##
**Coupled solution of the species conservation equations using unstructured finite-volume method.**
*(English)*
Zbl 1277.76053

Summary: A coupled solver was developed to solve the species conservation equations on an unstructured mesh with implicit spatial as well as species-to-species coupling. First, the computational domain was decomposed into sub-domains comprised of geometrically contiguous cells – a process similar to additive Schwarz decomposition. This was done using the binary spatial partitioning algorithm. Following this step, for each sub-domain, the discretized equations were developed using the finite-volume method, and solved using an iterative solver based on Krylov sub-space iterations, that is, the pre-conditioned generalized minimum residual solver. Overall (outer) iterations were then performed to treat explicitness at sub-domain interfaces and nonlinearities in the governing equations. The solver is demonstrated for both two-dimensional and three-dimensional geometries for laminar methane – air flame calculations with 6 species and 2 reaction steps, and for catalytic methane – air combustion with 19 species and 24 reaction steps. It was found that the best performance is manifested for sub-domain size of 2000 cells or more, the exact number depending on the problem at hand. The overall gain in computational efficiency was found to be a factor of 2-5 over the block (coupled) Gauss-Seidel procedure. All calculations were performed on a single processor machine. The largest calculations were performed for about 355 000 cells (4.6 million unknowns) and required 900MB of peak runtime memory and 19h of CPU on a single processor.

### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

76V05 | Reaction effects in flows |