High-order compact discretization scheme for non-hydrostatic free surface flows

The development of a new numerical model for non-hydrostatic free surface flow is presented with the objective of improving accuracy of existing high-order discretization schemes. Numerical dissipation which has been a problem with many schemes is significantly reduced. Compared with second-order accurate methods, the scheme requires one-eighth the number of grid points per wavelength for three-dimensional computations to achieve the same level of accuracy. It uses the explicit fourth-order Runge-Kutta method for time integration and a compact fourth-order method for spatial discretization.; A significant problem with existing schemes is the control of numerical dissipation, particularly for short waves. Being second-order accurate; they typically require smaller grid spacings to achieve an acceptable level of accuracy. The existing numerical solutions also use the staggered grid system which is necessary to eliminate what is referred to as the pressure-velocity decoupling problem.; The numerical scheme used is fourth-order accurate in both space and time. It is developed on a non-staggered grid system and tested to demonstrate the elimination of the problem of pressure-velocity decoupling. The testing includes well established methods such as comparison with analytical solutions of standing wave in a basin and the propagation of solitary wave. In all cases, the results have shown excellent agreement between the numerical and analytical results for all the flow variables. Other tests performed with the model are lock-exchange flow, in which the diffusive processes become important as well as the numerical solution of the dispersion equation and wind-driven circulation.; Extension of the numerical scheme to three-dimensional situations should be straight forward. Appropriate treatment of the boundaries should facilitate the model's capabilities for simulating wave transformation including refraction, diffraction and reflection in the ocean, coastal areas and lakes; simulation of internal waves in the ocean and lakes; buoyancy-driven flows in rivers, lakes and ocean as well as wind-driven circulation in lakes or confined water bodies.