A SEMI-IMPLICIT SEMI-LAGRANGIAN FINITE ELEMENT MODEL FOR NONLINEAR FREE SURFACE FLOW

Potential flow initial-boundary value problems describing fluid structure interaction with fully nonlinear free surface boundary conditions have been studies using a mixed Lagrangian Eulerian formulation. The two dimensional boundary value problem has been solved in the physical domain by means of a Bubnov-Galerkin formulation of the Laplace equation. The initial-value problem related to the behaviour of some of the moving boundaries has been discretized using a semi-implicit semi-Lagrangian two time level iterative scheme that is almost free from smoothing. Fluid responses to periodic examination of surface piercing and submerged bodies have been calculated. The impulsive response of tanks of various shapes has also been simulated. Resulting natural frequencies show good agreement with available data. A slender body representation of the flow around a hull advancing with forward speed in otherwise calm water has also been simulated. Numerical calculations of a number of quantities of engineering interest are presented for different length Froude numbers. Results compare favourably with experimental data.