A 5th order monotonicity-preserving upwind compact difference scheme

查看全文 作　　者：HE [1]ZhiWei;LI [1]XinLiang;FU [2]DeXun;MA [2]YanWen

机构地区：[1]The Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;[2]The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》索引2011年第54卷第3期,共12页

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 110632050, 10872205);the National Basic Research Program of China (Grant No. 2009CB724100);Projects of CAS INFO-115-B01 摘　　要：Based on an upwind compact difference scheme and the idea of monotonicity-preserving, a 5th order monotonicity-preserving upwind compact difference scheme (m-UCD5) is proposed. The new difference scheme not only retains the advantage of good resolution of high wave number but also avoids the Gibbs phenomenon of the original upwind compact difference scheme. Compared with the classical 5th order WENO difference scheme, the new difference scheme is simpler and small in diffusion and computation load. By employing the component-wise and characteristic-wise methods, two forms of the new difference scheme are proposed to solve the N-S/Euler equation. Through the Sod problem, the Shu-Osher problem and the two-dimensional Double Mach Reflection problem, numerical solutions have demonstrated this new scheme does have a good resolution of high wave number and a robust ability of capturing shock waves, leading to a conclusion that the new difference scheme may be used to simulate complex flows containing shock waves. 关键词：紧致差分格式迎风单调 ENO差分格式吉布斯现象欧拉方程马赫反射捕捉能力

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A 5th order monotonicity-preserving upwind compact difference scheme

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