Possibly a simulation of a self-propelling droplet governed by the Cahn-Hilliard-Navier-Stokes equations on a torus, i.e. a two-dimensional structure. To conform with the CHNS equations, we shall use the Scott-Vogelius pair, with some adaptive mesh refinement. The droplet will be self-propelled by a gradient in the chemical potential, which will be implemented as a source term in the Navier-Stokes equations. The droplet will be confined to a torus, which will be implemented either as a periodic boundary condition or as a three-dimensional object.
- error estimation and mesh adaptivity
- pressure-robust methods