A semi-implicit fractional step finite element method for viscous incompressible flows

Abstract

This paper describes a new semi-implicit finite element algorithm for time-dependent viscous incompressible flows. The algorithm is of a general type and can handle both low and high Reynolds number flows, although the emphasis is on convection dominated flows. An explicit three-step method is used for the convection term and an implicit trapezoid method for the diffusion term. The consistent mass matrix is only used in the momentum phase of the fractional step algorithm while the lumped mass matrix is used in the pressure phase and in the pressure Poisson equation. An accuracy and stability analysis of the algorithm is provided for the pure convection equation. Two different types of boundary conditions for the end-of-step velocity of the fractional step algorithm have been investigated.

Numerical tests for the lid-driven cavity at Re=1 and Re=7500 and flow past a circular cylinder at Re=100 are presented to demonstrate the usefulness of the method.