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SOMS——可压缩完全Navier-Stokes方程的一种差分格式

邬华谟,杨明亮   

  1. 中国科学院计算中心 ;中国科学院计算中心
  • 出版日期:1981-01-20 发布日期:1981-01-20

邬华谟,杨明亮. SOMS——可压缩完全Navier-Stokes方程的一种差分格式[J]. 数值计算与计算机应用, 1981, 2(1): 45-54.

SOMS-A DIFFERENCE SCHEME FOR COMPLETE COMPRESSIBLE NAVIER-STOKES EQUATIONS

  1. Wu Hua-mo;Yang Ming-liang Computing Centre, Academia Sinica
  • Online:1981-01-20 Published:1981-01-20
随着宇航事业的发展,飞行体表面的几何形状愈来愈复杂.在许多情形下必须考虑大范围流场内的粘性效应,求解可压缩完全Navier-Stokes方程(简称CCNS方程).我们知道,飞行速度很高时,飞行体周围将出现大梯度解(粘性击波层、附面层等),致使这一方程的数值求解成为很困难的课题,所以尽管对CCNS方程的数值求解已有十几年的历史,但目前尚处于二维问题的方法研究试算阶段.计算的问题只是一些模型问题,计算的参数也受到限制,往往是马赫数低或雷诺数小. 对于具有定常解的绕流问题,从目前已发表的文章来看,对CCNS方程的求解都是从
In this paper, we propose the SOMS (the second order monotone scheme) which combinesa first order accurate scheme with a second order one by using a new switch. Furthermore, themonotonicity theorem of this scheme is demonstrated. In order to apply this scheme to fluid dynamic calculations, we propose first of all theMDC (modified donor cell) method which is of first order accuracy and is monotone andstable without any artificial viscosity to the pressure term. The simple central scheme is usedas a second order scheme. The resulting scheme is tranformed into a semi-implicit form inorder to get a better computational stability. Some numerical results for complete compressible Navier-Stokes equations are obtained. Thetest calculations show monotonously rapid transition for shock waves and the second order accu-racy in regions where the solution is smooth.
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