Implicit Boundary and Adaptive Anisotropic Meshing

Abstract : Implicit boundary means that the boundaries and/or interfaces between domains are not anymore defined by an explicit boundary mesh but rather by an implicit function. It is the case with embedded boundary methods or immersed boundary methods. Here we consider a filtered level set methods and meshing is then performed using an anisotropic mesh adaptation framework applied to the level sel interpolation. The interpolation error estimate is driving the adaptive process giving rise to a new way of boundary recovery. The accuracy of the recovery process depends then on the user given parameter, an arbitrary thickness of the interface. The thickness is normally related to the mesh size, but it is shown that adaptive meshing enables to reverse this condition: fixing the thickness parameter and accounting for the adaptation process to fulfill the mesh size condition. Several examples are given to demonstrate the potential of this approach.