Mesh adaption for unsteady interfaces with deformation, stretching and curvature. – 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.

INRIA-Sophia: (1)MG adaptatives avec Lemma [R1], (2) adaptation norm-oriented, pour la CFD (Loseille, Rocquencourt), fluide-structure (E. Gauci) et pour l’identification (G. Cunha).
Cemef applies a levelset method for immersed object. The levelset is a flag to first locate and identify the elements and nodes close to the object boundary, then to prescribe a surrounding region at a mid-distance from the interface and finally to highlight all the nodes and elements far from the immersed object.
INRIA-Rocquencourt a travaillé sur ((1) MG adaptatives en CFD. (2) adaptation en FSI (3) adaptation Norm-oriented et certification en CFD. (4) maillage metric-aligned/orthogonal adaptés aux couches limites a fort étirement conservant une certaine orthogonalité (code FEFLOW).
UM2 a développé un nouveau schéma multirate par agglomération de volumes finis. UM2 a spécifié ATC2 .
INRIA-Bordeaux : méthode de génération de maillage courbe compatible avec un nouveau schéma d'ordre élevé (>=trois): applications aux profils d'aile à bord d'attaque arrondis.
Lemma: (1) mise en place du nouveau remailleur FEFLOW, (2) spécification et passage test Dam-break avant et après FEFLOW , (3) algorithme FMG adaptatif avec INRIA-Sophia, (4) extension a Navier-Stokes et a MPI, (5) étude en capillarité.
TSV: cas qualitatif d’éolienne 3D, validation des portance et trainée sur un NACA et un cercle (2D), validation en 3D est et inter comparaison. La plateforme Aéromines a été mise en place.

Passage a l'echelle pour les nouvelles methodes et demonstrateurs.

21 papiers dont 4 articles.

FEFLOW
Plateforme Aeromines
Film de vulgarisation

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.