AN EXPLICIT FEM FOR 3-D VISCOUS INCOMPRESSIBLE FLOWS, WITH A EBE/PCG ITERATIVE ALGORITHM

Abstract

SUMMARY A numerical procedure for the solution of the 3-D Navier-Stokes equations is developed and implemented for analyzing time-dependent incompressible viscous flows past arbitrary shapes. The equations are discretized using a finite element Galerkjn formulation with a streamwise upwinding option. The discretization in time is performed with fractional steps on the momentum equations to obtain the fractional step velocity field explicitly. The pressure field at each time level is obtained from an auxiliary potential function with the solution of a Poisson's equation, where an element-by-element (EBE) iteration procedure with preconditioned conjugate gradient (PCG) is employed. The method is used to study laminar flow past a circular cylinder with a swept bump. The flow field is solved for two different Reynolds numbers and the drag coefficient histories are obtained for the cylinder. The steady-state values of the drag coefficients show the 3-D relief effects on the cylinder. The computations are performed on an IBM 3090VF. The vectorization of the EBE algorithm allows a drastic reduction in terms of CPU time for each time step.