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 

作者机构：State Key Laboratory of Mechanics and Control for Aerospace StructuresNanjing University of Aeronautics and AstronauticsJiangsu 210000P.R.China Key Laboratory of Mathematical Modeling and High Performance Computing of Air VehiclesNanjing University of Aeronautics and AstronauticsJiangsu 210000P.R.China Jiangsu Key Laboratory of Hi-Tech Research for Wind Turbine DesignNanjing University of Aeronautics and AstronauticsJiangsu 210000P.R.China College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsJiangsu 210000P.R.China 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2023年第33卷第5期

页      面：1217-1239页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

主　　题：Local discontinuous Galerkin method multi-resolution WENO limiter triangular meshes Navier-Stokes equations 

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 *** MR-WENO limiter is a new extension of the finite volume MR-WENO *** 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 *** 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 *** linear weights of such new MR-WENO limiter can be any positive numbers on condition that their summation is *** 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 *** MR-WENO limiter is very simple to construct,and can be easily implemented to arbitrary high-order accuracy and in higher dimensions on unstructured *** spatial reconstruction methodology improves the robustness in the numerical simulation on the same compact spatial stencil of the original LDG methods on triangular *** classical viscous examples are given to show the good performance of this third-order LDG method with associated MR-WENO limiter.