Stephan Schmidt: Second Order Scheme to Compute Geometric Interfaces With Applications in Microfluids

Abstract:  We present a second-order numerical scheme to compute capillary bridges between arbitrary solids by minimizing the total energy of all interfaces. From a theoretical point of view, this approach can be interpreted as the computation of generalized minimal surfaces using a Newton-scheme utilizing the shape Hessian. In particular, we give an explicit representation of the shape Hessian for functionals on shells involving the normal vector without reverting back to a volume formulation. From an algorithmic perspective, we combine a resolved interface via a triangulated surface for the liquid with a level-set description for the constraints stemming from the arbitrary geometry. The actual shape of the capillary bridge is then computed via finite elements provided by the FEniCS environment, minimizing the shape derivative of the total interface energy.

This talk is part of the Mechanics Lunch Seminar series. Bring-your-own-lunch and lots of questions.