A Multigrid Algorithm for Hybrid Joint PDF Simulations in Complex Geometries

In hybrid joint probability density function (joint PDF) algorithms for turbulent reactive flows the equations for the mean flow discretized with a classical grid based method (e.g. finite volume methods (FVM)) are solved together with a Monte Carlo (particle) method for the joint velocity composition PDF. When applied for complex geometries, the solution strategy for such methods which aims at obtaining a converged solution of the coupled problem on a sufficiently fine grid becomes very important. This paper describes one important aspect of this solution strategy, i.e. multigrid computing, which is well known to be very efficient for computing numerical solutions on fine grids. Two sets of grid based variables are involved: cell-centered variables from the FVM and node-centered variables, which denote the moments of the PDF extracted from the particle fields. Starting from a given multiblock grid environment first a new (refined or coarsened) grid is defined retaining the grid quality. The projection and prolongation operators are defined for the two sets of variables. In this new grid environment the particles are redistributed. The effectiveness of the multigrid algorithm is demonstrated. Compared to solely solving on the finest grid, convergence can be reached about one order of magnitude faster when using the multigrid algorithm in three stages. Computation time used for projection or prolongation is negligible. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)