On the significance of the geometric conservation law for flow computations on moving meshes

The objective of this paper is to establish a firm theoretical basis for th e enforcement of discrete geometric conservation laws (D-GCLs) while solvin g flow problems with moving meshes. The GCL condition governs the geometric parameters of a given numerical solution method, and requires that these b e computed so that the numerical procedure reproduces exactly a constant so lution. In this paper, we show that this requirement corresponds to a time- accuracy condition. More specifically, we prove that satisfying an appropri ate D-GCL is a sufficient condition for a numerical scheme to be at least f irst-order time-accurate on moving meshes. (C) 2000 Elsevier Science S.A. A ll rights reserved.