Computational Aspects of the Mesh Adaptation for the Time Marching Procedure

Abstract

The paper deals with a construction of an adaptive mesh in the framework of the cell-centred finite volume scheme. The adaptive strategy is applied to the numerical solution of problems governed by hyperbolic partial differential equations. Starting from the adaptation techniques for the stationary problems (for a general overview see e.g. [9]), the nonstationary case is studied. The main attention is paid to an adaptive part of a time marching procedure. The main feature of the proposed method is to keep the mass conservation of the numerical solution at each adaptation step. We apply an anisotropic mesh adaptation from [1]. This is followed by a recovery of the approximate solution on the new mesh satisfying the geometric conservation law. The adaptation algorithm is formulated in the framework of an N-dimensional numerical solution procedure. A new strategy for moving a vertex of the mesh, based on a gradient method, is presented. The results from [4] are further developed. The general significance of the proposed method is the ability to solve problems with moving discontinuities. A numerical example is presented.