A mild-slope equation model in multiply connected domains

Abstract Nearshore waves are one of the most important dynamic factors in the nearshore marine environment, and the propagation of waves in nearshore waters has long been a key research topic in the field of coastal engineering. To adapt to complex and variable wave fields, this study modifies the traditional mild-slope equation model (suitable for simply connected computational domains) by constructing island boundary conditions, establishing a numerical simulation model for wave propagation in multiply connected domains where vertical island-like structures exist. The comparison between the numerical solution and analytical solution of the wave field around a cylinder demonstrates the scientific validity and rationality of the proposed model, which can be widely applied to the numerical simulation of wave fields in nearshore waters.