Section: New Results

Mesh adaptation by continuous deformation

Participants : Luca Arpaia, Mario Ricchiuto [Corresponding member] .

As discussed in section 3.3 Meshes and scalable discrete data structures an accurate resolution of time dependent flows requires a dynamic mesh adaptation procedure which is quite complex and costly, especially when combined with parallel distributed memory implementations. To alleviate this cost, and still allow mesh adaptation for time dependent problems we have started to look into adaptation techniques which do not involve any re-meshing. In particular, we have studied methods based on continuous mesh deformation. These methods require, at each time step, the solution of a PDE for the mesh as well as for the flow variables. This year we have settled several fundamental questions related to the basic formulation of the method, and its coupling with either implicit or explicit time discretisation methods of the flow variables. Initial applications to free surface flows have been considered showing the generality and potential of our results [39] .