High-order compact finite volume methods on unstructured grids with adaptive mesh refinement for solving inviscid and viscous flows  

作　　者：Jianhua PAN Qian WANG Yusi ZHANG Yuxin REN 

机构地区：[1]School of Aerospace Engineering,Tsinghua University

出　　处：《Chinese Journal of Aeronautics》2018年第9期1829-1841,共13页中国航空学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.91752114 and 11672160)

摘　　要：In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.

关 键 词：Adaptive mesh refinement Compact stencil High-order finite volume scheme Unstructured grids Variational reconstruction 

分 类 号：O35[理学—流体力学] O241.82[理学—力学]