BOUNDARY LAYERS

Abstract. Textbook multigrid efficiencies for high Reynolds number simulations based on the incom-pressible Navier-Stokes equations are attained for a model problem of flow past a finite flat plate. Elements of the Full Approximation Scheme multigrid algorithm, including distributed relaxation, defect correction, and boundary treatment, are presented for the three main physical aspects encountered: entering flow, wake flow, and boundary layer flow. Textbook efficiencies, i.e., reduction of algebraic errors below discretization errors in one full multigrid cycle, are attained for second order accurate simulations at a laminar Reynolds number of 10,000. Key words, incompressible Navier-Stokes equations, textbook multigrid efficiency, distributive relax-ation, defect-correction iteration Subject classification. Applied and Numerical Mathematics 1. Introduction. In the mid-70's, Beam and Warming [1] presented an implicit scheme for the com-pressible Navier-Stokes equations which had a significant impact on the field known as Computational Fluid Dynamics (CFD). The method they presented, based upon a spatial factoring of the implicit equations in delta form, used alternating tridiagonal line relaxations to solve high Reynolds number viscous simulations. This method proved to be much more efficient than other approaches. The basic methodology is still widel