A PROCEDURE FOR THE TREATMENT OF THE VELOCITY-PRESSURE COUPLING PROBLEM IN INCOMPRESSIBLE FLUID FLOW

Abstract

A new block implicit procedure (BID) is introduced which utilizes a simple incomplete decomposition of the matrix resulting from the discretization of the momentum and mass conservation equations for incompressible fluid flow problems. In contrast to the conventional methods, the new method is not of the segregated type, and does not require an explicit equation for pressure. The complete, coupled block system is solved in its primitive form. In this way, mass and momentum conservation are satisfied simultaneously at all grid points, while pressure is calculated implicitly. Only a couple of overall iterations are required for the treatment of the nonlinearities of the problem. Tests show that the new procedure converges fast for any E value (in an E-factor formulation), and therefore virtually the E-factor formulation is not necessary.