Section: New Results

High order mesh generation and mesh adaptation

• Participants: Luca Arpaia , Cécile Dobrzynski, Ghina El Jannoun, Léo Nouveau, Mario Ricchiuto

• Corresponding member: Cécile Dobrzynski

This year several new algorithmic improvements have been obtained which will allow to enhance our meshing tools:

• We have enhanced our work on $r$-adaptation techniques for time dependent equations. These techniques are based on mesh deformations obtained by solving continuous differential equations for the local displacements. These equations are controlled by an error monitor. Several improvements have been made. We have studied in depth the formulation of the coupling of the mesh movement with the flow solver. We have found that for both finite volume and residual distribution methods, a coupling of mesh and solution evolution (by means of an ALE method) provides accuracy enhancements, and is to be preferred to a simpler adapt-project-evolve approach. The method has been fully tested in two space dimensions and preliminary results have been performed in three dimensions. We have applied this technic to immersed boundary methods to compressible simulations. For problems with source terms, and in particular problems admitting some important physical invariants as the shallow water equations, we have solved the conflict between the conservation of either mass or the invariant, allowing for the conservation of both quantities up to machine accuracy. In parallel we have proposed a modified formulation of an elasticity equation allowing to reduce the nonlinearity of the mesh PDE to the force imposed in the right hand side. Initial validation has been shown in [56] and in the PhD of L. Nouveau ;