Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations

In this paper, we describe an iterative linear system solution methodology used for parallel unstructured finite element simulation of strongly coupled fluid flow, heat transfer, and mass transfer with nonequilibrium chemical reactions. The nonlinear/linear iterative solution strategies are based on a fully coupled Newton solver with preconditioned Krylov subspace methods as the underlying linear iteration. Our discussion considers computational efficiency, robustness and a number of practical implementation issues. The evaluated preconditioners are based on additive Schwarz domain decomposition methods which are applicable for totally unstructured meshes. A number of different aspects of Schwarz schemes are considered including subdomain solves, use of overlap and the introduction of a coarse grid solve (a two-level scheme). As we will show, the proper choice among domain decomposition options is often critical to the efficiency of the overall solution scheme. For this comparison we use a particular spatial discretization of the governing transport/reaction partial differential equations (PDEs) based on a stabilized finite element formulation. Results are presented for a number of standard 2D and 3D computational fluid dynamics (CFD) benchmark problems and some large 3D flow, transport and reacting flow application problems.