TY - JOUR

T1 - A Robust Multigrid Method for a Discretization of the Incompressible Navier-Stokes Equations in General Coordinates

AU - Oosterlee, C. W.

AU - Wesseling, P.

PY - 1993/6

Y1 - 1993/6

N2 - The stationary incompressible Navier-Stokes equations are discretized with a finite volume method in curvilinear coordinates. The arbitrarily shaped domain is mapped onto a rectangular block, resulting in a boundary-fitted grid. In order to obtain accurate discretizations of the transformed equations certain requirements on geometric quantities should be met. The choice of velocity components is of importance. Contravariant flux unknowns and the pressure are used as primary unknowns on a staggered grid. The system of discretized equations is solved with a nonlinear multigrid algorithm, in which a robust line smoother, called Symmetric Coupled Alternating Lines, is implemented. All unknowns on a line of cells are updated simultaneously with alternating zebra sweeping. The solution algorithm shows satisfying average reduction factors for arbitrary domains, even when highly stretched cells are present.

AB - The stationary incompressible Navier-Stokes equations are discretized with a finite volume method in curvilinear coordinates. The arbitrarily shaped domain is mapped onto a rectangular block, resulting in a boundary-fitted grid. In order to obtain accurate discretizations of the transformed equations certain requirements on geometric quantities should be met. The choice of velocity components is of importance. Contravariant flux unknowns and the pressure are used as primary unknowns on a staggered grid. The system of discretized equations is solved with a nonlinear multigrid algorithm, in which a robust line smoother, called Symmetric Coupled Alternating Lines, is implemented. All unknowns on a line of cells are updated simultaneously with alternating zebra sweeping. The solution algorithm shows satisfying average reduction factors for arbitrary domains, even when highly stretched cells are present.

UR - http://www.scopus.com/inward/record.url?scp=0005636588&partnerID=8YFLogxK

U2 - 10.1006/icse.1993.1006

DO - 10.1006/icse.1993.1006

M3 - Article

AN - SCOPUS:0005636588

SN - 0899-8248

VL - 5

SP - 128

EP - 151

JO - IMPACT of Computing in Science and Engineering

JF - IMPACT of Computing in Science and Engineering

IS - 2

ER -