Multigrid for hypersonic viscous two- and three-dimensional flows (original) (raw)

Progress with multigrid schemes for hypersonic flow problems

Journal of Computational Physics, 1995

JOURNAL OF COMPUTATIONAL PHYSICS 1X6, 103-122 (1995) Progress with Multigrid Schemes for Hypersonic Flow Problems R. Radespiel DLR, Braunschweig, Germany AND R, C. SWANSON NASA Langley Research Center, Hampton, Virginia 23681 Received March 2, Î992; ...

Author ' s personal copy Textbook-efficiency multigrid solver for three-dimensional unsteady compressible Navier – Stokes equations

2008

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 imp...