Numerical simulation of the dynamics of non-uniform compressible media based on the CIP-CUP method on dynamically adaptive Soroban grids

We compare the efficiency of the CIP-CUP method on a stationary uniform staggered grid and the modifications of this method on a non-staggered dynamically adaptive Soroban grid and a non-staggered stationary uniform grid in their use for computing problems of wave propagation in uniform (liquid) and non-uniform (with the presence of gas–gas and gas–liquid contact boundaries) media. We show that as compared with the initial version of the CIP-CUP method on a stationary uniform staggered grid, its modification on a Soroban grid allows one to conduct computations with similar or even higher accuracy and to apply significantly smaller number of grid vertices. The modification of the CIP-CUP method on a stationary uniform non-staggered grid is least efficient. Moreover, it can lead to non-monotonic solutions.