Levelsets and anisotropic mesh adaptation

In this paper, we focus on the problem of adapting dynamic tri- angulations during numerical simulations to reduce the approximation errors. Dynamically evolving interfaces arise in many applications, such as free sur- faces in multiphase flows and moving surfaces in fluid-structure interactions. In such simulations, it is often required to preserve a high quality interface discretization thus posing significant challenges in adapting the triangulation in the vicinity of the interface, especially if its geometry or its topology changes dramatically during the simulation. Our approach combines an e!cient levelset formulation to represent the interface in the flow equations with an anisotropic mesh adaptation scheme based on a Riemannian metric tensor to prescribe size, shape and orientation of the elements. Experimental results are provided to emphasize the e"ectiveness of this technique for dynamically evolving inter- faces in flow simulations.