fluids Article A Near-Shore Linear Wave Model with the Mixed Finite Volume and Finite Difference Unstructured Mesh Method Yong G. Lai 1,* and Han Sang Kim 2 1 Technical Service Center, U.S. Bureau of Reclamation, Denver, CO 80225, USA 2 Bay-Delta Office, California Department of Water Resources, Sacramento, CA 95814, USA;
[email protected] * Correspondence:
[email protected]; Tel.: +1-303-445-2560 Received: 5 October 2020; Accepted: 1 November 2020; Published: 5 November 2020 Abstract: The near-shore and estuary environment is characterized by complex natural processes. A prominent feature is the wind-generated waves, which transfer energy and lead to various phenomena not observed where the hydrodynamics is dictated only by currents. Over the past several decades, numerical models have been developed to predict the wave and current state and their interactions. Most models, however, have relied on the two-model approach in which the wave model is developed independently of the current model and the two are coupled together through a separate steering module. In this study, a new wave model is developed and embedded in an existing two-dimensional (2D) depth-integrated current model, SRH-2D. The work leads to a new wave–current model based on the one-model approach. The physical processes of the new wave model are based on the latest third-generation formulation in which the spectral wave action balance equation is solved so that the spectrum shape is not pre-imposed and the non-linear effects are not parameterized. New contributions of the present study lie primarily in the numerical method adopted, which include: (a) a new operator-splitting method that allows an implicit solution of the wave action equation in the geographical space; (b) mixed finite volume and finite difference method; (c) unstructured polygonal mesh in the geographical space; and (d) a single mesh for both the wave and current models that paves the way for the use of the one-model approach.