Compressible turbulent flow simulation with a multigrid multiblock method

Hans Kuerten and Bernard Geurts

Department of Applied Mathematics, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands


An important field of interest for the aeronautical industry is the simulation of compressible turbulent flow around complex geometries such as the multi-element aerofoil. For these applications a multiblock method has the advantages of a flexible use of different physical models in different blocks and ease of implementation of the turbulence model. We developed a multiblock solver, based on a finite volume method with central differencing for the spatial discretization including nonlinear artificial dissipation and a time-explicit multistage Runge-Kutta method for integration towards the steady-state solution.

In view of computational efficiency the use of a multigrid method and implicit residual averaging is indispensable. In a multigrid multiblock multistage method there are various possibilities of intertwining these different loops. From the viewpoint of parallel processing the amount of data transfer between the blocks should be kept to a minimum. It was found, however, that the convergence rate becomes unacceptable even if the block loop is situated outside the stage loop, yielding an inaccurate steady-state solution. With the block loop inside the stage loop an efficient simulation method is obtained, with a total speed-up of at least a factor of 20, compared to a single grid calculation. The resulting steady-state solution corresponds well with wind-tunnel measurements for turbulent flow around the NLR7301 profile plus flap.