Section: New Results

Residual distribution schemes

Participants : Rémi Abgrall [Corresponding member] , Mario Ricchiuto, Dante De Santis, Algiane Froehly, Cécile Dobrzynski.

We have understood how to approximate the advection diffusion problem in the context of residual distribution schemes. A third order version for scalar problem has been written. It is uniformly accurate, from pure viscous to pure convection problems. This scheme has been generalised to the laminar Navier Stokes equations. An extension to the turbulent case (with Spalart Allmaras model) has also been written and tested. We have studied the (iterative) convergence issues using Jacobian Free techniques or the LUSGS algorithm. Tests in two and three dimensions have been carried out. This work is submitted in [37] and has been the topic of [20] .

A. Froehly has submitted her PhD thesis about the extension of the residual distribution scheme using isogeometric analysis. In particular, we have foccussed on mesh adaption, including at the boundary. A paper is being written to summarized the work.