Section: New Results
Previous work on interpolation free adaptation for compressible flows  has been further extended to account for non-ideal gas effects. Simulations are carried out to assess grid adaptation criteria in presence of these effects . We have found that for some cases, especially in presence of a strong non-ideal dependence of the speed of sound on the density and the temperature, Mach number estimators prove to be more effective.
We have also completed the study of adaptive mesh deformation for shallow water flows, and proposed a comprehensive study of the efficiency of different techniques based on a adapt-project-evolve paradigm, or on a fully coupled ALE approach. The issue of marrying mass conservation and well-balancedness, which is peculiar to shallow water models, has been treated by means of a high order projection of the topography . Preliminary results on the extension of these techniques have also been obtained .