A Highly Efficient Numerical Method for Rotating Oceanographic Flows Modeled by Saint-Venant System with Coriolis Forces (Communications in Computational Physics, 2019)
In order to overcome the strong limitation of the computational cost forclassic explicit schemes in quasi-geostrophic limit typically involved in oceanographicflows, in this study, a highly efficient numerical method for rotating oceanographicflows modeled by Saint-Venant system with Coriolis forces is developed. To efficientlydeal with the rotating flows in the low Rossby and Froude number regime, the coreidea is splitting fast varying flux terms into stiff and non-stiff parts, and implicitly approximating the fast dynamic waves using central difference method with an iterationalgorithm and explicitly approximating slow dynamic waves using a finite-volume hyperbolic solver with minmod limiter. The proposed approach has a second order convergence rate in the quasi-geostrophic limit. The temporal evolution is approximatedusing a high-order implicit-explicit Runge-Kutta method. The proposed semi-implicitscheme is proved to be uniformly asymptotically consistent in the quasi-geostrophiclimit when Froude and Rossby numbers→0. The proposed numerical methods arefinally verified by numerical experiments of rotating shallow flows. The tests showthat the proposed numerical scheme is stable and accurate with any grid size with lowRossby and Froude numbers, which leads to significant reduction of the computationalcost comparing with classic explicit schemes.