Abstract
This paper illustrates the application of error estimates based on k-exactness of approximation schemes for building mesh adaptive approaches able to produce better numerical convergence to continuous solution. The cases of k = 1 and k = 2, i.e. second-order and third-order accurate approximations with steady and unsteady flows are considered.
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References
2nd AIAA Sonic Boom Prediction Workshop. Grapevine, Texas (2017)
Agouzal, A., Lipnikov, K., Vasilevskii, Y.: Adaptive generation of quasi-optimal tetrahedral meshes. East-West J. 7(4), 223–244 (1999)
Alauzet, F., Loseille, A.: High order sonic boom modeling by adaptive methods. J. Comp. Phys. 229, 561–593 (2010)
Barth, T.J., Frederickson, P.O.: Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. AIAA Paper 90-13 (1990)
Barth, T.J., Larson, M.G.: A-posteriori error estimation for higher order Godunov finite volume methods on unstructured meshes. In: Herbin, R., Kröner, D. (eds.) Finite Volumes for Complex Applications III, pp. 41–63. HERMES Science, London (2002)
Belme, A., Dervieux, A., Alauzet, F.: Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows. J. Comp. Phys. 231(19), 6323–6348 (2012)
Brèthes, G., Allain, O., Dervieux, A.: A mesh-adaptative metric-based full multigrid for the Poisson problem. Int. J. Num. Meth. in Fluids 79(1), 30–53 (2015)
Carabias, A.: Analyse et adaptation de maillage pour des schémas non-oscillatoires d’ordre élevé (in French). PhD, Université de Nice-Sophia-Antipolis, France (2013)
Carabias, A., Belme, A., Loseille, A., Dervieux, A.: Anisotropic goal-oriented error analysis for a third-order accurate CENO Euler discretization. Int. J. Num. Meth. in Fluids 86(6), 392–413 (2018)
Castro-Díaz, M.J., Hecht, F., Mohammadi, B., Pironneau, O.: Anisotropic unstructured mesh adaptation for flow simulations. Int. J. Num. Meth. in Fluids 25, 475–491 (1997)
Coulaud, O., Loseille, A.: Very high order anisotropic metric-based mesh adaptation in 3D. 25th International Meshing Roundtable. Procedia Eng. 163, 353–365 (2016)
Dompierre, J., Vallet, M.G., Fortin, M., Bourgault, Y., Habashi, W.G.: Anisotropic mesh adaptation: towards a solver and user independent CFD. In: AIAA 35th Aerospace Sciences Meeting and Exhibit, AIAA-1997-0861, Reno (1997)
Ferro, N., Micheletti, S., Perotto, S.: Anisotropic mesh adaptation for crack propagation induced by a thermal shock in 2D. Comput. Methods Appl. Mech. Engrg. 331, 138–158 (2018)
Formaggia, L., Perotto, S.: Anisotropic a priori error estimates for elliptic problems. Numer. Math. 94, 67–92 (2003)
Frazza, L., Loseille, A., Alauzet, F. Dervieux, A.: Nonlinear corrector for RANS equations. AIAA 2018-3242 (2018)
Frey, P.J., Alauzet, F.: Anisotropic mesh adaptation for CFD computations. Comp. Meth. Applied Mech. Eng. 194(48–49), 5068–5082 (2005)
Gauci, E., Belme, A., Carabias, A., Loseille, A., Alauzet, F., Dervieux, A.: A priori error-based mesh adaptation in CFD (SCPDE17, Hong Kong). J. Methods Appl. Anal. Special Issue (2019, in progress)
Huang, W.: Metric tensors for anisotropic mesh generation. J. Comp. Phys. 204, 633–665 (2005)
Ivan, L., Groth, C.P.T.: High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows. J. Comp. Phys. 257, 830–862 (2014)
Loseille, A., Alauzet, F.: Continuous mesh framework. Part I: well-posed continuous interpolation error. SIAM J. Numer. Anal. 49(1), 38–60 (2011)
Loseille, A., Alauzet, F.: Continuous mesh framework. Part II: validations and applications. SIAM Num. Anal. 49(1):61–86 (2011)
Loseille, A., Löhner, R.: Adaptive anisotropic simulations in aerodynamics. In: 48th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2010-169, Orlando (2010)
Loseille, A., Dervieux, A., Alauzet, F.: Anisotropic norm-oriented mesh adaptation for compressible flows. In: 53rd AIAA Aerospace Sciences Meeting. AIAA-2015-2037, Kissimmee (2015)
Vasilevski, Y.V., Lipnikov, K.N.: Error bounds for controllable adaptive algorithms based on a Hessian recovery. Computational Mathematics and Mathematical Physics, 45(8), 1374–1384, (2005)
Yano, M., Darmofal, D.: An optimization framework for anisotropic simplex mesh adaptation: application to aerodynamics flows. AIAA Paper, 2012-0079 (2012)
Acknowledgements
This work has been supported by French National Research Agency (ANR) through project MAIDESC no ANR-13-MONU-0010. This work was granted access to the HPC resources of CINES under the allocations 2017-A0022A05067 and 2017-A0022A06386 made by GENCI (Grand Equipement National de Calcul Intensif).
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Dervieux, A. et al. (2020). Mesh Adaptation for k-Exact CFD Approximations. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_7
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DOI: https://doi.org/10.1007/978-3-030-30705-9_7
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