Journal of Computational Physics July 1980 [antikvár]

journal of computational physics 36, 135-153 (1980) Finite Element Simulation of Flow in Deforming Regions Daniel R. Lynch Resource Policy Center, Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755 and William G. Gray Water Resources Program, Department of Civil Engineering, Princeton University, Princeton, Afew Jersey 08540 Received September 6, 1978; revised July 11, 1979 A finite element technique for solving multidimensional flow problems with moving boundaries is developed by means of Galerkin's procedure. The method accounts auto-matically for continuous grid déformation during simulation, and utilizes finite différence techniques in the time domain. In the absence of grid déformation, the method reduces to the standard Galerkin finite element formulation. Utility of the approach is demonstrated by application to one- and two-dimensional flow problems. Introduction There are many engineering situations in which the flow of fluid in the vicinity of a moving boundary is of interest. Among the examples which are commonly encoun-tered are vertical wave motion in open channels and containers, unconfined flow of groundwater, and propagation of tidal waves into dry coastal areas. These problems ail share the feature that the spatial domain occupied by the fluid deforms during the course of motion, while the rate of boundary déformation at any time is determined by the state of the fluid at the boundary. The finite element method has been applied successfully to many kinds of transient field problems, and several works on this subject are now available (Zienkiewicz, 1971 ; Oden et al, 1974; Connor and Brebbia, 1976; Gray et al, 1977; Pinder and Gray, 1977; Bathe et al, 1977; Brebbia et al, 1978). By far the bulk of this work pertains to problems with fixed domains. A common approach has been to use the Galerkin method to generate a set of ordinary differential équations in the time domain. Finite différence methods are typically used to integrate these équations in time, although other methods have been used to advantage (e.g., transform methods or finite element représentations in time). 0021-9991/80/080135-19802.00/0 Copyright © 1980 by Academie Press, Inc. A1I rights of reproduction in any form reserved.