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**High order finite volume scheme and conservative grid overlapping technique for complex industrial applications.**
*(English)*
Zbl 1365.76168

Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 295-303 (2017).

Summary: The numerical foundation of the CFD solver FLUSEPA (French trademark N. 13400926) is presented. It is a Godunov’s type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around 3D complex geometries and general non-Cartesian grids. First, a family of \(k\)-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along curved cell faces. Then, a re-centering process is used to reduce as far as possible numerical diffusion. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors (cells which have common faces) of the mesh cells. To address complex geometries, a conservative grid intersection technique is used. Compressible numerical test cases are investigated to demonstrate the accuracy and the robustness of the presented numerical scheme, then, supersonic RANS/LES computations around the Ariane 5 space launcher are presented to shows the capability of the scheme to predict flows with shocks, vortical structures and complex geometries.

For the entire collection see [Zbl 1371.65001].

For the entire collection see [Zbl 1371.65001].

### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76F65 | Direct numerical and large eddy simulation of turbulence |

### Software:

FLUSEPA
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\textit{G. Pont} and \textit{P. Brenner}, Springer Proc. Math. Stat. 200, 295--303 (2017; Zbl 1365.76168)

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### References:

[1] | Barth, T.J., Frederickson, P.: Higher order solution of the euler equations on unstructured grids using quadratic reconstruction, pp. 90–0013. Technical report. AIAA Paper (1990) |

[2] | Brenner, P.: Unsteady flows about bodies in relative motion. In: 1st AFOSR Conference on Dynamic Motion CFD Proceedings. Rutgers University, New Jersey, USA (1996) |

[3] | Haider, F., Brenner, P., Courbet, B., Croisille, J.P.: Efficient implementation of high order reconstruction in finite volume methods. In: Finite Volumes for Complex Application VI-Problem & Perspectives. Springer Proceedings in Mathematics, vol. 4, pp. 553–560 (2011) · Zbl 1246.76096 |

[4] | McCorquodale, P., Colella, P.: A high-order finite-volume method for conservation laws on locally refined grids. Commun. Appl. Math. Comput. Sci. 6, 1–25 (2011) · Zbl 1252.65163 |

[5] | Pont, G.: Self adaptive turbulence models for unsteady compressible flows. Ph.D. thesis, Arts et Métiers ParisTech (2015) |

[6] | Pont, G., Brenner, P., Cinnella, P., Robinet, J.C., Maugars, B.: Multiple-correction hybrid k-exact schemes for high-order compressible RANS-LES simulations on general unstructured grids. J. Comput. Phys. (Submmited in May 2016) · Zbl 1380.76066 |

[7] | Spalart, P.R., Deck, S., Shur, S., Squires, M., Strelets, M., Travin, A.: A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20, 181–195 (2006) · Zbl 1112.76370 |

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