Fast, adaptive finite element scheme for viscous incompressible flows

Abstract

This paper presents an adaptive finite element procedure for solving viscous incompressible flows. The methodology is based on adaptive remeshing for the solution of the steady-state Navier-Stokes equations for an incompressible fluid. Solutions are obtained in primitive variables by an Uzawa algorithm using a highly accurate element. Two error estimators are presented and compared for a problem with a known analytical solution. The methodology is then applied to a problem of practical interest, and predictions are compared with experimental measurements. The proposed adaptive scheme is shown to lead to improved accuracy of the finite element predictions. C E e h L n p Q q 5 U u, V x, y 6 v a V v = Nomenclature constant velocity error error in the solution element size dissipation energy plate length number of elements in the mesh pressure pressure error test function for pressure error step and fence height velocity vector velocity components test function for velocity error coordinates element size predicted by adaptation module strain rate tension, Vi^vU + Vf/ 7) relative error on a mesh similarity variable in a boundary layer absolute viscosity of the fluid kinematic viscosity of the fluid deviatoric stress sensor, 2pe gradient operator