Goal-oriented mesh adaptation for moving mesh FSI problems
Résumé
Keywords : Fluid-structure interaction, Mesh adaptation, ALE : Arbitrary Lagrangian Eulerian, Adjoint In anisotropic mesh adaptation, the optimal metric has to be derived from the minimization of a model of an approximation error. In general it leads to an Hessian-based anisotropic adaptation which depends on the computed solution. But the link with the original PDE is sometimes too weak. In contrast, goal-oriented mesh adaptation takes into account the PDE, via the introduction of an adjoint state and improves the simulation efficiency. A goal-oriented anisotropic mesh-adaptation methods for unsteady Euler flows was already proposed in [3] but doesn't deal with moving-mesh problems. Here, we propose to couple ALE-method [1], [2] and unsteady adjoint mesh adaptation. We will present a global fixed point algorithm for solving the coupled system made by the unsteady state in ALE, the unsteady adjoint in ALE and the adapted meshes. We split the time interval into mesh-adaptation sub-intervals. During the time-forward computation we store all checkpoints in order to evaluate time-backward the adjoint state throughout the sub-interval. At each fixed point iteration, an error estimate is computed. In terms of flow solver, a second-order vertex-centered finite volume scheme is considered to solve an ALE-formulation of the Euler equations. This work will be illustrated with an unsteady blast-wave problem. References [1] N. Barral, F. Alauzet, Large displacement body-fitted FSI simulations using a mesh-connectivity-change moving mesh strategy.