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High accuracy numerical methods for thermally perfect gas flows with chemistry. (English) Zbl 0888.76053
The compressible Navier-Stokes equations can be extended to model multi-species, chemically reacting gas flows. The result is a large system of convection-diffusion equations with stiff source terms. In this paper, we develop the framework needed to apply modern high accuracy numerical methods from computational gas dynamics to this extended system. We implement these developments with a particular high accuracy characteristic-based method, the finite difference ENO space discretization with the third-order TVD Runge-Kutta time discretization, combined with the second-order accurate Strang time splitting of the reaction terms. We illustrate the capabilities of this approach with calculations of a one-dimensional reacting shock tube and a two-dimensional combustor.

76M20 Finite difference methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
92E20 Classical flows, reactions, etc. in chemistry
80A32 Chemically reacting flows
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