A robust deformation method for unstructured meshes subject to large boundary movements
Résumé
Many applications involving Fluid-Structure Interaction (FSI) feature large displacements of the boundaries of the computational domain. Despite recent progress in this field, Finite-Element and Finite-Volume simulations of such problems are still challenging. On one hand, interface-capturing techniques such as the level-set or the phase-fields methods can deal with large boundary deformations, but they often fail to correctly take into account the jump in mechanical properties of materials at the interface, and they can only approximate important geometrical singularities such as corners and edges. On the other hand, standard mesh deformation techniques coupled with ALE solvers are appropriate for problems of Fluid-Structure Interaction involving small displacements, but their capacity to maintain the validity and the quality of the mesh under large boundary movements is limited. In this work, we develop a robust mesh deformation method aimed at simulations subject to large boundary displacements. At each time step of the simulation, a displacement is applied to the boundary and the mesh is regularized and improved by means of a continuous optimization technique. A local mesh adaptation procedure involving topological operations is triggered in case the mesh quality falls below a user-given threshold after the optimization stage. The main feature of the algorithm is its robustness with respect to boundary displacements of arbitrary amplitude. We demonstrate the performance of our approach on academic mesh movement test cases and apply it to Finite-Element ALE simulations.