Symmetry techniques for the numerical solution of the 2D Euler equations at impermeable boundaries.

*(English)*Zbl 0918.76055Summary: We consider the implementation of boundary conditions at rigid, fixed wall boundaries in inviscid Euler solutions by upwind, finite volume methods. Some current methods are reviewed. Two new boundary condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique, are then presented. Their behaviour in relation to the problem of the subsonic flow about blunt and slender elliptic bodies is analyzed, and the subsonic flow inside the Stanitz elbow is computed. The symmetry technique is proven to be as accurate as one of the current methods, second-order pressure extrapolation technique. Finally, for arbitrary curved geometries, we show dramatic advantages of the curvature-corrected symmetry technique over other methods.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

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

76G25 | General aerodynamics and subsonic flows |

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

##### Keywords:

blunt bodies; curvature-corrected symmetry technique; slender elliptic bodies; Stanitz elbow; second-order pressure extrapolation technique
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\textit{A. Dadone}, Int. J. Numer. Methods Fluids 28, No. 7, 1093--1108 (1998; Zbl 0918.76055)

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##### References:

[1] | Moretti, High Speed Comput. Fluid Dyn., Phys. Fluids, Supplement II pp 13– (1969) |

[2] | Moretti, AIAA J. 4 pp 2136– (1966) |

[3] | Moretti, Comput. Fluids 7 pp 191– (1979) |

[4] | Dadone, AIAA J. 26 pp 409– (1988) |

[5] | Chakravarthy, AIAA J. 21 pp 699– (1983) |

[6] | Marcum, AIAA J. 25 pp 1054– (1987) |

[7] | Rizzi, Z. A. M. M. 58 pp t301– (1978) · doi:10.1002/zamm.19780580508 |

[8] | and , ’Advances in upwind relaxation methods’, in (ed.), State-of-the-Art Surveys of Computational Mechanics, Ch. 4, ASME publication, 1988. |

[9] | Dadone, AIAA J. 30 pp 2219– (1992) |

[10] | Dadone, Proc. 4th Int. Symp. Comp. Fluid Dyn., Davis, CA 1 pp 258– (1991) |

[11] | Dadone, Notes Numer. Fluid Dyn. 43 pp 171– (1993) |

[12] | and , ’Surface boundary conditions for the numerical solution of the Euler equations’, AIAA Paper 93-3334-CP (1993). |

[13] | AIAA J. 32 pp 285– (1994) |

[14] | Roe, Annu. Rev. Fluid Mech. 18 pp 337– (1986) |

[15] | ’Design of 2-D channels with prescribed velocity distributions along the channel walls, I–Relaxation Solutions’, NACA TN 2593 (1952). |

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.