Miniati, Francesco; Colella, Phillip A modified higher-order Godunov’s scheme for stiff source conservative hydrodynamics. (English) Zbl 1117.76039 J. Comput. Phys. 224, No. 2, 519-538 (2007). Summary: We present an efficient second-order accurate scheme to treat stiff source terms within the framework of higher-order Godunov methods. We employ Duhamel formula to devise a modified predictor step which accounts for the effects of stiff source terms on the conservative fluxes and recovers the correct isothermal behavior in the limit of an infinite cooling/reaction rate. Source term effects on the conservative quantities are fully accounted for by means of a one-step, second-order accurate semi-implicit corrector scheme based on the deferred correction method of A. Dutt et al. [BIT 40, No. 2, 241–266 (2000; Zbl 0959.65084)]. We demonstrate the accurate, stable and convergent results of the proposed method through a set of benchmark problems for a variety of stiffness conditions and source types. Cited in 2 ReviewsCited in 10 Documents MSC: 76M12 Finite volume methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory) Keywords:Duhamel formula; semi-implicit corrector scheme; deferred correction method Citations:Zbl 0959.65084 PDFBibTeX XMLCite \textit{F. Miniati} and \textit{P. Colella}, J. Comput. Phys. 224, No. 2, 519--538 (2007; Zbl 1117.76039) Full Text: DOI arXiv References: [1] Berger, M. J.; Colella, P., Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys., 82, 64-84 (1989) · Zbl 0665.76070 [2] Caflisch, R. E.; Jin, S.; Russo, G., Uniformly accurate schemes for hyperbolic systems with relaxation, SIAM J. Sci. Comput., 34, 1, 246-281 (1997) · Zbl 0868.35070 [3] Chen, G. 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