for the development of high-order compact schemes has been proposed *** 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 *** 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 *** weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock *** 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 *** high-order compact GKS can be used in 3D applications with complex geometry.

关键词： Compact scheme High-order GKS WENO reconstruction tetrahedral mesh

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An h-Adaptivity DG Method on Locally Curved tetrahedral mesh for Solving Compressible Flows

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Transactions of Nanjing University of Aeronautics and Astronautics 2020年第5期37卷 702-712页

作者： AN Wei HUANG Zenghui LYU Hongqiang College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016P.R.China Key Laboratory of Aerodynamic Noise Control China Aerodynamics Research and Development CenterMianyang 621000P.R.China State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang 621000P.R.China

For the numerical simulation of compressible flows,normally different mesh sizes are expected in different *** 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 ***,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)***,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 ***,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel *** 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 ***,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel *** results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.

关键词： h-adaptivity discontinuous Galerkin(DG)method curved mesh tetrahedral mesh compressible flows

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Generating tetrahedral Volume mesh from Surface Model

Generating Tetrahedral Volume Mesh from Surface Model

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E-Business·Creative Design·Manufacturing——2009 IEEE 10th International Conference on Computer-Aided Industrial Design & Conceptual Design（CAID&CD’2009）

作者： 1Chun-Kai LI 2Ming-Yong PANG 1Department of Educational Technology Nanjing Normal University Nanjing Jiangsu Province 210097 China 2Department of Educational Technology Nanjing Normal University Nanjing Jiangsu Province 210097 China

In this paper,we present an efficient algorithm to generate tetrahedral meshes from surface *** algorithm first subdivides the axis-aligned bounding box of a surface model into a number of uniform tetrahedra,and then generates an initial indention mesh after removing all the tetrahedra outside the surface model by employing a signed distance function,defined by the vertices of the surface ***,our algorithm deals with the rough indention mesh according to the relationship between the surface model and the vertices of the tetrahedra bestriding the mesh ***,the algorithm uses Laplacian smoothing operator to improve the quality of the tetrahedral *** show that the volume mesh models created by our algorithm have smooth boundary and high-quality interior cells.

关键词： tetrahedral mesh Octree Red Green Refinement Signed Distance Function Laplacian Smoothing

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Open Volumetric mesh-An Efficient Data Structure for tetrahedral and Hexahedral meshes

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Computer Aided Drafting,Design and Manufacturing 2013年第3期23卷 23-27页

作者： XIAN Chu-hua LI Gui-qing GAO Shu-ming School of Computer Science and Engineering South China University of Technology State Key Lab. Of CAD & CG Zhejiang University

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.

关键词： tetrahedral mesh hexahedral mesh geometry modeling data structure generic programming

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Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

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Science China Mathematics 2023年第4期66卷 855-886页

作者： Peng Yang Xiang Wang Yonghai Li School of Mathematics Jilin UniversityChangchun 130012China BNU-UIC Research Center for Mathematics Beijing Normal UniversityZhuhai 519087China

We construct and analyze a family of quadratic finite volume method(FVM)schemes over tetrahedral *** 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 *** 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 *** 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 *** 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 *** 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 *** experiments are presented to illustrate our theoretical results.

关键词： finite volume method tetrahedral mesh orthogonal condition minimum V-angle condition stability and convergence

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A Parallel Algorithm for Adaptive Local Refinement of tetrahedral meshes Using Bisection

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Numerical Mathematics(Theory,Methods and Applications) 2009年第1期2卷 65-89页

作者： Lin-Bo Zhang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

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.

关键词： Adaptive refinement bisection tetrahedral mesh parallel algorithm MPI.

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Assisted System for Precise Surgery Based on Medical Image Computing and VR

Assisted System for Precise Surgery Based on Medical Image C...

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第30届中国控制与决策会议

作者： Zhang Mingshi Sha Hengyu Ren Zebin Tan Wenjun School of Computer Science and Engineering Northeastern University Key Laboratory of Medical Image Computing of Ministry of Education Northeastern University

Virtual assisted surgery system in the preoperative planning, teaching, communication between doctors and patients has an important application value. Due to the hardware and computer technology constraints, most of the research on the virtual surgery system based on 3 D software model simulation to simulate human tissue. To solve the problem, an assisted system for precise surgery based on medical image computing and VR is designed in this paper. Firstly, this work designed the overall scheme of the system, including function design, hardware design scheme, software design scheme and key technology, starting from the system requirements and feasibility. Secondly, the work studies the key technologies of virtual assistant surgery system, such as the generation of human tissue model and the collision detection. In order to improve the quality of grid generation and remove noise, a tetrahedral mesh generation method based on grid and improved Laplacian smoothing algorithm is adopted in this work. Finally, the modular idea is used, respectively, to start UI and virtual surgery scene construction and interaction,independent units and the overall integration test to ensure that the system is running without errors and fluent, to achieve the original design of virtual assistant surgery system.

关键词： Virtual assisted surgery system tetrahedral mesh Grid collision detection Bounding box

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