Modeling the Gasdynamic Problems Using Locally Adaptive Meshes Based on Quadtree

Abstract

The asymptotics of computational costs for simulations of gas flow with shock waves using adaptively refined dynamic meshes of the quadtree class is estimated. The Euler equations in Cartesian coordinates are numerically solved using the finite-volume CWENO method with a compact stencil. A simple criterion for splitting and recombination of computational cells is proposed based on an estimate of the local density gradient. A comparison is made with simulations with the finite-difference WENO method of the same order of approximation on a uniform grid. It is shown that the time and memory costs when refining locally-adapted grids increase significantly slower than for uniform grids.