Séance Séminaire

Séminaire ACSIOM

High order immersed computations: from the Shifted Boundary Method towards a high order Penalization.

In this presentation, we will talk about immersed or embedded boundary (IB/EB) methods for CFD. Those methods are characterized by the absence of an explicit discretization of the geometry in the mesh, the boundary conditions (BC) being accounted differently [1]. They are particularly appealing in the context of complex geometries and/or moving interfaces as meshing/remeshing constraints are removed. After some general considerations on IB/EB methods, we will talk about the specific EB approach called the Shifted Boundary Method [2]. This technique aims at imposing the BC on a surrogate interface, composed by edges of the background mesh close the true boundary (not discretized). To account for the discrepancy between this surrogate interface location and the real one, one-sided Taylor expansions are employed to modify the imposed BC, allowing to preserve the accuracy of the underlying Finite Element scheme. Darcy problems and free surface flow applications will be proposed. Finally, we will discuss how this Taylor expansion strategy can be employed to improve the accuracy of the Penalization IB method [3], by properly defining a volumic source term in the involved PDEs, to accurately impose Dirichlet boundary conditions. Illustration with advection-diffusion problems will be presented.

[1] R. Mittal and G. Iaccarino. Immersed boundary methods. Annu Rev Fluid Mech, 37:239-261, 2005.

[2] A. Main, G. Scovazzi, The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems. Journal of Computational Physics, 372, 2018.

[3] E. Arquis and J.P. Caltagirone. Sur les conditions hydrodynamiques au voisinage d'une interface milieu fluide - milieu poreux: application à la convection naturelle. C. R. Acad. Sci. Paris série II, 299(1), 1984.

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