MAIDESC

Mesh adaptive numerical methods have been recently developed with a considerable success. They allow computations which are not possible without mesh adaptation. The teams of the proposing consortium are among those who have contributed to important recent advances in the field. They have converged towards a common framework and are in position, by combining their competence, to make breakthroughs, in both methods and applications. A fundamental factor is that this framework offers high-order convergence in singular cases where the other approximation methods do not. We address in the proposed research several well identified main obstacles in order to maintain a high-order convergence for unsteady Computational Mechanics involving moving interfaces separating and coupling continuous media. A priori and a posteriori error analysis of Partial Differential Equations on static and moving meshes will be developed from interpolation error, goal-oriented error, and norm-oriented error. From the minimization of the chosen error, an optimal unsteady metric is defined. The optimal metric is then converted into a sequence of anisotropic unstructured adapted meshes by means of mesh regeneration, deformation, high stretching, and curvature. A particular effort will be devoted to build an accurate representation of physical phenomena involving curved boundaries and interfaces. In association with curved boundaries, a part of studies will address third-order accurate mesh adaption. Mesh optimality produces a nonlinear system coupling the physical fields (velocities, etc.) and the geometrical ones (unsteady metric, including mesh motion). Parallel solution algorithms for the implicit coupling of these different fields will be developed. Each innovative advance will be performed on a complementary standpoint: a theory and a platform developed by the partners with best expertise. Methods and results will be described in details in reports and published. Addressing efficiently these issues is a compulsory condition for the simulation of a number of challenging physical phenomena related to industrial unsolved or insufficiently solved problems. This involves the thermo-capillarity coupling arising in spatial tanks, wake instability in a probe/parachute system, moving rigid body interface with fluid structure coupling in a windmill, breaking waves on moving structures, high Reynolds Aerodynamics. Non-trivial benchmark tests will be shared by consortium partners and by external attendees to workshops organized by the consortium. The various advances will be used by SME partners and proposed in software market.