A nonlinear elasticity model for structured mesh adaptation

We propose a 2D structured mesh adaptation method, for steady or unsteady problems, based on a nonlinear elasticity model. The points motion is governed by an energy minimization problem. The unknown is the deformation of the mathematical domain. A constraint on its gradient allows a control of the evolution of the deformation in time. This problem is discretized in the physical domain and solved by a Newton-Raphson's method. We apply our method to the resolution of the Navier-Stokes equations. The coupling of the adaptation procedure and the how solver consists in writing the Euler part of the equations in an Arbitrary Lagrangian-Eulerian (ALE) form. The ability of the method to produce suitable grids, adapted to the behavior of an arbitrary or realistic physical solution, is illustrated.