Many reacting flow applications mandate coupled solution of the species conservation equations. A low-memory coupled solver was developed to solve the species transport equations on an unstructured mesh. The first step was the decomposition of the domain into sub-domains comprised of geometrically contiguous cells—a process termed internal domain decomposition (IDD). This was done using the binary spatial partitioning (BSP) algorithm. Following this step, for each subdomain, the discretized equations were set up, written in block implicit form, and solved using two different solvers: a direct solver using Gaussian elimination and an iterative solver based on Krylov sub-space iterations, i.e., the Generalized Minimum Residual (GMRES) solver. Overall (outer) iterations were then performed to treat explicitness at sub-domain boundaries and non-linearities in the governing equations. The solver is demonstrated for a simple two-dimensional multi-component diffusion problem involving 5 species. Sample calculations show that the solver with direct solution for each block is most efficient if the number of cells in each block is small—typically tens of cells, while the solver with iterative solution for each block is most efficient if the number of cells is relatively large—typically hundreds of cells. Overall the iterative solution based solver performed best, with maximum efficiency gain of a factor of seven over a block Gauss-Seidel (GS) solver and was found to be comparable or better in efficiency than a block-implicit Alternating Direction Implicit (ADI) solver. The gain in efficiency was found to increase with increase in cell aspect ratios.

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