Free-surface Flow Simulations in the Presence of Inclined Walls

Difficulties associated with free-surface finite element flow simulations are related to a) nonlinear and advective nature of most hydrodynamic flows, b) requirements for compatibility between velocity and pressure interpolation, c) maintaining a valid computational mesh in the presence of moving boundaries, and d) enforcement of the kinematic conditions at the free surface. Focusing on the last issue, we present an extension of the free surface elevation equation to cases where the prescribed direction of the surface node motion is not uniformly vertical. The resulting hyperbolic generalized elevation equation is discretized using a Galerkin/Least-Squares formulation applied on the surface mesh. The elevation field so obtained is then used to impose displacement boundary conditions on the elastic mesh update scheme that governs the movement of interior mesh nodes. The proposed method is used to solve a two-dimensional problem of sloshing in a trapezoidal tank, and a three-dimensional application involving flow in a trapezoidal channel with bridge supports.