A novel coastal wave model with improved nonhydrostatic equations

Waves are one of the essential factors triggering disastrous hazards in coastal and estuary areas. Simulation and understanding of their propagation process from deep water to nearshore are important for management and protection of coastal regions. Development of nonhydrostatic models has received increased attention in recent years and depth-integrated nonhydrostatic models have been widely used in large-scale applications. However, most existing depth-integrated nonhydrostatic models neglect the vertical advection and dissipation terms in the vertical momentum equation and assume linear distribution of pressure and flow velocities. These simplified equations are therefore not able to depict the physical details of certain wave dynamics,  prohibiting the application in wave prediction in relative deep water.

This paper adopts the quadratic polynomials to describe both the pressure and velocity terms to improve the linearity and nonlinearity accuracy of the formulation. As the derived nonhydrostatic wave equations involve only the first- and second-order spatial derivatives and are formulated at a similar frame to the previous depth-integrated models, they can be numerically solved using the standard numerical schemes adopted in the previous models. Specifically, a fractional step method is adopted to divide the numerical solution procedure into the hydrostatic and nonhydrostatic steps. A second-order MUSCL-Hancock Godunov-type scheme is employed in the hydrostatic step to obtain the temporary solution; then a finite difference method is used in the nonhydrostatic step to calculate the hydrodynamic pressure by solving the Poisson's equation to achieve the final numerical solution over a full time step. The proposed model is validated against a series of experiment tests. Higher solution accuracy is confirmed by comparing the simulation results with those produced by existing depth-integrated nonhydrostatic models.

Keywords: Nonhydrostatic Model; Coastal Hazards; Finite-Volume Method; Finite-Difference Method; Wave Propagation