Thick interface coupling technique for weakly dispersive models of waves

Abstract

The primary focus of this work is the coupling of dispersive free-surface flow models through the utilization of a thick interface coupling technique. The initial step involves introducing a comprehensive framework applicable to various dispersive models, demonstrating that classical weakly dispersive models are encompassed within this framework. Next, a thick interface coupling technique, well-established in hyperbolic framework, is applied. This technique enables the formulation of unified models across different subdomains, each corresponding to a specific dispersive model. The unified model preserves the conservation of mechanical energy, provided it holds for each initial dispersive model. We propose a numerical scheme that preserve the projection structure at the discrete level and as a consequence is entropy-satisfying when the continuous model conserve the mechanical energy. We perform a deep numerical analysis of the waves reflected by the interface. Finally, we illustrate the usefulness of the method with two applications known to pose problems for dispersive models, namely the imposition of a time signal as a boundary condition or the imposition of a transparent boundary condition, and wave propagation over a discontinuous bathymetry.