A shallow-water equation based one-dimensional dynamic wave model with non-hydrostatic pressure

Author(s): Wei, Z.; Jia, Y.

Coastal wave is one of major forces that dominate coastal hydronydamics, sediment transport, morphology and threaten coastal infrastructures. In recent years, the non-hydrostatic technique for solving Reynolds-averaged Navier-Stokes equations has been developed for wave propagation study. It has been shown that this method has a comparable accuracy for wave simulation to Boussinesq-type approaches and a better computing efficiency.

In this paper, a one-dimensional depth-integrated non-hydrostatic pressure wave model for wave propagation, breaking and run-up is developed based on the numerical method proposed by Stelling and Duinmeijer. In this numerical method, the non-conservative form of Navier-Stokes equation is solved for either momentum conservation or energy head conservation by applying different advection approximation methods. The method is, therefore, able to handle rapidly varied water flows (such as wave breaking) in wide range of Froude numbers. When wave run-up is concerned, wetting and drying treatment plays a key role for many numerical models. The wet & dry handling approach in the method is simple, efficient and capable of reserving positive water depth.

In this non-hydrostatic wave model development, the fractional time step method is adopted. The shallow water equations without non-hydrostatic pressure terms are solved for approximation of velocity; a tri-diagonal equation for non-hydrostatic pressure terms is then solved, and the approximate velocity is corrected by non-hydrostatic pressure terms. The free surface elevation is calculated by the depth-averaged continuity equation to satisfy global mass conservation. This model will be validated by an analytical solution and several benchmark wave dynamics test cases; it is anticipated the model can predict wave breaking and run-up processes effectively.

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