Numerical Simulation on the Free Surface using implicit boundary condition

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This describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows of fluid behaviour with free-surface. The elliptic differential equations governing the flows have been linearized by means of finite-difference approximations, and the resulting equations have been solved via a fully-implicit iterative method. The free-surface is defined by the motion of a set of marker particles and interface behaviour was investigated by way of a 'Lagrangian' technique. Using the GALA concept of Spalding, the conventional mass continuity equation is modified to form a volumetric or bulk-continuity equation. The use of this bulk-continuity relation allows the hydrodynamic variables to be computed over the entire flow domain including both liquid and gas regions. Thus, the free-surface boundary conditions are imposed implicitly and the problem formulation is greatly simplified. The numerical procedure is validated by comparing the predicted results of a periodic standing waves problems with analytic solutions or experimental results from the literature. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.