运动激波自适应网格算法中权函数问题的研究

STUDY ON WEIGHT FUNCTION OF ADAPTIVE GRID TECHNIQUE APPLIED TO MOVING SHOCK PROBLEMS

变分原理的自适应网格技术被应用到运动激波问题的求解上 ,在解的大梯度区自动加密网格 ,从而非常成功地算出了激波。

Adaptive grid techniques through a variational approach are applied to moving shock problems with exact solutions. Two kinds of weight functions are first tested. One only considering solution gradient can concentrate more grid points in the center of the shock wave, while the other using the second derivative term can distribute more grid points on both ends of the shock wave, where many oscillations are easily produced. So, the weight function with the second derivative term included is more effective to capture the shock wave. The history of the grid points position shows that more grid points are redistributed in the shock regions and can tightly trace the moving shock wave in response to numerical solution; thus the shock wave can be captured successfully. Compared to the numerical solution by using fixed grids, the results show that the adaptive grid techniques have excellent qualities in improving accuracy of the numerical solution and reducing CPU time.