A multigrid method for an invariant formulation of the incompressible navier—stokes equations in general Co‐ordinates

Abstract

AbstractThe stationary incompressible Navier—Stokes equations are discretized with a finite volume method in curvilinear co‐ordinates. 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, some requirements on geometric quantities should be met. The choice of velocity components is also of importance. Contravariant flux unknowns and pressure p are used as primary unknowns on a staggered grid arrangement.The system of discretized equations is solved with a non‐linear multigrid algorithm, into which a smoother, called Symmetric Coupled Gauss—Seidel, is implemented. Cell by cell, all unknowns in the grid cell are updated by solving four momentum equations and a continuity equation simultaneously. The solution algorithm shows satisfying average reduction factors for several domains.