An adaptive finite volume method for non-stationary problems

Abstract

The subject-matter of this paper is the numerical simulation of the multidimensional inviscid compressible transonic gas flow governed by hyperbolic partial differential equations. An adaptive mesh is constructed in the framework of the cell-centred finite volume scheme.

Two non-stationary adaptation strategies are presented. A recovery of the approximate solution on the new mesh is discussed.

The main feature of the proposed method is to keep the mass conservation of the numerical solution at each adaptation step. To do this the geometric conservation law is employed.