混合气体流动的一种数值模拟方法

A numerical simulation model for mixing gases flows

本文建立一个数值模拟完全气体混合流动的理论模型。该模型首先应用混合气体的Euler方程和每种气体组分的质量分数方程来控制流动。为了消除混合网格内气体组分界面附近出现的非物理振荡,我们假定混合气体的每种组分达到了动力学平衡状态然而尚未达到热力学平衡状态。这种思想导致需要另外给定每种气体组分的总能量方程。为使用高分辨格式来求解这组双曲型偏微分方程并且简化对所需要的Jacobi矩阵的推导,混合气体的压力方程也被耦合起来。Godunov型的波传播方法被采用来离散求解所获得的控制方程。从典型算例结果来看,一维问题的数值解与精确解一致,二维问题的数值解与理论分析一致。这说明本文的理论模型是合理的。

<Abstrcat> A theory model is constructed to numerically simulate the mixing perfect gases flows. In the model, the Euler equations for the mixing gases and mass fraction equation for each gas species are applied, and to eliminate the non-physical oscillations near species interfaces within mixture cells, the assumption that each species of the mixing gases arrives at dynamic equilibrium yet not thermodynamic equilibrium is adopted. This idea requires solving additional total energy equations for all species. In order to simplify the derivation on Jacobian matrices of the differential equations for high resolution scheme, pressure equation for the mixing gases is included in the governing system. Wave propagation scheme of Godunov-type is used to discretize and solve the non-conservation hyperbolic laws gotten. From the representative comparison of 1D problems to exact solutions and 2D ones to physics analysis, they are very accordant with each other. The results demonstrate that the method by this paper is reasonable.