Improvement of Convergence to Steady State Solutions of Euler Equations with Weighted Compact Nonlinear Schemes  

作　　者：Shu-hai ZHANG Xiao-gang DENG Mei-liang MAO Chi-Wang SHU 

机构地区：[1]State Key Laboratory of Aerodynamics,China Aerodynamics Research and Development Center [2]China Aerodynamics Research and Development Center [3]Division of Applied Mathematics,Brown University,Providence

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第3期449-464,共16页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grants11172317,91016001);973 Program 2009CB724104,Supported by 973 program 2009CB723800;Supported by AFOSR Grant FA9550-09-1-0126;NSF grants DMS-0809086 and DMS-1112700

摘　　要：The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes （WCNS） [Deng X. and Zhang H. （2000）, J. Comput. Phys. 165, 22–44 and Zhang S., Jiang S. and Shu C.-W. （2008）, J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. （2007）, J. Sci. Comput. 31, 273–305 and Zhang S., Jiang S and Shu. C.-W. （2011）, J. Sci. Comput. 47, 216–238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes （WCNS） [Deng X. and Zhang H. （2000）, J. Comput. Phys. 165, 22–44 and Zhang S., Jiang S. and Shu C.-W. （2008）, J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. （2007）, J. Sci. Comput. 31, 273–305 and Zhang S., Jiang S and Shu. C.-W. （2011）, J. Sci. Comput. 47, 216–238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.

关 键 词：weighted compact schemes convergence to steady state solution nonlinear weights 

分 类 号：O175[理学—数学]