Discontinuous Galerkin formulation for 2D hydrodynamic modelling: Trade-offs between theoretical complexity and practical convenience

Second-order discontinuous Galerkin flood model: Comparison with industry-standard finite volume models

“…relative to a instead of analysing all local evaluations at the four Gaussian points (see Fig. 1) spanning the full piecewise-planar solution (Kesserwani et al, 2018). This measure for dry element detection is consistent with the way dry elements are detected in FV-based approaches.…”

“…It has been demonstrated to reduce the runtime cost per element by 2.6 times compared to a standard DG2 solver while preserving second-order accuracy (Kesserwani et al, 2018). In this section, this DG2 solver (Sec.…”

“…Both limits at for are equal, , as Eq. 3ensures the continuity property (Kesserwani et al, 2018). Dummy limits that are depth-positivity preserving, denoted with the '*' symbol, are reconstructed for the components of the flow vector, as: (Kesserwani et al, 2008).…”

Modeling Swash Zone Hydrodynamics Using Discontinuous Galerkin Finite-Element Method

“…The DGFEM has been shown to reasonably accurately simulate solutions for some wetting/drying flows: the solution for a periodic, non-breaking wave on a beach of Carrier and Greenspan (1958) (see Bunya et al 2009); the transient solution of Carrier and Greenspan (1958) (see Duran et al 2013;Duran and Marche 2014); the case of inundation of a tsunami (solitary wave) on a bay due to Zelt (1986) (see Duran and Marche 2014). DGFEM has also been shown to simulate accurately a 2D solution for a wetting/drying flow in a parabolic basin: the periodic, curved-surface solution of Thacker (1981) (see Bunya et al 2009;Ern et al 2008;Karna et al 2011;Kesserwani et al 2018;solution of Thacker (1981) (see Marras et al 2018;Kesserwani and Liang 2010); a revolving, 2D flat-surface solution of Thacker (1981) (see Duran et al 2013). These solutions, though not swash flows, are demanding (particularly the less well-studied latter), and therefore a good test of robustness of the modelling, particularly if velocities are examined.…”

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

“…This curse of dimensionality is commonly alleviated by exploiting the localised multiscale nature of wavelets: dynamic adaptivity can be implemented via multiresolution analysis (Le Maître et al, 2004b;Tryoen et al, 2012;, or the wavelet basis can be truncated to remove basis functions representing fine-scale cross-dependencies (Le Maître et al, 2004a). Basis truncation has been proven to preserve robustness measures in the deterministic case for a discontinuous Galerkin hydrodynamic model (Kesserwani et al, 2018), but the impact of truncation has yet to be studied for probabilistic hydrodynamic modelling.…”