Kesserwani, G. and Sharifian, M.K. orcid.org/0000-0002-3150-5162 (2020) (Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: robust 2D approaches. Advances in Water Resources, 144. 103693. ISSN 0309-1708
Abstract
Multiwavelets (MW) enable the compression, analysis and assembly of model data on a multiresolution grid within Godunov-type solvers based on second-order discontinuous Galerkin (DG2) and first-order finite volume (FV1) methods. Multiwavelet adaptivity has been studied extensively with one-dimensional (1D) hydrodynamic models (Kesserwani et al., 2019), revealing that MWDG2 can be 20 times faster than uniform DG2 and 2 times faster than uniform FV1, while preserving the accuracy and robustness of the underlying formulation. The potential of the MWDG2 scheme has yet to be studied for two-dimensional (2D) modelling, but this requires a design that robustly and efficiently solves the 2D shallow water equations (SWE) with complex source terms and wetting and drying. This paper presents a two-dimensional MWDG2 scheme that: (1) adopts a slope-decoupled DG2 solver as a reference scheme, for its ability to deliver well-balanced piecewise-planar solutions shaped by a simplified 3-component basis; and, (2) adapts the multiresolution analysis of multiwavelets for compatibility with the slope-decoupled DG2 basis. A scaled reformulation of slope-decoupled DG2 is presented alongside two multiwavelet approaches that yield MWDG2 schemes with similar properties, and a Haar wavelet FV1 (HFV1) variant for adapting piecewise-constant model data. The performance of the adaptive HFV1 and MWDG2 solvers is explored alongside their uniform counterparts, while analysing their accuracy, efficiency, grid-coarsening ability, reliability in handling wet-dry fronts across steep bed-slopes, and ability to capture features relevant to practical hydraulic modelling. The results indicate a particular multiwavelet approach that allows the MWDG2 scheme to exploit its grid-coarsening ability for the widest range of flow types. Results also indicate that the proposed (multi)wavelet-based adaptive schemes are even more efficient for the 2D case. Accompanying model software is openly available online.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Elsevier Ltd. This is an author produced version of a paper subsequently published in Advances in Water Resources. 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: | Scaled discontinuous Galerkin and finite volume hydraulic models; Adaptive multiresolution schemes; robust and efficient 2D approaches; Performance analyses and comparisons |
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: | 16 Jul 2020 12:11 |
Last Modified: | 20 Jan 2022 14:08 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.advwatres.2020.103693 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:163338 |