Parallel Adaptive Mesh Refinement Scheme for Three-Dimensional Turbulent Non-Premixed Combustion

A parallel adaptive mesh refinement (AMR) algorithm is described for predicting turbulent non-premixed gaseous combusting flows in three space dimensions. The Favreaveraged Navier-Stokes equations governing a reactive mixture of thermally perfect gases, the two transport equations of the k-ω turbulence model, and the time-averaged species transport equations, are all solved using a fully coupled finite-volume formulation on bodyfitted multi-block hexahedral mesh. The numerical algorithm adopts a cell-centred upwind finite-volume discretization procedure and uses limited solution reconstruction, approximate Riemann solver based flux functions to determine the inviscid (hyperbolic) flux at cell interfaces. The viscous (elliptic) components of the cell face flux are evaluated by employing a hybrid average gradient-diamond path approach. For the treatment of near-wall turbulence, both low-Reynolds-number and wall-function formulations of the k-ω model are used, with a procedure for automatically switching from one to the other, depending on mesh resolution. A flexible block-based hierarchical octree data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. This AMR approach allows for anisotropic mesh refinement and the block-based data structure readily permits efficient and scalable implementations of the algorithm on multi-processor architectures. Numerical results for turbulent non-premixed methane-air diffusion flames are described to demonstrate the validity and potential of the parallel AMR approach for predicting complex combusting flows.