二维移动网格矢通量分裂法

Two-dimensional Moving Grid Vector Flux Splitting Method

针对二维欧拉方程组的数值求解问题,构造基于移动网格的矢通量分裂格式。采用移动网格法对网格进行合理剖分,使得在间断区域网格自适应加密,且整个计算区域的网格不再规则化;用守恒型迎风格式代替中心格式以减少数值耗散。在空间方向上构造新的二阶迎风矢通量分裂格式对方程进行半离散,在时间方向上采用三阶强稳定的龙格-库塔方法进行推进。数值结果表明,新算法具有良好的间断捕捉能力和高分辨率。

Aiming at the numerical solution of the two-dimensional Euler equations,a vector flux splitting scheme based on a moving grid was constructed.The moving grid method was used to reasonably divide the grid,so that the grid in the discontinuous area was adaptively encrypted;and the grid in the calculation area was no longer regular.The conservative upwind style was used instead of central format to reduce numerical dissipation.A new second-order upwind vector flux splitting scheme was constructed in the space direction to semi-discrete the equation;and a third-order strong stable Runge-Kuta method was used for propulsion in the time direction.The numerical results showed that the new algorithm had good intermittent capture capability and high resolution.