This paper describes the development of a calculation procedure for fluid flow in arbitrary domains. This method is based on the finitevolume formulation in the arbitrary Lagrangian-Eulerian (ALE) grid. Coordinate transformation is not necessary and the physical geometrical quantities are directly applied. The derivations are obtained by the divergence theorem, and the diffusion terms in the governing equations on the control surfaces are represented by a two-point related gradient expression. A split velocity concept is employed to link the interferences of adjacent pressure nodes and eliminate the pressure wiggle problem. The total mass flux is kept unchanged in the split velocity field, as in the original velocity field determined from the momentum equations, which implies the consistency of the pressure correction process. Three typical test problems of flow in a gradual expansion duct. flow in a double bent channel, and hatural convection between concentric and eccentric annuli have been calculated to indicate the feasibility and performances of the present formulation. Results showed that this method is a robust and efficient tool to determine the fluid flow characteristic and heat transfer process for problems with complicated boundaries. (c) 1994 Acadernic Press. Inc.