(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models

Wavelet-based local mesh refinement for rainfall–runoff simulations

“…For the constant topographic slope, the slope-based criterion predicts uniform refinement at level (6), just one level below L max = (7). Similar behavior is reported in [18] for a dam break over sloped bed. In contrast, the curvature-based refinement criterion predicts no refinement at all, which implies that in the absence of curvature, the curvature-based refinement criterion is not fit for purpose.…”

“…In this work, M s is constructed such that the perturbation error representing the deviation relative to M [12] is forced to remain below a user-specified error threshold ε. Performing multiresolution analysis to predict M s has been applied in a 1D × 1D manner using the Haar wavelet, by following the procedure reported in [18].…”

“…Starting from M , the maximum number of refinement levels L max is assigned in order to perform multiresolution analysis to predict the refinement levels of M s . A suitable choice of ε is accepted to be proportional to the finest feature that needs capturing in the modeling [12,18], which is here the finest resolution on M . The coarsest length of mesh resolution on M s relative to Ω is denoted by ∆x, which is chosen such that ∆x = W if W < L, or otherwise it is set to ∆x = L. A cell size on the mesh M is related to the coarsest mesh size ∆x by L max dyadic subdivision.…”

Probabilistic Godunov-type hydrodynamic modelling under multiple uncertainties: robust wavelet-based formulations

“…This lake-at-rest test (Sharifian et al, 2018) was initially used to verify the well-balancedness of deterministic models for various topographic shapes and steepness levels in the presence of wet/dry zones and fronts. Under a lake-at-rest, an initially still water level should be preserved indefinitely without generating spurious non-zero discharge flow, which is achieved by the underlying deterministic finite volume discretisation (Kesserwani et al, 2019). To verify that well-balancedness is preserved by the intrusive model, a probabilistic variant of this test is proposed by perturbing the initial water elevation and topography so that both are uncertain.…”

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

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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.

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