(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: Robust 2D approaches

• Published in: Advances in water resources Vol. 144; p. 103693
• Main Authors: Kesserwani, Georges, Sharifian, Mohammad Kazem
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2020
• Subjects: Adaptive multiresolution schemes; Performance analyses and comparisons; Robust and efficient 2D approaches; Scaled discontinuous Galerkin and finite volume hydraulic models; Performance analyses and comparisons; Scaled discontinuous Galerkin and finite volume hydraulic models; Adaptive multiresolution schemes; Robust and efficient 2D approaches
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2020.103693

•Second-order discontinuous Galerkin (DG2) solver with well-balanced piecewise-planar solutions adopted as a reference scheme.•Two approaches for multiwavelet (MW) adaptivity are tailored to the DG2 solver to form a robust and efficient MWDG2 scheme.•An HFV1 scheme is formed using the Haar wavelet to adapt piecewise-constant solutions of the first-order finite volume (FV1) solver.•MWDG2 and HFV1 schemes robustly handle wet-dry fronts across very steep bed-slopes.•MWDG2 can achieve the accuracy of DG2 but can be up to 15X more efficient than FV1 for 2D hydraulic modelling. 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.