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 the enforcement of discrete geometric conservation laws (D-GCLs) while solving flow problems with moving meshes. The GCL condition governs the geometric parameters of a given numerical solution method, and requires that these be computed so that the numerical procedure reproduces exactly a constant solution. In this paper, we show that this requirement corresponds to a time-accuracy condition. More specifically, we prove that satisfying an appropriate D-GCL is a sufficient condition for a numerical scheme to be at least first-order time-accurate on moving meshes. (C) 2000 Elsevier Science S.A. All rights reserved.