The two following videos present the solution and adapted mesh for two 2D test cases.
The implementation was done during my PhD in the computational code Realfluids (INRIA Bordeaux Sud Ouest).
From a referential mesh, we perform a ** constant connectivity** mesh adapation to both the level set
representing the solid and the solution. Methodology provided in the PhD thesis and INRIA research report.

Oscillating Naca0015 airfoil (Vorticity) and oscillating cylinder (u-velocity).

The following images show the result of different simulations (2D and 3D) of steady penalized compressible Navier Stokes flow. The h-adaptation strategy (remeshing) has been adopted here. The RealFluids computational code (INRIA Bordeaux Sud Ouest) provide the Navier-Stokes (penalized) resolution and the MMG platform has beem employed to adapt the meshes. Methodology provided in PhD thesis and CMAME article.

The following images propose the resolution using a multiscale scheme of the 3D (steady) flow in a porous media with discontinuous permeabilities. Although the formulation is written with discontinuous functions, the multiscale strategy allows to solve a system with a number of unknowns equivalent to a continuous approach (in mixed form), while keeping a final discontinuous solution.