A discontinuous Galerkin method for free surface flows with fluid-solid interaction

Abstract

This paper presents a monolithic and a partitioned Arbitrary Lagrangian Eulerian (ALE) method for free surface flows over immersed movable rigid bodies. A discontinuous Galerkin (DG) method is used to discretize the incompressible Navier-Stokes equations, while rigid body equations are used to model the motion of solids. Lagrange multipliers are used on the fluid boundary to weakly enforce boundary conditions, which enables tracking free fluid surfaces and moving solid boundaries. The evolution of the discrete mesh in the fluid domain due to the motion of the solid and free surface is determined by the deformation of a fictitious structure. A fully implicit and an implicit-explicit scheme are used for the solution of monolithic and partitioned methods, respectively. We examine the performance and stability of these methods in two aspects: the motion of ultra-light solids that has been challenging to model computationally and the role of the numerical fluxes used for the viscous term. The latter relates this work to prior studies on the stability of various interior penalty and DG formulations for elliptic PDEs. Representative examples in both two and three dimensions show the capability to solve flows over moving and rotating objects.