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**Generation of viscous grids at ridges and corners.**
*(English)*
Zbl 1156.76432

Summary: An extension of R. Löhner [Matching semi-structured and unstructured grids for Navier-Stokes calculations. AIAA-93-3348-CP (1993)] for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for Reynolds-averaged Navier-Stokes computations. Multiple point normals are introduced along ridges and corners. The original technique generates a semi-structured boundary layer of prismatic elements growing along point normals. Therefore, extra degenerated faces must be introduced to take into account the multiple growth curves at ridges and corners and produce a valid topological surface triangulation. The major task of the algorithm consists in recovering conformity in the surface mesh triangulation, which has been lost due to the introduction of the virtual faces. The procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges. Each case is highlighted in detail. Special boundary conditions such as symmetry planes and periodic boundary conditions are also handled. Several complex geometries have been chosen to illustrate the proposed procedure, and timings are given, showing that the new module does not place any extra burden on the previous semi-structured approach.

### Keywords:

unstructured grid generation; anisotropic grid; multiple point normal; corner; ridges; RANS
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\textit{R. Aubry} and \textit{R. Löhner}, Int. J. Numer. Methods Eng. 77, No. 9, 1247--1289 (2009; Zbl 1156.76432)

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### References:

[1] | Sagaut, Large-Eddy Simulation for Incompressible Flows-An Introduction (2001) · Zbl 0964.76002 |

[2] | Löhner R. Matching semi-structured and unstructured grids for Navier-Stokes calculations. AIAA-93-3348-CP, 1993. |

[3] | Pirzadeh S. Viscous unstructured three dimensional grids by the advancing-layers method. AIAA Paper 94-0417, 1994. · Zbl 0900.76487 |

[4] | Löhner, Generation of non-isotropic unstructured grids via directional enrichment, International Journal for Numerical Methods in Engineering 49 pp 219– (2000) · Zbl 0970.76058 |

[5] | Hassan, Unstructured tetrahedral mesh generation for three-dimensional viscous flows, International Journal for Numerical Methods in Engineering 39 pp 549– (1996) · Zbl 0844.76051 |

[6] | Connell, Semistructured mesh generation for three dimensional Navier-Stokes calculations, AIAA Journal 33 (6) pp 1017– (1995) · Zbl 0846.76079 |

[7] | Marcum DL. Generation of unstructured grids for viscous flow applications. AIAA-95-0212, 1995. |

[8] | Peraire, Unstructured mesh generation including directional refinement for aerodynamic flow simulation, Finite Elements in Analysis and Design 25 (3-4) pp 343– (1997) · Zbl 0914.76069 |

[9] | Garimella, Boundary layer mesh generation for viscous flow simulations, International Journal for Numerical Methods in Engineering 49 pp 193– (2000) · Zbl 0960.76074 |

[10] | Kallinderis Y, Ward Y. Prismatic grid generation with an efficient algebraic method for aircraft configurations. AIAA-92-2721, 1992. |

[11] | Athanasiadis, A folding/unfolding algorithm for the construction of semi-structured layers in hybrid grid generation, Computer Methods in Applied Mechanics and Engineering 194 pp 5051– (2004) · Zbl 1094.76050 |

[12] | Bottasso, A procedure for tetrahedral boundary layer mesh generation, Engineering Computations 18 pp 66– (2002) · Zbl 1021.68568 |

[13] | Ito Y, Nakahashi K. Unstructured mesh generation for viscous flow computations. Proceedings of the 11th International Meshing Roundtable, Ithaca, NY, 2002; 367-377. |

[14] | Ito Y, Nakahashi K. An approach to generate high quality unstructured hybrid meshes. AIAA-2006-0530, 2006. |

[15] | Sharov, Unstructured Navier-Stokes grid generation at corners and ridges, International Journal for Numerical Methods in Fluids 43 (6-7) pp 717– (2003) · Zbl 1032.76601 |

[16] | Aubry, On the ’most normal’ normal, Communications in Numerical Methods in Engineering (2007) · Zbl 1157.65328 |

[17] | Löhner, Applied CFD Techniques (2001) |

[18] | Löhner, Regridding surface triangulations, Journal of Computational Physics 126 pp 1– (1996) · Zbl 0862.65010 |

[19] | Borouchaki, Surface mesh enhancement with geometric singularities identification, Computer Methods in Applied Mechanics and Engineering 194 pp 4884– (2005) · Zbl 1093.65010 |

[20] | Ito, Direct surface triangulation using stereolithography data, AIAA Journal 40 (3) pp 490– (2002) |

[21] | Kellogg J. The NRL MITE air vehicle. 2001. |

[22] | Boender, Reliable Delaunay-based mesh generation and mesh improvement, Communications in Numerical Methods in Engineering 10 pp 773– (1994) · Zbl 0812.65104 |

[23] | Frey PJ. About surface remeshing. Proceedings of the 9th International Meshing Roundtable, Sandia National Laboratories, New Orleans, Louisiana, U.S.A., 2000; 123-136. |

[24] | Frey, Maillages, Applications aux Elements Finis (1999) |

[25] | George, Quality mesh generation, Comptes Rendus de l’Académie des Sciences Paris 328 pp 505– (2000) · Zbl 1007.76038 |

[26] | Löhner R. A fast finite element solver for incompressible flows. AIAA-90-0398, 1990. |

[27] | Martin D, Löhner R. An implicit linelet-based solver for incompressible flows. AIAA-92-0668, 1992. |

[28] | Ramamurti, A parallel implicit incompressible flow solver using unstructured meshes, Computers and Fluids 5 pp 119– (1996) · Zbl 0866.76046 |

[29] | Löhner, An unstructured grid-based, parallel free surface solver, Applied Numerical Mathematics 31 pp 271– (1999) · Zbl 0951.76040 |

[30] | Jeong, On the identification of a vortex, Journal of Fluid Mechanics 285 pp 69– (1995) · Zbl 0847.76007 |

[31] | Choi, The application of preconditioning in viscous flows, Journal of Computational Physics 105 pp 207– (1993) · Zbl 0768.76032 |

[32] | Turkel, Preconditioning techniques in computational fluid dynamics, Annual Review of Fluid Mechanics 31 pp 385– (1999) |

[33] | van Leer B, Lee WT, Roe P. Characteristic time-stepping or local preconditioning of the Euler equations. AIAA-91-1552, 1991. |

[34] | Löhner, Renumbering strategies for unstructured-grid solvers operating on shared-memory, cache-based parallel machines, Computer Methods in Applied Mechanics and Engineering 163 pp 95– (1998) · Zbl 0960.76075 |

[35] | Löhner, A parallel advancing front grid generation scheme, International Journal for Numerical Methods in Engineering 51 pp 663– (2001) · Zbl 1012.76077 |

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