Kesserwani, G. and Liang, Q. (2014) RKDG2 shallow-water solver on non-uniform grids with local time steps: Application to 1D and 2D hydrodynamics. Applied Mathematical Modelling, 39 (3-4). pp. 1317-1340. ISSN 1872-8480
Abstract
This paper investigates local time stepping (LTS) with the RKDG2 (second-order Runge–Kutta Discontinuous Galerkin) non-uniform solutions of the inhomogeneous SWEs (shallow water equations) with source terms. A LTS algorithm – recently designed for homogenous hyperbolic PDE(s) – is herein reconsidered and improved in combination with the RKDG2 shallow-flow solver (LTS-RKDG2) including topography and friction source terms as well as wetting and drying. Two LTS-RKDG2 schemes that adapt 3 and 4 levels of LTSs are configured on 1D and/or 2D (quadrilateral) non-uniform meshes that, respectively, adopt 3 and 4 scales of spatial discretization. Selected shallow water benchmark tests are used to verify, assess and compare the LTS-RKDG2 schemes relative to their conventional Global Time Step RKDG2 alternatives (GTS-RKDG2) considering several issues of practical relevance to hydraulic modelling. Results show that the LTS-RKDG2 models could offer (depending on both the mesh setting and the features of the flow) comparable accuracy to the associated GTS-RKDG2 models with a savings in runtime of up to a factor of 2.5 in 1D simulations and 1.6 in 2D simulations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 Elsever. This is an author produced version of a paper subsequently published in Applied Mathematical Modelling. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 29 Jan 2015 13:11 |
Last Modified: | 26 Mar 2018 18:10 |
Published Version: | http://dx.doi.org/10.1016/j.apm.2014.08.009 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.apm.2014.08.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:81768 |