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An adaptive numerical scheme for high-speed reactive flow on overlapping grids. (English) Zbl 1134.76427

Summary: We describe a method for the numerical solution of a high-speed reactive flow in complex geometries using overlapping grids and block-structured adaptive mesh refinement. We consider flows described by the reactive Euler equations with an ideal equation of state and various stiff reaction models. These equations are solved using a second-order accurate Godunov method for the convective fluxes and a Runge-Kutta time-stepping scheme for the source term modeling the chemical reactions. We describe an extension of the adaptive mesh refinement approach to curvilinear overlapping grids. Numerical results are presented showing the evolution to detonation in a quarter-plane provoked by a temperature gradient and the propagation of an overdriven detonation in an expanding channel. The first problem, which considers a one-step Arrhenius reaction model, is used primarily to validate the numerical method, while the second problem, which considers a three-step chain-branching reaction model, is used to illustrate mechanisms of detonation failure and rebirth for the channel geometry.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
80A32 Chemically reacting flows
80M25 Other numerical methods (thermodynamics) (MSC2010)
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76V05 Reaction effects in flows
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