Simple and robust h-adaptive shock-capturing method for flux reconstruction framework  

作　　者：Lintao HUANG Zhenhua JIANG Shuai LOU Xin ZHANG Chao YAN 

机构地区：[1]School of Aeronautic Science and Engineering,Beihang University,Beijing 100191,China [2]Research Office No.12,Beijing Institute of Astronautical Systems Engineering,Beijing 100076,China

出　　处：《Chinese Journal of Aeronautics》2023年第7期348-365,共18页中国航空学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11721202).

摘　　要：In this paper,a simple and robust shock-capturing method is developed for the Flux Reconstruction(FR)framework by combining the Adaptive Mesh Refinement(AMR)technique with the positivity-preserving property.The adaptive technique avoids the use of redundant meshes in smooth regions,while the positivity-preserving property makes the solver capable of providing numerical solutions with physical meaning.The compatibility of these two significant features relies on a novel limiter designed for mesh refinements.It ensures the positivity of solutions on all newly created cells.Therefore,the proposed method is completely positivity-preserving and thus highly robust.It performs well in solving challenging problems on highly refined meshes and allows the transition of cells at different levels to be completed within a very short distance.The performance of the proposed method is examined in various numerical experiments.When solving Euler equations,the technique of Local Artificial Diffusivity(LAD)is additionally coupled to damp oscillations.More importantly,when solving Navier-Stokes equations,the proposed method requires no auxiliaries and can provide satisfying numerical solutions directly.The implementation of the method becomes rather simple.

关 键 词：Adaptive mesh refinement Flux reconstruction Positivity-preserving scheme Robustness SHOCK-CAPTURING 

分 类 号：O35[理学—流体力学]