GSMAC finite element method for unsteady incompressible Navier–Stokes equations at high reynolds numbers

Abstract

Abstract A new finite element technique is developed for predicting the velocity and the pressure in transient incompressible viscous fluid flows at high Reynolds numbers. The new method is based on the generalized and simplified marker‐and‐cell method (GSMAC) and has two characteristics: one is an application of the Bernoulli function and the implicit pressure solution algorithm to the explicit fractional time step method; the other is a high‐order flux calculation to prevent the pressure field from oscillating. Two examples, driven cavity flows at high Reynolds numbers and vortex shedding behind a circular cylinder, are presented. Satisfactory agreement with experiment is demonstrated.