Contradiction between the C‐property and mass conservation in adaptive grid based shallow flow models: cause and solution

Liang, Qiuhua; Hou, Jingming; Xia, Xilin

doi:10.1002/fld.4005

Cited by 14 publications

(6 citation statements)

References 41 publications

(63 reference statements)

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“…The use of multiresolution analysis makes it possible to readily overcome at least two major limitations of classical adaptive mesh refinement methods (e.g. Li, 2010;Liang, 2012;Kesserwani and Liang, 2012a;Zhou et al, 2013;Liang et al, 2015). Firstly, it unconditionally allows any gap in resolution level across two adjacent sub-elements (Caviedes-Voullième et al, 2020), as opposed to standard quadtree approaches that are constrained by the 2:1 rule (Liang, 2012).…”

Section: Update Of the Dg2 Modes On G A C (T)mentioning

confidence: 99%

“…As the initial free-surface elevation and zero discharges do not vary in time, the adaptive grids are solely selected according to the features of the terrain blocks. This allows to also investigate the potential of the adaptive well-balanced solvers for use as multiresolution grid generators (Liang et al, 2015;Hou et al, 2018). Fig.…”

Section: Lake-at-rest Over Terrain Blocks With Wet-dry Zones and Frontsmentioning

confidence: 99%

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

Kesserwani

Sharifian

2020

Advances in Water Resources

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Multiwavelets (MW) enable the compression, analysis and assembly of model data on a multiresolution grid withinGodunov-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.

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Section: Update Of the Dg2 Modes On G A C (T)mentioning

confidence: 99%

Section: Lake-at-rest Over Terrain Blocks With Wet-dry Zones and Frontsmentioning

confidence: 99%

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

Kesserwani

Sharifian

2020

Advances in Water Resources

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“…25 Moreover, most of the available AMR developments lack a general adaptivity sensor, so that they either need separate criteria for refinement/coarsening 26,27 or problem specific criteria 28,29 or are reported to be highly dependent on the type of refinement criteria. 24,[31][32][33] Multiscale methods based on the multiresolution analysis (MRA) of wavelets provide an alternative that can preserve the quality of numerical methods on adaptive meshes. 24,[31][32][33] Multiscale methods based on the multiresolution analysis (MRA) of wavelets provide an alternative that can preserve the quality of numerical methods on adaptive meshes.…”

Section: Introductionmentioning

confidence: 99%

“…30 In addition, deploying a classical AMR method dictates extra corrections in the numerical scheme to address the loss of well-balancedness property for the case of the NSW equations. 24,[31][32][33] Multiscale methods based on the multiresolution analysis (MRA) of wavelets provide an alternative that can preserve the quality of numerical methods on adaptive meshes. [34][35][36][37][38] Theoretical analyses show that only one error threshold value is needed with this category of adaptive solvers in order to bound the accumulated errors and preserve the accuracy of the reference uniform solver at the finest resolution grid.…”

mentioning

confidence: 99%

Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi equations

Sharifian

Hassanzadeh

Kesserwani

et al. 2019

Numerical Methods in Fluids

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Summary This paper presents a multiresolution discontinuous Galerkin (DG) scheme for the adaptive solution of Boussinesq‐type equations. The model combines multiwavelet (MW)–based grid adaptation with a DG solver based on the system of fully nonlinear and weakly dispersive Green‐Naghdi (GN) equations. The key feature of the adaptation procedure is to conduct a multiresolution analysis using MWs on a hierarchy of nested grids to improve the efficiency of the reference DG scheme on a uniform grid by computing on a locally refined adapted grid. This way, the local resolution level will be determined by manipulating MW coefficients controlled by a single user‐defined threshold value. The proposed adaptive multiwavelet DG solver for GN equations is assessed using several benchmark problems related to wave propagation and transformation in nearshore areas. The numerical results demonstrate that the proposed scheme retains the accuracy of the reference scheme, while significantly reducing the computational cost.

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“…This case has been extensively used for validation of shallow water solvers, for example (Aureli et al, 2008;Dazzi et al, 2018;Liang et al, 2015;Murillo and García-Navarro, 2010;Vacondio et al, 2014;Zhao et al, 2019), because of its rather complex Period T = 2.242851 s 2D nature and the presence of moving wet/dry fronts. The topography is again given by Equation 8with the same choice of parameters and discretisation as before.…”

mentioning

confidence: 99%

SERGHEI (-SWE) v1.0: a performance portable HPC shallow water solver for hydrology and environmental hydraulics

Caviedes‐Voullième¹,

Morales-Hernändez

Norman

et al. 2022

Preprint

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Abstract. The Simulation Environment for Geomorphology, Hydrodynamics and Ecohydrology in Integrated form (SERGHEI) is a multi-dimensional, multi-domain and multi-physics model framework for environmental and landscape simulation, designed with an outlook towards Earth System Modelling. It aims to provide a modelling environment for hydrodynamics, ecohydrology, morphodynamics, and, most importantly, interactions and feedbacks among such processes at different levels of complexity and across spatiotemporal scales. The small scale feedbacks and interactions, which warrant high resolution, can result in emergent behaviours manifesting at larger scales, thus warranting large model domains. At the core of SERGHEI's technical innovation is its HPC implementation, built from scratch on the Kokkos portability layer. Consequently, SERGHEI achieves performance-portability from personal computers to top HPC systems, including GPU-based and heterogeneous systems. SERGHEI relies Kokkos to handle memory spaces, thread management and execution policies for the required backend programming models. In this work we explore combinations of MPI and Kokkos using OpenMP and CUDA backends. In this contribution, we introduce the SERGHEI model framework, and present with detail its first operational module for solving shallow water equations (SERGHEI-SWE). This module is designed to be applicable to hydrological, environmental and consequently Earth System Modelling problems, but also to classical engineering problems such as fluvial or urban flood modelling. We also provide evidence of its applicability by testing it against several well-known benchmarks. We also evaluate its performance on several benchmarks and large scale problems. Finally, SERGHEI-SWE is evaluated in terms of scaling (on several TOP500 HPC systems).

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Contradiction between the C‐property and mass conservation in adaptive grid based shallow flow models: cause and solution

Cited by 14 publications

References 41 publications

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

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

Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi equations

SERGHEI (-SWE) v1.0: a performance portable HPC shallow water solver for hydrology and environmental hydraulics

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