Vers des méthodes immerées generalisées:une approche Shifted Boundary P1 avec des flux d'ordre pour les équations de Darcy

In this paper, we propose to extend the recent embedded boundary method known as "shifted boundary method" to the Darcy flow problems. The aim is to provide an improved formulation that would give, using linear approximation, at least second order accuracy on bothflux and pressure variables, for any kind of boundary condition, considering embedded simulations.The strategy adopted here is to enrich the approximation of the pressure using Taylor expansionsalong the edges. The objective of this enrichment is to give a quadratic shape to the pressure. The resulted scheme provides high order accuracy on both variables for embedded simulations with an overall second order accuracy, that is bumped to third order for the pressure when only Dirichletboundaries are embedded

Anisotropic boundary layer mesh generation for immersed complex geometries

International audienceWe propose a new anisotropic boundary layer mesh adaptation procedure for immersed geometry. It is based on the use of multi-levelset method to locate the boundary layer, to control the mesh size distribution, shape and orientation ensuring a smooth gradation. Taking into account the physical parameters for the simulation and the curvature of the geometry, the numerical 2D and 3D applications show that, starting from an arbitrary coarse domain, it provides accurate representation of the immersed interfaces and their boundary layers for complex geometries. More specifically, when the solution displays anisotropic behaviour, we combine it with an edge based error estimator and dynamic anisotropic mesh adaptation to detect automatically all flow features under the constraint of a fixed number of elements. Some applications in aerodynamics at high Reynolds number for the prediction of the drag and lift coefficients [1] as well as complex gas-solid-liquid flows [2] will be presented. The proposed method is robust and simple to implement. It was validated using several test cases from the literature and some experimental results.REFERENCES[1] L. Billon, Y. Mesri, E. Hachem, Anisotropic boundary layer mesh generation for immersed complex geometries, Engineering with Computers, pp. 1-12, 2016[2] M. Khalloufi, Y. Mesri, R. Valette, E. Hachem, High fidelity anisotropic adaptive variational multiscale method for multiphase flows with surface tension, Computer Methods in Applied Mechanics and Engineering, Vol. 307, pp.44-67, 201

Anisotropic boundary layer mesh generation for immersed complex geometries

International audienceThis paper proposes a new method to build boundary layer meshes over an immersed complex geometry. It allows to generate an anisotropic semi-structured mesh with a smooth gradation of mesh size from a geometry immersed into an arbitrary coarse domain, while capturing and keeping the interface. The idea is to generate an a priori mesh fitting the geometry boundary layer which is ready for simulations. The mesh size distribution is driven by a levelset distance function and is determined using physical parameters available before the simulation, based on the boundary layer theory. The aspect ratio is then determined knowing the shape of the geometry, and all is applied in a metric tensor field using a gradation thanks to the new multi-levelset method. Then, the mesh generator adapt the initial mesh on the given metric field to create the desired boundary layer mesh