A Discontinuous ALE formulation (DiscALE) for the modeling of polygonal mesh (r,h)-adaptation in finite volume context

Philippe Hoch (1)

1 DAM/DIF - DAM Île-de-France

We introduce a finite volume Discontinuous Arbitrary Lagrangian-Eulerian (DiscALE) alternative to the computation of compressible fluid dynamics. This new proposed framework take naturally into account dynamical refinement/coarsening/reconnection on a direct discretization of a new {\bf non-smooth kinematic} mesh contribution. Two practical interesting properties of the method are -1- to deal with arbitrary polygonal mesh (initial or at each time step) and -2- to recover exactly Lagrangian, Eulerian or classical continuous ALE mode by omitting this non-smooth velocity. Moreover, it also appears that many meshing tools techniques can be seen as a direct discretization of this new discontinuous kinematic equation on a generic edge based patch. In this context, polygonal ALE-AMR (conformal or not) as well as edge swapping on simplices are special cases. Moreover, all underlying local mesh modification must verify a natural locality hypothesis (CFL constraint) and all associated Discrete Geometric Conservation Laws (DGCL) are exactly solved without computing any polygons/polygons intersections. The classical remapping fluxing scheme (swept or self intersection) has been extended to take into account the topological transformation of the boundary between two adjacent cells that generalize simplicial swapping.

Mots clés: DGCL; Discontinuous kinematic of mesh; ALE-AMR; arbitrary mesh reconnection; (r; h)-adaptation; refinement/coarsening; boundary transformation between two adjacent cells as generalized swapping; mesh sliding; DGCL.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Analyse numérique [math.NA]

Philippe Hoch. A Discontinuous ALE formulation (DiscALE) for the modeling of polygonal mesh (r,h)-adaptation in finite volume context. 2012. ⟨hal-01064701⟩