DEVELOPMENT OF AN ARTIFICIAL COMPRESSIBILITY METHODOLOGY USING FLUX VECTOR SPLITTING

An implicit, upwind arithmetic scheme that is efficient for the soluti on of laminar, steady, incompressible, two-dimensional flow fields in a generalised co-ordinate system is presented in this paper. The devel oped algorithm is based on the extended flux-vector-splitting (FVS) me thod for solving incompressible flow fields. As in the case of compres sible hows, the FVS method consists of the decomposition of the convec tive fluxes into positive and negative parts that transmit information from the upstream and downstream how field respectively. The extensio n of this method to the solution of incompressible flows is achieved b y the method of artificial compressibility, whereby an artificial time derivative of the pressure is added to the continuity equation. In th is way the incompressible equations take on a hyperbolic character wit h pseudopressure waves propagating with finite speed. In such problems the 'information' inside the field is transmitted along its character istic curves. In this sense, we can use upwind schemes to represent th e finite volume scheme of the problem's governing equations. For the r epresentation of the problem variables at the cell faces, upwind schem es up to third order of accuracy are used, while for the development o f a time-iterative procedure a first-order-accurate Euler backward-tim e difference scheme is used and a second-order central differencing fo r the shear stresses is presented. The discretized Navier-Stokes equat ions are solved by an implicit unfactored method using Newton iteratio ns and Gauss-Siedel relaxation. To validate the derived arithmetical r esults against experimental data and other numerical solutions, variou s laminar flows with known behaviour from the literature are examined. (C) 1997 by John Wiley & Sons, Ltd.