A high order accurate difference scheme for complex flow fields.

*(English)*Zbl 0882.76054Summary: A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed. It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convective terms of the compressible Navier-Stokes equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage Runge-Kutta method is used to advance in time. In order to improve the shock resolution, the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76F10 | Shear flows and turbulence |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

##### Keywords:

coherent structure; mixing layers; wavepackets; method of group velocity control; shock resolution; fifth-order accurate upwind compact difference relation; Navier-Stokes equations; sixth-order accurate symmetric compact difference relation; Runge-Kutta method; method of diffusion analogy
PDF
BibTeX
XML
Cite

\textit{D. Fu} and \textit{Y. Ma}, J. Comput. Phys. 134, No. 1, 1--15 (1997; Zbl 0882.76054)

Full Text:
DOI

**OpenURL**

##### References:

[1] | S. K. Lele, 1989 |

[2] | Lee, S.; Lele, S.K.; Moin, P., Phys. fluids A, 3, (1991) |

[3] | Sandham, N.D.; Reynolds, W.C., J. fluid mech., 224, 133, (1991) |

[4] | Papamoschou, D.; Roshko, A., J. fluid mech., 197, 453, (1988) |

[5] | Bogdanoff, D.W., Aiaa j., 21, 926, (1983) |

[6] | Ragab, S.A.; Wu, J.L., Phys. fluids A, 1, 957, (1989) |

[7] | Sandham, N.D.; Reynolds, W.C., Aiaa j., 28, 618, (1990) |

[8] | Tam, C.K.W.; Hu, F.Q., J. fluid mech., 203, 51, (1986) |

[9] | D. Fu, Y. Ma, H. Liu, 1993, Proceedings, 5th International Symposium on CFD, Sendai, 1993, 1, 184 |

[10] | Lele, S.K., J. comput. phys., 103, 16, (1992) |

[11] | Chi-Wang, Shu; Osher, S., J. comput. phys., 77, 439, (1988) |

[12] | Ma, Y.; Fu, D., Sci. China ser. A, 35, 1090, (1992) |

[13] | J. L. Steger, R. F. Warming |

[14] | D. Papamoschou, A. Roshko, 1986 |

[15] | Michalke, A., J. fluid mech., 19, 543, (1964) |

[16] | Moser, R.D.; Rogers, M.M., J. fluid mech., 247, 265, (1993) |

[17] | L. Trefethen, SIAM Rev. 24, 136 |

[18] | A. Harten, 1986, Proceedings, International Conference on Hyperbolic Problems, Saint-Etieme, 1986 |

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.