High-Order Local Discontinuous Galerkin Method with Multi-Resolution WENO Limiter for Navier-Stokes Equations on Triangular Meshes  

作　　者：Yizhou Lu Jun Zhu Shengzhu Cui Zhenming Wang Linlin Tian Ning Zhao 

机构地区：[1]State Key Laboratory of Mechanics and Control for Aerospace Structures,Nanjing University of Aeronautics and Astronautics,Jiangsu 210000,P.R.China [2]Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles,Nanjing University of Aeronautics and Astronautics,Jiangsu 210000,P.R.China [3]Jiangsu Key Laboratory of Hi-Tech Research for Wind Turbine Design,Nanjing University of Aeronautics and Astronautics,Jiangsu 210000,P.R.China [4]College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Jiangsu 210000,P.R.China

出　　处：《Communications in Computational Physics》2023年第5期1217-1239,共23页计算物理通讯（英文）

摘　　要：In this paper,a new multi-resolution weighted essentially non-oscillatory(MR-WENO)limiter for high-order local discontinuous Galerkin(LDG)method is designed for solving Navier-Stokes equations on triangular meshes.This MR-WENO limiter is a new extension of the finite volume MR-WENO schemes.Such new limiter uses information of the LDG solution essentially only within the troubled cell itself,to build a sequence of hierarchical L^(2)projection polynomials from zeroth degree to the highest degree of the LDGmethod.As an example,a third-order LDGmethod with associated same orderMR-WENO limiter has been developed in this paper,which could maintain the original order of accuracy in smooth regions and could simultaneously suppress spurious oscillations near strong shocks or contact discontinuities.The linear weights of such new MR-WENO limiter can be any positive numbers on condition that their summation is one.This is the first time that a series of different degree polynomials within the troubled cell are applied in a WENO-type fashion to modify the freedom of degrees of the LDG solutions in the troubled cell.This MR-WENO limiter is very simple to construct,and can be easily implemented to arbitrary high-order accuracy and in higher dimensions on unstructured meshes.Such spatial reconstruction methodology improves the robustness in the numerical simulation on the same compact spatial stencil of the original LDG methods on triangular meshes.Some classical viscous examples are given to show the good performance of this third-order LDG method with associated MR-WENO limiter.

关 键 词：Local discontinuous Galerkin method multi-resolution WENO limiter triangular meshes Navier-Stokes equations 

分 类 号：O17[理学—数学]