Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
For an ALE code a crucial part is the interpolation of physical variables from the Lagrangian grid to the rezoned grid. The remapping can easily ruin the accuracy of the Lagrangian scheme. In this work we have constructed a full 2D remapping method to be used on a staggered polygonal mesh. This technique has been implemented into an ALE code. It combines and generalizes previous work on the Lagrangian and rezoning phases. This subcell remapping method is high-order (preserving linear field), conservative (mass, momentum and total energy), maximum principle preserving (and positivity preserving) and reversible (if the old and new meshes are identical the physical variables are kept unchanged).
We showed the efficiency of this approach in 1D and 2D on classical problems of compressible hydrodynamics.
