守恒格式稳定性分析与耗散守恒格式

本文从守恒格式出发,建立分析稳定性和耗散性的启发性方法和Fourier分析方法,给出了耗散守恒格式的严格定义及三点耗散守恒格式的充要条件。应用本文的方法,重新分析了三点格式,得到如下结论:某些常系数耗散格式,在某些情况下,之所以会得到非物理解或发生非线性不稳定,是由于该格式在这些情况下,已经是零耗散的或是负耗散

STABILITY ANALYSIS OF CONSERVATIVE SCHEME AND DISSIPATIVE CONSERVATION SCHEME

In this paper we have discussed heuristic and Fourier methods of analyising stability anddissipation for conservative scheme, given exact definition of dissipative conservation schemeand necesary and sufficient condition for three-point scheme of dissipative conservation. Ma-king use of those methods and therems in this paper, we give a new analysis for some lineardissipative scheme the result indicates that for some special situation the calculation by somelinear dissipative scheme for conservative laws obtains nonphysical solution or takes place ofnonlinear instabilities, the real reason is that the schemes are not dissipative and not stable, orhave negative dissipation.