激波计算不稳定现象机理研究

The Research of the Mechanism of Numerical Shock Instability

激波计算不稳定问题是激波捕获格式的一个重要缺陷,多年来受到学术界的广泛关注与研究。本文针对Roe格式,对这一问题进行了机理研究,提出了新的观点,认为造成这一问题的原因在于激波计算格式未能真正考虑流动的多维性,而保留了本应消失的类动量插值机制,即界面修正速度中的压力梯度项。通过这一机理认识,提出了简明的修正方案,改进了Roe格式。数值算例表明这一改进的Roe格式可以有效地消除激波不稳定现象。

The numerical shock instability is a famous and important problem for the shock-capturing scheme.For the classical Roe scheme,the mechanism of this problem is researched by the paper.A new viewpoint is proposed to explain the reason.In detail of the explanation,flow multi-dimensional property is not really reflected by the shock-capturing scheme,and thus a mechanism similar to the momentum interpolation method,the term of pressure gradient in the modified interface velocity,is held although it should disappear.Based on this viewpoint for the mechanism,the improved Roe scheme is proposed by a concise method.The numerical examples show that the improved Roe scheme can cure the shock instability.