北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (5): 776-785.doi: 10.13700/j.bh.1001-5965.2014.0326

• 论文 • 上一篇    下一篇

Euler方程的分裂型通量分裂双时间步隐式方法

董海涛, 陈喆, 刘福军   

  1. 北京航空航天大学 航空科学与工程学院, 北京 100191
  • 收稿日期:2014-06-06 修回日期:2014-12-05 出版日期:2015-05-20 发布日期:2015-06-02
  • 通讯作者: 董海涛(1963—),男,北京人,副教授,htdong@buaa.edu.cn,主要研究方向为大时间步长格式. E-mail:htdong@buaa.edu.cn

Split-type implicit scheme using flux splitting and dual-time step for Euler equations

DONG Haitao, CHEN Zhe, LIU Fujun   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-06-06 Revised:2014-12-05 Online:2015-05-20 Published:2015-06-02

摘要:

传统隐式方法有格式复杂、计算量大等缺点,在Euler方程的差分离散过程中,利用算子分裂思想,结合通量分裂法、双时间步法等隐式离散方法,构造了一种更简单的分裂型隐式计算方法.通过对典型空气动力学问题的计算,检验了该方法的有效性和可靠性,并对其性能做了具体讨论.该方法具有稳定性好、时间步长约束小等隐式格式的普遍优点,同时具有格式简单、程序易实现等优点;避免了传统隐式方法单步推进时的方程组常规求解及矩阵求逆过程,计算量小;比LU-SGS方法收敛速度快.

关键词: Euler方程, 算子分裂, 通量分裂, 双时间步, 隐式方法

Abstract:

There are some shortcomings of the traditional implicit schemes such as complex forms and large amount of computations. Using the idea of operator splitting combining with implicit discrete schemes—flux vector splitting and dual-time step scheme—a simpler split-type implicit difference scheme for Euler equations was developed. The validity and reliability of the new implicit scheme were verified by performing numerical experiments on some typical problems in aerodynamics, and the properties of the new scheme were discussed in detail at the same time. The new scheme has common advantages of good stability and few constraints on time step just like other implicit schemes. In addition, the new scheme has the following advantages: it has simple formulas; it is easy for programming; it needs smaller amount of computations by avoiding solving systems of equations and doing inverse matrix operation compared with conventional implicit schemes in single time step; it has faster convergence rate compared with LU-SGS scheme.

Key words: Euler equations, operator splitting, flux vector splitting, dual-time step, implicit scheme

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