AN EFFICIENT LEAST-SQUARES FINITE ELEMENT METHOD FOR INCOMPRESSIBLE FLOWS AND TRANSPORT PROCESSES

Abstract

SUMMARY A numerical procedure based on a least-squares finite element method (LSFEM) and Jacobi conjugate gradient method (JCG) is presented for the numerical solution of fluid flow and transport problems. Unlike many finite element methods, the LSFEM does not involve any upwinding factor. Furthermore, the LSFEM leads to a symmetric and positive definite linear system of equations which can be solved satisfactorily by a preconditioned conjugate gradient method. Four examples, lid-driven cavity flow, thermally-driven cavity flow, Rayleigh-Benard convection and doubly-diffusive flow, are presented to validate the preconditioned conjugate gradient method. A comparison of the least-squares finite element method and theGalerkin finite clement method (GFEM) is also given. Finally, we demonstrate that the least-squares finite element method with the Jacobi conjugate gradient iterative technique is a promising approach to solve three-dimensional fluid flow and transport problems.