Elliptic Harbor Wave Model with Perfectly Matched Layer and Exterior Bathymetry Effects

Author (s): Modesto, D., Fernández-Méndez, S., and Huerta, A.
Journal: Journal of Waterway, Port, Coastal, and Ocean Engineering

Volume: 142, Issue 5
Date: 2016

Standard strategies for dealing with the Sommerfeld condition in elliptic Mild-Slope models require strong assumptions on the wave field in the region exterior to the computational domain. More precisely, constant bathymetry along (and beyond) the open boundary, and parabolic-approximations based boundary conditions are usually imposed. In general, these restrictions require large computational domains, implying higher costs for the numerical solver. An alternative method for coastal/harbor applications is proposed here. This approach is based on a Perfectly Matched Layer (PML) that incorporates the effects of the exterior bathymetry. The model only requires constant exterior depth in the alongshore direction, a commonly used approach for idealizing the exterior bathymetry in elliptic models. In opposition to standard open boundary conditions for Mild-Slope models, the features of the proposed PML approach include: (a) completely non-collinear coastlines, (b) better representation of the real unbounded domain using two different lateral sections to define the exterior bathymetry, and (c) generation of reliable solutions for any incoming wave direction in a small computational domain. Numerical results of synthetic tests demonstrate that solutions are not significantly perturbed when open boundaries are placed close to the area of interest. In more complex problems, this provides important performance improvements in computational time as shown for a real application of harbor agitation.



@article {DM-MFH:16,
        Author = {David Modesto and Sonia Fern\'andez-M\'endez and Antonio Huerta},
        Title = {Elliptic Harbor Wave Model with Perfectly Matched Layer and Exterior Bathymetry Effects},
        Fjournal = {Journal of Waterways, Port, Coastal, and Ocean Engineering},
        Journal = {J. Waterw. Port Coast. Ocean Eng.},
        Volume = {142},
        Number = {5},
        Pages = {04016008},
        Year = {2016},
        Doi = {10.1061/(ASCE)WW.1943-5460.0000336},
        URL = {http://dx.doi.org/10.1061/(ASCE)WW.1943-5460.0000336},
        eprint = {http://dx.doi.org/10.1061/(ASCE)WW.1943-5460.0000336}