A mimetic spectral element method for free surface flows

Abstract

We derive a compatible high order discretization method that relies heavily on the underlying geometric structure and obeys the topological sequences for 2D free surface flows with fully submerged structures. The flow is assumed inviscid and irrotational. This allows us to write the continuity and Navier–Stokes equations using a velocity potential as a Laplace equation and the differential form of the unsteady Bernoulli’s equation. We use a mixed variational formulation and results confirm the theoretical results that we obtain global and local divergence free solutions.