Theoretical Aspects of Composite Grid Methods in Computational Fluid Dynamics

Abstract

The composite grid methods considered in this paper refer to overlapping grid methods and adaptive Cartesian grid method. This paper reviews some recent work concerning the theoretical aspects, such as stability, accuracy, convergence, uniqueness, and conservation, of composite grid methods used in Computational Fluid Dynamics, in order to clarify some hotly debated questions. The most important point to be remarked is that, for composite overlapping grid method, only a nonconservative treatment can stably lead to conservative results. Another important result is that, the adaptive Cartesian grid method is as stable and accurate as the conventional smoothly refined curvilinear grid method, provided they are based on the same difference approximations and that the ratio between the finest mesh and the coarsest mesh is the same.