# American Institute of Mathematical Sciences

January & February  2009, 23(1&2): 165-183. doi: 10.3934/dcds.2009.23.165

## Levelsets and anisotropic mesh adaptation

 1 UPMC Univ Paris 06, UMR 7598, Laboratoire J.L. Lions, F-75005 Paris, France, France 2 Universidad de Chile, UMI 2807, Centro de Modelamiento Matem´atico, Santiago, Chile

Received  December 2007 Revised  May 2008 Published  September 2008

In this paper, we focus on the problem of adapting dynamic triangulations during numerical simulations to reduce the approximation errors. Dynamically evolving interfaces arise in many applications, such as free surfaces 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 efficient 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 effectiveness of this technique for dynamically evolving interfaces in flow simulations.
Citation: Vincent Ducrot, Pascal Frey, Alexandra Claisse. Levelsets and anisotropic mesh adaptation. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 165-183. doi: 10.3934/dcds.2009.23.165
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