(Multi)wavelet-based Godunov-type simulators of flood inundation: Static versus dynamic adaptivity

Real-world flood simulators often use first-order finite volume (FV1) solvers of the shallow water equations with efficiency enhancements exploiting parallelisation on Graphical Processing Units (GPUs) and the use of static adaptivity on fixed grids. A second-order discontinuous Galerkin (DG2) solver greatly increases the accuracy in the predictions on uniform grids, where it is comparatively costly to run, but its practical utility as an alternative for flood simulations using static adaptivity is not yet assessed. This is also the case for the dynamic adaptivity using the multiresolution analysis (MRA) of the Haar wavelet (HW) scaling FV1 piecewise-constant solutions (HWFV1) and of the smoother Multiwavelets (MWs) that scales DG2 piecewise-planar solutions (MWDG2) to adapt the resolution of their grids over time. Therefore, dynamic MWDG2 and HWFV1 adaptivity is newly explored for practical real-world simulations, to find out when they yield better predictions than static DG2 and FV1 adaptivity. A new GPU implementation is proposed to include dynamic MWDG2 adaptivity to also assess how far GPU parallelisation renders its runtime practically feasible. Dynamic and static adaptivity are assessed for three tests involving slow, gradual to rapid flood flows with analyses of their predictive accuracy and computational costs with reference to uniform grid DG2 simulations at the finest resolution of the digital elevation model (DEM). Findings suggest favouring static FV1 adaptivity for long-duration simulations of slowly to gradually propagating floods and dynamic MWDG2 adaptivity to simulate events driven by rapidly propa-gating flows. On the GPU, dynamic MWDG2 adaptivity is faster than uniform DG2, leading to a higher speedup ratio with higher reduction in the elements on its initial, fixed grid.

Automated summary

Real-world flood simulators often use first-order finite volume (FV1) solvers of the shallow water equations with efficiency enhancements exploiting parallelisation on GPUs and static adaptivity on fixed grids. However, the practical utility of a second-order discontinuous Galerkin (DG2) solver for flood simulations using static adaptivity is not yet assessed. This study explores the dynamic adaptivity using multiresolution analysis (MRA) and wavelets to find out when they yield better predictions than static adaptivity. Findings suggest that static FV1 adaptivity is favored for long-duration simulations of slow to gradual floods, while dynamic MWDG2 adaptivity is suitable for rapidly propagating flows. The proposed GPU implementation shows that dynamic MWDG2 adaptivity is faster than uniform DG2, leading to a higher speedup ratio with reduced grid elements.