Textbook-efficiency multigrid solver for three-dimensional unsteady compressible Navier-Stokes equations

  • Authors:

  • Wei Liao;Boris Diskin;Yan Peng;Li-Shi Luo

  • Affiliations:

  • Department of Mathematics and Statistics, Center for Computational Sciences, Old Dominion University, Norfolk, VA 23529, USA;National Institute of Aerospace, Hampton, VA 23666, USA and Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746, USA;Department of Mathematics and Statistics, Center for Computational Sciences, Old Dominion University, Norfolk, VA 23529, USA;Department of Mathematics and Statistics, Center for Computational Sciences, Old Dominion University, Norfolk, VA 23529, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

Quantified Score

Hi-index 31.45

Visualization

Abstract

Implicit time-integration techniques are envisioned to be the methods of choice for direct numerical simulations (DNS) for flows at high Reynolds numbers. Therefore, the computational efficiency of implicit flow solvers becomes critically important. The textbook multigrid efficiency (TME), which is the optimal efficiency of a multigrid method, is achieved if accurate solutions of the governing equations are obtained with the total computational work that is a small (less than 10) multiple of the operation count in one residual evaluation. In this paper, we present a TME solver for unsteady subsonic compressible Navier-Stokes equations in three dimensions discretized with an implicit, second-order accurate in both space and time, unconditionally stable, and non-conservative scheme. A semi-Lagrangian approach is used to discretize the time-dependent convection part of the equations; viscous terms and the pressure gradient are discretized on a staggered grid. The TME solver for the implicit equations is applied at each time level. The computational efficiency of the solver is designed to be independent of the Reynolds number. Our tests show that the proposed solver maintains its optimal efficiency at high Reynolds numbers and for large time steps.