Extension of artificial viscosity technique for solving 2D non-hydrostatic shallow water equations

Abstract

Abstract This study highlights the solution of the 2D non-hydrostatic shallow water equations using an artificial viscosity (AV) technique. The model recently proposed by the first author in Ginting (2017) is extended in this paper by reconstructing the flow variables using the Monotonic Upwind Scheme for Conservation Laws (MUSCL) technique to achieve second-order accuracy and by adding the non-hydrostatic terms, where the Runge–Kutta second-order scheme is used for temporal discretization. To reduce computational time, a novel way is proposed, where the AV technique as well as the non-hydrostatic terms are computed in a hybrid manner, only once per single time step. The solution of the non-hydrostatic terms forms a system of linear equations and the conjugate gradient method is therefore employed to solve it. The results show this technique is robust and accurate for simulating a set of problems of coastal engineering, thus could become a promising method for non-hydrostatic shallow flow applications.