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A semi-implicit numerical scheme for reacting flow. II: Stiff, operator-split formulation. (English) Zbl 0958.76061
From the summary: We construct a stiff operator-split projection scheme for simulation of unsteady two-dimensional reaction flows with detailed kinetics. The scheme is based on compressible conservation equations for an ideal gas mixture in the zero-Mach-number limit. The equations of motion are spatially discretized by using second-order centered differences, and are advanced in time using a new stiff predictor-corrector approach. The new scheme is a modified version of the additive stiff scheme introduced in part I [the authors, ibid. 143, No. 2, 381-402, Art. No. CP975856 (1998; Zbl 0936.76064)].
The performance and behavior of the operator-split scheme are first analyzed based on tests for a nonlinear reaction-diffusion equation in one space dimension, followed by computations with a detailed $$C_1C_2$$ methane-air mechanism in one and two dimensions. The tests are used to verify that the scheme is effectively second order in time, and to suggest guidelines for selecting integration parameters, including the number of fractional diffusion steps and tolerance levels in the stiff integration. For two-dimensional simulations with the present reaction mechanism, flame conditions, and resolution parameters, speedup factors of about 5 are achieved over the previous additive scheme, and about 25 over the original explicit scheme.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76M22 Spectral methods applied to problems in fluid mechanics 76V05 Reaction effects in flows 92E20 Classical flows, reactions, etc. in chemistry 80A32 Chemically reacting flows
##### Software:
CHEMKIN; CHEMSODE; GEAR; ODEPACK; PREMIX; RODAS; VODE
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