Parallel Implicit Adaptive Mesh Refinement Scheme for Unsteady Fully-Compressible Reactive Flows

摘要

An accurate and robust parallel implicit adaptive mesh refinement (AMR) algorithm is proposed and described for the prediction of unsteady behaviour of laminar flames. The scheme is applied to the solution of the system of the partial-differential equations governing time-dependent, three-dimensional, compressible laminar flows for reactive thermally perfect gaseous mixtures. A high-resolution finite-volume spatial discretization procedure is used to solve the conservation form of these equations on body-fitted multi-block hexa-hedral mesh. A local preconditioning technique is used to remove numerical stiffness and maintain solution accuracy for low-Mach-number, nearly incompressible flows. A flexible block-based octree data structure has been developed and is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. The data structure also enables an efficient and scalable parallel implementation via domain decomposition. The parallel implicit formulation makes use of a dual-time-stepping like approach with an implicit second-order backward discretization of the physical time, in which a Jacobian-free inexact Newton method with a preconditioned generalized minimal residual (GMRES) algorithm is used to solve the system of nonlinear algebraic equations arising from the temporal and spatial discretization procedures. An additive Schwarz global pre-conditioner is used in conjunction with block incomplete LU type local preconditioners for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. Numerical results for steady and unsteady laminar co-flow diffusion and premixed methane-air flames demonstrate the capabilities of the proposed approach for a range of reactive-flow applications. The scheme is shown to accurately predict key characteristics of the diffusion flames. For a premixed flame under terrestrially gravity, the scheme is also shown to accurately predict the frequency of the natural buoyancy induced oscillations.