基于Roe格式的可压与不可压流的统一计算方法

摘要：以Navier-Stokes方程为基础，基于有限体积的时间推进的预处理技术．提出了一个可以用来求解可压与不可压流场的统一的计算方法，原始变量选用压力、速度与温度，通过矩阵变换与重构，使得对流项系数矩阵在可压与小可压条件下都不会奇异．将可压与不可压流场的计算方法统一起来。采用Roe格式计算对流通量，采用中心差分格式计算扩散通量．算例表明，该方法可以进行高Mach数、中等Mach数、低Mach数及不可压流场的计算。由于采用了Roe格式，该方法还可以捕获不连续流场的间断面。

Unified Computation of Flow With Compressible and Incompressible Fluid Based on Roe's Scheme

A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm.The primitive variables were pressure,velocities and temperature.The time integration scheme was used in conjunction with a finite volume discretization.The preconditioning was coupled with a high order implicit upwind scheme based on the definition of a Roe's type matrix.Computational capabilities are demonstrated through computations of high Mach number,middle Mach number,very low Mach number,and incompressible flow.It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe's scheme.