Discretization of incompressible flows on evolving surfaces

Navier-Stokes on surfaces

In LLS20 we introduced \(H(\operatorname{div}_\Gamma)\)-conforming finite elements for the discretization of incompressible Navier-Stokes equations on stationary surfaces. In this project we want to extend this to evolving surfaces.

Navier-Stokes on evolving surfaces

The equation for the evolving surfaces is given in [1] (see equation (3.12)).

Compared to the work in LLS20 the following features need be added:

• an equation for an additional scalar field for the normal field
• evolution of the surface
• computation of discrete curvatures (Gaussian/mean curvature)

References

[1] T. Jankuhn, M. Olshanskii, A. Reusken. Incompressible Fluid Problems on Embedded Surfaces: Modeling and Variational Formulations, Interfaces and Free Boundaries, 20(3), 353-377.