SUMMARYA volume of fluid (VOF) method is developed combining a first-order limited downwind scheme with higher order accurate schemes. The method is characterized by retaining a sharp fluid interface and a reduction in numerical diffusion near the interface, but avoids complicated geometrical reconstruction as occurs in most volume tracing algorithms. To demonstrate the accuracy and robustness of the method, a selection of numerical experiments are presented involving a pure advection problem, a water wave impact caused by a dam breaking and liquid sloshing in a partially filled tank.

A mixed¯nite-element¯nite-di®erence numerical method is developed to calculate nonlinear°uid{solid interaction problems. In this study, the structure is assumed to be rigid with large motion and the°uid°ow is governed by nonlinear, viscous or non-viscous,¯eld equations with nonlinear boundary conditions applied to the free surface and°uid{solid interaction interfaces. A moving coordinate system¯xed at a point in the structure is used to describe the°uid°ow, and for numerical analysis purposes, an arbitrary Lagrangian{Eulerian mesh system is constructed relative to this moving system. This provides a convenient method of overcoming the di±culties of matching°uid meshes with large solid motion. Nonlinear numerical equations describing nonlinear°uid{solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. A selection of numerical examples illustrates the developed mathematical model and through numerical simulations it is shown that the proposed approach is practical and useful.

A numerical method to simulate nonlinear fluid – rigid structure interaction problems is developed herein. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid - solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block approach is adopted allowing relative motion between moving overset grids which are independent of one another. This provides a convenient method to overcome the difficulties of matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid - solid interaction dynamics are derived through a numerical discretisation scheme of study. A coupling iteration process is used to solve these numerical equations. A numerical example is presented to demonstrate applications of the developed numerical model.

This investigation continues the development of an anti-diffusive volume of fluid method [1] by improving accuracy through the addition of an artificial diffusion term, with a negative diffusion coefficient, to the original advection equation describing the evolution of the fluid volume fraction. The advection and diffusion processes are split into a set of two partial differential equations (PDEs). The improved anti-diffusive Volume of Fluid (VOF) method is coupled with a two-fluid flow solver to predict free surface flows and illustrated by examples given in two-dimensional flows. The first numerical example is a solitary wave travelling in a tank. The second example is a plunging wave generated by flow over a submerged obstacle of prescribed shape on a horizontal floor. The computational results are validated against available experimental data.