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Thierry Coupez, CEMEF – Mines-Paristech – UMR 7635

Implicit Boundary and Anisotropic Mesh Adaptation for Multiphase Flow Simulations

Vendredi 9 mars, 11h, Amphi 1bis, Bat W1, Ecole Centrale de Lyon.

Implicit Boundary and Anisotropic Mesh Adaptation for Multiphase Flow Simulations

A wider use of numerical simulation is still depending on meshing and adaptive meshing capabilities when complex geometry, multi-domain, moving interface and multiphase flow are involved. This task becomes more and more difficult when it is combined with a posteriori adaptive meshing or/and dealing with moving interfaces and boundary layers and also when running on massively parallel computers. In order to overcome the lack of flexibility of the common body fitted method, the alternative proposed here, is based on an implicit representation of the interfaces by a local distance function using a hyperbolic tangent filter. Therefore, the geometries can be interpolated and contribute to the numerical error which is detected by an a posteriori error estimate.
This approach favours the full usage of anisotropic adaptive meshing techniques providing an optimal capture of the interfaces within the volume mesh, whatever is the complexity of the geometry involved. From the flow solver side, unstructured meshes with highly distorted elements (however solution aligned) need to rely on a robust solution framework. The interface condition transfer is enforced by following the immersed boundary/volume (IVM) methodologies for fluid/fluid and or fluid/structure interaction. The proposed multiphase flow solver, including the convected local level set technique is based on a stabilized finite element method (VMS) that can afford with anisotropic meshing even with high aspect ratio elements. The general stabilization approach including the interface stabilization term and the dynamic will be introduced with a quasi-optimal calculation of the stabilization parameter for anisotropic finite elements. The multiphase navier stokes error estimation and the associated metric calculation will be discussed and various application examples will be proposed.

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Milk crown phenomenon: Falling droplet with surface tension and liquid gas interaction
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Wind mill turbine : fluid moving solid interaction by a monolithic immersed method
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Flow past a car : high Reynolds flow and comlex geometries

- T. Coupez, Metric construction by length distribution tensor and edge based error for anisotropic adaptive meshing, J. of Comp. Physics 230: 2391-2405 (2011)
- T. Coupez, E. Hachem, “Solution of high Reynolds Incompressible Flow with Stabilized Finite Element and Adaptive Anisotropic Meshing”, Comp. Meth. in App. Mech. and Engng Vol. 267, pp. 65-85, (2013)
- T. Coupez, L. Silva, E. Hachem, Implicit boundary and adaptive anisotropic meshing, SEMA SIMAI Springer Series, Vol. 5, pp. 1-18, (2014)
- L Silva, T Coupez, H Digonnet, Massively parallel mesh adaptation and linear system solution for multiphase flows, International Journal of Computational Fluid Dynamics 30 (6), 431-436, (2016)
- E Hachem, S Feghali, T Coupez, R Codina 2015 ‘A three‐field stabilized finite element method for fluid‐structure interaction: elastic solid and rigid body limit’, International Journal for Numerical Methods in Engineering 104 (7), 566-584


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