## Abstract

We numerically integrate the compressible Navier-Stokes equations by means of finite-volume technique on the domain exterior to an airfoil. The curvilinear grid we use for discretization of the Navier-Stokes equations is obviously finite, it covers only a certain bounded region around the airfoil, consequently we need to set some artificial boundary conditions (ABCs) at the external boundary of this region. The ABCs we use here are nonlocal in space. They are constructed specifically for the case of a steady-state solution. In constructing the ABCs, we linearize the Navier-Stokes equations around the far-field solution and apply the Difference Potentials Method (DPM). The resulting global conditions are implemented together with a pseudo-time multigrid iteration procedure for achieving the steady state. The main goal of this paper is to describe the numerical procedure itself, therefore we primarily emphasize below the computation of ABCs and the combined usage of these ABCs and the original algorithm for integrating the Navier-Stokes equations. The underlying theory which justifies the proposed numerical techniques will accordingly be addressed more briefly. We also present some results of computational experiments which show that for the different flow regimes (subcritical and supercritical, laminar and turbulent) as well as for the different geometries (i.e., different airfoils) the global ABCs appear to be essentially more robust, i.e., they may provide far better convergence properties and much weaker dependence of the solution on the size of computational domain than standard external boundary conditions which are usually based on extrapolation of physical and/or characteristic variables.

Original language | English |
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State | Published - 1995 |

Externally published | Yes |

Event | 33rd Aerospace Sciences Meeting and Exhibit, 1995 - Reno, United States Duration: 9 Jan 1995 → 12 Jan 1995 |

### Conference

Conference | 33rd Aerospace Sciences Meeting and Exhibit, 1995 |
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Country/Territory | United States |

City | Reno |

Period | 9/01/95 → 12/01/95 |

### Bibliographical note

Publisher Copyright:© 1995 by Yongseung Cho. Published by the American Institule of Aeronautics and Astronautics, Inc.