In this talk we describe a robust iterative linear system solution methodology used for parallel unstructured finite element simulation of strongly coupled fluid flow, heat and mass transfer with non-equilibrium chemical reactions. The linear system solvers are based on preconditioned Krylov subspace methods. Our discussion considers computational efficiency, robustness and some implementation issues related to the proposed preconditioned Krylov solution schemes. The evaluated preconditioners include: i) simple point and block iterative methods, ii) overlapping Schwarz domain decomposition methods with subdomain solvers based on incomplete factorizations, iii) some initial multilevel preconditioners. For this comparison we use a particular spatial discretization of the governing transport-reaction PDEs based on a Galerkin Least Squares (GLS) finite element formulation. Our parallel solution implementation employs automated partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations, an inexact Newton method and parallel Krylov subspace iterative solvers. We present results for a number of standard 2D CFD benchmark problems and some large 3D reacting flow application problems.
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