Textbook Multigrid Efficiency for the Incompressible Navier-Stokes Equations: High Reynolds Number Wakes and Boundary Layers

James L. Thomas
Computational Modeling and Simulation Branch
Mail Stop 128
NASA Langley Research Center
Hampton, Virginia 23681

Boris Diskin
Institute for Computer Applications in Science and Engineering
Mail Stop 132C
NASA Langley Research Center
Hampton, Virginia 23681

Achi Brandt
The Weizmann Institute of Science
Rehovot 76100, Israel


Abstract

Textbook multigrid efficiencies for high Reynolds number simulations based on the incompressible Navier-Stokes equations are atained for a model problem of flow past a finiter rate 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 discetization errors in one full multigrid cycle, are attained for second order accurate simulations at a laminar Reynods number of 10,000.

Keywords. incompressible Navier-Stokes equations, textbook multigrid efficiency, distributiverelaxation, defect-correction iteration

Subject classification. Applied and Numerical Mathematics