Comparison of Wall Boundary Conditions for Numerical Viscous Free Surface Flow Simulation

A spectral/hp element code, incorporating a velocity-pressure formulation, is used to simulate free surface flows. Non-linear pressure and velocity boundary conditions are applied on the moving free surface, the tracking of which is facilitated by the implementation of an Arbitrary Lagrangian Eulerian (ALE) formulation. The derived algorithm is validated by comparing the numerical results evaluated here with an analytical method which predicts the damping of a freely sloshing, viscous fluid for a range of Reynolds number: 3 ≤ Re ≤ 3 × 10 where Re = (gd) d/ν and g, d and ν are gravity, depth of fluid and kinematic viscosity respectively. The free surface wall contact point is investigated and a number of approximations to overcome the contradiction of a moving contact point and the wall no-slip condition are presented. The numerical procedure which utilises these approximations is tested against a linear, analytical method which predicts viscous diffusion in the vicinity of the containing walls for a freely sloshing fluid. It is found that the numerical results using the various formulated boundary conditions converge as the Reynolds number increases.