Sharifian, M.K., Kesserwani, G. and Hassanzadeh, Y. (2018) A discontinuous Galerkin approach for conservative modelling of fully nonlinear and weakly dispersive wave transformations. Ocean Modelling, 125. pp. 61-79. ISSN 1463-5003
Abstract
This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modelling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2018 Elsevier. This is an author produced version of a paper subsequently published in Ocean Modelling. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Green–Naghdi equations; Second-order Discontinuous Galerkin; Well-balanced scheme with dispersive terms; Nearshore wave processes |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/R007349/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Apr 2018 10:46 |
Last Modified: | 30 Mar 2019 01:42 |
Published Version: | https://doi.org/10.1016/j.ocemod.2018.03.006 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.ocemod.2018.03.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:129289 |