Numerical simulation of coastal flows in open multiply-connected irregular domains

Abstract

We develop a numerical method for the simulation of coastal flows in multiply-connected domains with irregular boundaries that may contain both closed and open segments. The governing equations are the shallow-water model. Our method involves splitting of the original nonlinear operator by physical processes and by coordinates. Specially constructed finite-difference approximations provide second-order unconditionally stable schemes that conserve the mass and the total energy of the discrete inviscid unforced shallow-water system, while the potential enstrophy results to be bounded, oscillating in time within a narrow range. This allows numerical simulation of coastal flows adequate both from the mathematical and physical standpoints. Several numerical experiments, including those with complex boundaries, demonstrate the skilfulness of the method.