应用于双曲型方程的变区域有限元法

A Variable Domain Finite Element Scheme for Hyperbolic Equations

有些流动是用双曲型方程来描叙的,这时特征线概念起着重要作用。在有两个自变量的问题中,存在表示扰动传播方向的特征线。本文中建议一种有限元法,应用时将整个区域分为若干个以一根或两根特征线为边界的子区域。因特征线的位置在计算前是未知的,可用变区域有限元法来依次求解每个子区域中的流动。用此法计算了水击问题,结果和以往用特征线法求出的符合良好,这一方法也可用于其他双曲型方程。

For the type of flow governed by hyperbolic differential equations in two independent variables a numerical method is suggested, in which the whole domain is divided into a sequence of subregions bounded by one or two characteristic curves. Since the location of the characteristics are not known a priori, a Variable Domain Finite Element Scheme is used to compute the flow in the subregions successively. Water hammer pressure computed by this method agrees well with previous results.