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Modeling low Mach number reacting flow with detailed chemistry and transport. (English) Zbl 1203.80025
Summary: An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method. The resulting construction is second-order convergent, and has superior efficiency due to the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. We demonstrate the construction in 1D and 2D flames, and examine consequences of splitting errors. By including the above enhancements, performance tests using 2D computations with a detailed \(C_{1}C_{2}\) methane-air mechanism and a mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the starting split-stiff scheme.

MSC:
80M25 Other numerical methods (thermodynamics) (MSC2010)
80A32 Chemically reacting flows
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N15 Gas dynamics, general
76V05 Reaction effects in flows
Software:
RKC; VODE
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