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

摘要

A multigrid method for convergence acceleration is used for solving both fluid and turbulence transport equations. Due to the hyperbolic character of the governing equations in supersonic flows and the occurence of shock waves, modifications to standard multigrid techniques are necessary. For turbulence closure a low-Reynolds-number q-ω turbulence model is employed which requires very fine grids in the near wall regions. Due to the fine grids convergence of most iterative solvers slows down, making the use of multi-grid techniques especially attractive. However, special care has to be taken on the strong non-linear turbulent source terms during restriction from fine to coarse grids. A simple and effective method is presented which enables the multi-grid scheme to converge. A strong reduction in the required number of multigrid cycles and work units is achieved for different test cases, including a Mach 2 flow over a backward facing step.