An Evaluation of Multigrid Methods for the Simulation of Turbulent Combustion

Abstract

Turbulent combustion simulations based on finite-rate chemistry require tremendous CPU times if the number of species is large. The computational eort is further increased by the requirement to account for turbulence chemistry interaction. This paper investigates multigrid methods for convergence acceleration in case of turbulent combustion, where standard multigrid methods usually fail or do not achieve significant accelerations. Reasons for these failures are analyzed using a simple one dimensional model equation. It will be shown that the local, spatially limited appearance of non-linear source terms and changes in the damping properties of the solver are responsible for bad coarse grid corrections. A filtering of the restricted residual is introduced to identify regions where the fine grid residual distribution is not smooth enough to be represented accurately on a coarser grid. In these regions the coarse grid residuals are adapted in order to achieve a better fine grid representation or, if this is impossible, are reduced to zero. The new approach stabilizes multigrid combustion simulations. Beside a simple scalar convection-diusion equation with source term supersonic hydrogen and methane flames are investigated. It will be shown that the proposed multigrid method is able to achieve a strong reduction in required CPU time in comparison to one grid solutions.