Abstract: 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.

Key words: adaptive grid techniques, weight funct ion, shock