一种低耗散、无伪振荡的实用差分格式

A practical low-dissipation bounded difference scheme

探寻一种优化的差分格式一直是计算流体力学与计算传热学中的热门课题。本文在分析 SOUCU P格式的基础上 ,将二阶迎风格式和中心差分格式进行加权得到了 WSUC格式。分析表明 ,WSUC格式具有整体二阶空间精度 ,且半离散 WSUC格式具有总变差有界性 ,因而格式可以抑制伪振荡 ;另外还证明了 WSUC格式是无条件对流稳定的。两个典型算例的结果表明 :WSUC格式的数值解的精度较 SOUCUP格式有了显著的提高 ,而计算量没有明显增加。

WT5”BZ]This paper presents an effective discretization scheme for approximating convevtive transport. The discretization scheme is called the WSUC scheme, which is a weighted second order upwind and central difference scheme. According to the theoretical analysis, the WSUC scheme is total variation bounded and unconditionally stable in the sense of numerical convective stability. Two typical numerical tests show that the WSUC scheme is better in accuracy and resolution than the first order upwind scheme, the second order upwind scheme, the SOUCUP scheme and the MSOUCUP scheme. Moreover, in the paper, a thermal stratification in thermal storage tank is calculated by using WSUC scheme. [WT5HZ]