二维欧拉流体动力学方程的完全守恒差分格式

一、引言 众所周知,描述流体动力学三个守恒律的偏微分方程组是质量方程、散度型或非散度型的动量方程和散度型的总能量方程。后者也可以写成非散度型的比内能方程或熵的方程。流体动力学偏微分方程组可以用各种形式来表达,它们是等价的,即从一种形式能够转换成另一种形式,反之亦然。但是,在一般情形下,逼近一种形式偏微分方程组的差分方程不一定能够推导出逼近其它等价的偏微分方程的差分方程。因而,在这种情况下,或者导致破坏总能量守恒律,或者不保持内能和动能的各自平衡。为了消除这个缺点,2]

TWO KINDS OF COMPLETELY CONSERVATIVE DIFFERENCE SCHEMES FOR UNSTEADY EULER EQUATIONS OF FLUID DYNAMICS FOR TWO-DIMEN SIONAL PROBLEMS

In this paper two kinds of Completely conservative difference schemes for uns-teady Eulerian equations of fluid dynamics in two dimensions are presented. The firstscheme uses an Eulerian mesh of rectangular cells as used in 5, 6]. Velocities aredefined at cell boundaries while pressure, density and specific internal energy are defin-ed at cell centers. For the second difference scheme, all field variables are calculatedat the centers of the polygonal grids of arbitrary shape.