High accuracy numerical methods for thermally perfect gas flows with chemistry.

*(English)*Zbl 0888.76053The 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.

##### MSC:

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 |

##### Keywords:

Navier-Stokes equations; large system of convection-diffusion equations; stiff source terms; ENO space discretization; third-order TVD Runge-Kutta time discretization; second-order accurate Strang time splitting; shock tube; combustor##### Software:

CHEMKIN
PDF
BibTeX
Cite

\textit{R. P. Fedkiw} et al., J. Comput. Phys. 132, No. 2, 175--190 (1997; Zbl 0888.76053)

Full Text:
DOI

##### References:

[1] | Anderson, J.D., Hypersonic and high temperature gas dynamics, (1989), McGraw-Hill New York |

[2] | Anderson, J.D., Modern compressible flow, (1990), McGraw-Hill New York |

[3] | Atkinson, K.E., An introduction to numerical analysis, (1989), Wiley New York · Zbl 0718.65001 |

[4] | W. Don, C. Quillen, 1994, Numerical simulation of shock-cylinder interactions. Part I. Resolution · Zbl 0840.76067 |

[5] | B. Engquist, B. Sjogren, March 1989, Numerical approximation to hyperbolic conservation laws with stiff terms |

[6] | B. Engquist, B. Sjogren, March 1991, Robust difference approximations to stiff inviscid detonation waves |

[7] | R. P. Fedkiw, 1996, A Survey of Chemically Reacting, Compressible Flows, UCLA |

[8] | R. Fedkiw, B. Merriman, S. Osher, January 1996, Numerical methods for a mixture of thermally perfect and/or calorically perfect gaseous species with chemical reactions |

[9] | E. Katzer, S. Osher, May 1988, Efficient implementation of essentially non-oscillatory schemes for systems of nonlinear hyperbolic differential equations |

[10] | M. Kee, Jefferson, March 1986, CHEMKIN: A general purpose problem independent, transportable Fortran chemical kinetics code package, SAND 80-8003, Sandia National Laboratories |

[11] | Oran, E.S.; Boris, J.P., Numerical simulation of reactive flow, (1987), Elsevier Amsterdam/New York · Zbl 0762.76098 |

[12] | Shu, C.W.; Osher, S., Efficient implementation of essentially non-oscillatory shock capturing schemes, J. comput. phys., 83, 32-78, (1989) · Zbl 0674.65061 |

[13] | Stall, D.R.; Prophet, H., JANAF thermochemical tables, National standard reference data series, (1971) |

[14] | Strikwerda, J.C., Finite difference schemes and partial differential equations, (1989), Wadsworth Belmont · Zbl 0681.65064 |

[15] | V. Ton, 1993, A Numerical Method for Mixing/Chemically Reacting Compressible Flow with Finite Rate Chemistry, UCLA |

[16] | V. Ton, A. Karagozian, B. Engquist, S. Osher, October 1991, Numerical simulation of inviscid detonation waves |

[17] | Theor. comput. fluid dyn., 6, 161-179, (1994) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.