AN IMPLICIT MULTIGRID SCHEME FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH LOW-REYNOLDS-NUMBER TURBULENCE CLOSURE

A multigrid method for convergence acceleration is used for solving co upled fluid and turbulence transport equations. For turbulence closure a low-Reynolds-number q-w turbulence model is employed, which require s very fine grids in the near wall regions. Due to the use of fine gri ds, convergence of most iterative solvers slows down, making the use o f multigrid techniques especially attractive. However, special care ha s to be taken on the strong nonlinear turbulent source terms during re striction from fine to coarse grids. Due to the hyperbolic character o f the governing equations in supersonic flows and the occurrence of sh ock waves, modifications to standard multigrid techniques are necessar y. A simple and effective method is presented that enables the multigr id scheme to converge. A strong reduction in the required number of mu ltigrid cycles and work units is achieved for different test cases, in cluding a Mach 2 flow over a backward facing step.