Godunov方法在复杂流场数值模拟中的应用

本文根据Ｖａｎ Ｌｅｅｒ提出的方法给出了求解三维非定常Ｅｕｌｅｒ方程和三维定常Ｅｕｌｅｒ方程的二阶Ｇｏｄｕｎｏｖ方法。方法要点为：在各体积离散单元中，用流动变量的分段线性分布代替一阶方法中的分段常量分布，在确定线性分布的斜率中引入单调性限制条件；在离散单元界面构造Ｒｉｅｍａｎｎ问题，由Ｒｉｅｍａｎｎ间断解确定单元侧面的通量；用预测－修正两步法对离散方程推进求解，用上述方法结合单区网格或多区重迭网格

Application of the Godunov Method in the Numerical Simulation of Complicated Flow Fields

A second order Godunov method is used to solve 3 D unsteady and steady Euler equations. The main points of the method are as following. In every cell a piecewise linear distributions of flow variables replace the piecewise constant distributions of the first order Godunov scheme, the slope of linear distribution are determined by using monotony limiter. The fluxes over faces of cell are calculated by the solution of Riemann problem. A predictor Corrector method is used to solve the discreting equations of Euler equations. The overlapping grid technique is used to generate the multizonal grid system for combination consisting of multi bodies. Numerical results are presented for the flowfield around bodies with complicated shape.