Multigrid-Based Grid-Adaptive Solution of the Navier-Stokes Equations

A finite volume scheme for solution of the incompressible Navier-Stokes equations in 2D and axisymmetry is described. Solutions are obtained on non-orthogonal, solution adaptive BFC grids, based on the Brackbill-Saltzman generator. Adaptivity is achieved by the use of a single control function based on the local kinetic energy production. Non-staggered allocation of pressure and Cartesian velocity components avoids the introduction of curvature terms associated with the use of a grid-direction vector-base. A special interpolation of the pressure correction equation in the SIMPLE algorithm ensures firm coupling between velocity and pressure field. Steady-state solutions are accellerated by a full approximation (FAS) multigrid scheme working on the decoupled grid-flow problem, while an algebraic multigrid scheme is employed for the pressure correction equation.