Abstract
We propose a new mesh adaptation technique to solve the thermal problem of the impingement jet cooling. It relies on a subscales error estimator computed with bubble functions to locate and evaluate the PDE-dependent approximation error. Then, a new metric tensor \(\mathcal {H}_{aniso}^{\,\,new}\) based on the subscales error estimator is suggested for anisotropic mesh adaptation. We combine the coarse scales anisotropic interpolation error indicator with the subscales error estimator allowing us to take into account the anisotropic variations of the solution but also the sub-grid information. The results show that the resulting meshes of this parallel adaptive framework allow to capture the turbulently generated flow specificities of the impingement jet cooling and in particular, the secondary vortexes.
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References
Mesri, Y., Khalloufi, M., Hachem, E.: On optimal simplicial 3d meshes for minimizing the Hessian-based errors. Appl. Numer. Math. 106, 235–249 (2016)
Bazile, A., Hachem, E., Larroya-Huguet, J.C., Mesri, Y.: Variational Multiscale error estimator for anisotropic adaptive fluid mechanic simulations: application to convection–diffusion problems. Comput. Methods Appl. Mech. Eng. 331, 94–115 (2018)
Granzow, B.N., Shephard, M.S., Oberai, A.A.: Output-based error estimation and mesh adaptation for variational multiscale methods. Comput. Methods Appl. Mech. Eng. 322, 441–459 (2017)
Hughes, T.J.R.: Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput. Methods Appl. Mech. Eng. 127(1), 387–401 (1995)
Irisarri, D., Hauke, G.: A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method. Comput. Methods Appl. Mech. Eng. 311, 648–670 (2016)
Codina, R.: Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Methods Appl. Mech. Eng. 191(39–40), 4295–4321 (2002)
Brooks, A.N., Hughes, T.J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. n32(1), 199–259 (1982)
Cooper, D., Jackson, D.C., Launder, B.E., Liao, G.X.: Impinging jet studies for turbulence model assessment—I. Flow-field experiments. Int. J. Heat Mass Transf. n36(10), 2675–2684 (1993)
Mesri, Y., Digonnet, H., Coupez, T.: Hierarchical adaptive multi-mesh partitioning algorithm on heterogeneous systems. Lect. Notes Comput. Sci. Eng. n74, 299–306 (2010)
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Mesri, Y., Bazile, A., Hachem, E. (2020). A Variational Multi-Scale Anisotropic Mesh Adaptation Scheme for Aerothermal Problems. 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_18
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DOI: https://doi.org/10.1007/978-3-030-30705-9_18
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