2015
DOI: 10.1002/fld.4005
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Contradiction between the C‐property and mass conservation in adaptive grid based shallow flow models: cause and solution

Abstract: SummaryWhen performing shallow flow simulations on adaptive grids, the C‐property (i.e. conservation property) and the mass conservation may not be simultaneously preserved, that is, either C‐property or mass conservation is likely to be violated following grid refining or coarsening. The cause of such a contradiction is analyzed in detail in this work, which essentially links to the reconstruction of bed and flow information in those newly created cells during grid adaptation. An effective approach is subsequ… Show more

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Cited by 14 publications
(6 citation statements)
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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%
See 1 more Smart Citation
“…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%
“…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%
“…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%