An immersed boundary method using unstructured anisotropic mesh adaptation combined with level-sets and penalization techniques

Abstract

The interest on embedded boundary methods increases in Computational Fluid Dynamics (CFD) because they simplify the mesh generation problem in the case of the Navier–Stokes equations. The same simplifications occur for the simulation of multi-physics flows, the coupling of fluid–solid interactions in situation of large motions or deformations, to give a few examples. Nevertheless an accurate treatment of the wall boundary conditions remains an issue of the method. In this work, the wall boundary conditions are easily taken into account through a penalization technique, and the accuracy of the method is recovered using mesh adaptation, thanks to the potential of unstructured meshes. Several classical examples are used to demonstrate that claim.