Residual Schemes Applied to an Embedded Method Expressed on Unstructured Adapted Grids

The interest on embedded boundary methods is increasing in Computational Fluid Dynamics because they simplify the mesh generation problem when dealing with the Navier-Stokes equations. To give a few examples, they simplify the simulation of multi-physics flows, the coupling of fluid-solid interactions in situation of large motions or deformations. Nevertheless an accurate treatment of the wall boundary conditions remains an issue of the method. In this work, a penalty term added to the Navier-Stokes equations accounts for the wall boundary conditions and accuracy is recovered using mesh adaptation, thanks to the potential of unstructured meshes.