Comparison of Wetting and Drying Between a RKDG2 Method and Classical FV Based Second-Order Hydrostatic Reconstruction

Vater, Stefan; Beisiegel, Nicole; Behrens, Jörn

doi:10.1007/978-3-319-57394-6_26

Cited by 5 publications

(5 citation statements)

References 17 publications

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“…The computational model to generate the tsunami scenario is StormFlash2D, which solves the nonlinear shallow water equations using an explicit Runge-Kutta discontinuous Galerkin discretization combined with a sophisticated wetting and drying treatment for the inundation at the coast (Vater and Behrens 2014;Vater et al 2015Vater et al , 2017. A tsunami is triggered by a (possibly time-dependent) perturbation of the discrete bathymetry.…”

Section: Earthquake-tsunami Coupled Modelingmentioning

confidence: 99%

Coupled, Physics-Based Modeling Reveals Earthquake Displacements are Critical to the 2018 Palu, Sulawesi Tsunami

Ulrich

Vater

Madden

et al. 2019

Pure Appl. Geophys.

127

125

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The September 2018, M w 7.5 Sulawesi earthquake occurring on the Palu-Koro strike-slip fault system was followed by an unexpected localized tsunami. We show that direct earthquakeinduced uplift and subsidence could have sourced the observed tsunami within Palu Bay. To this end, we use a physics-based, coupled earthquake-tsunami modeling framework tightly constrained by observations. The model combines rupture dynamics, seismic wave propagation, tsunami propagation and inundation. The earthquake scenario, featuring sustained supershear rupture propagation, matches key observed earthquake characteristics, including the moment magnitude, rupture duration, fault plane solution, teleseismic waveforms and inferred horizontal ground displacements. The remote stress regime reflecting regional transtension applied in the model produces a combination of up to 6 m left-lateral slip and up to 2 m normal slip on the straight fault segment dipping 65 East beneath Palu Bay. The time-dependent, 3D seafloor displacements are translated into bathymetry perturbations with a mean vertical offset of 1.5 m across the submarine fault segment. This sources a tsunami with wave amplitudes and periods that match those measured at the Pantoloan wave gauge and inundation that reproduces observations from field surveys. We conclude that a source related to earthquake displacements is probable and that landsliding may not have been the primary source of the tsunami. These results have important implications for submarine strike-slip fault systems worldwide. Physics-based modeling offers rapid response specifically in tectonic settings that are currently underrepresented in operational tsunami hazard assessment.

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Section: Earthquake-tsunami Coupled Modelingmentioning

confidence: 99%

Coupled, Physics-Based Modeling Reveals Earthquake Displacements are Critical to the 2018 Palu, Sulawesi Tsunami

Ulrich

Vater

Madden

et al. 2019

Pure Appl. Geophys.

127

125

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“…Furthermore, DG methods better approximate the near-shore velocity in certain situations. 7,10 While there is theoretically no barrier to extend the DG method to higher-order accuracy, several practical aspects impede this endeavor. For the time discretization, appropriate integration schemes (such as strong stability preserving methods) have to be applied, which maintain crucial properties of the governing equations.…”

Section: Introductionmentioning

confidence: 99%

“…Concerning coastal modeling, Kesserwani and Wang 7 argue that the extra complexity associated with DG discretizations pays off by providing higher-quality solution behavior on very coarse meshes. Furthermore, DG methods better approximate the near-shore velocity in certain situations 7,10 .…”

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confidence: 99%

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A limiter‐based well‐balanced discontinuous Galerkin method for shallow‐water flows with wetting and drying: Triangular grids

Vater

Beisiegel

Behrens

2019

Numerical Methods in Fluids

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Summary A novel wetting and drying treatment for second‐order Runge‐Kutta discontinuous Galerkin methods solving the nonlinear shallow‐water equations is proposed. It is developed for general conforming two‐dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a nondestructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well balancing with an innovative velocity‐based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme, even on unstructured grids, and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near‐realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, superlinear convergence, mass conservation, well balancedness, and stability are verified.

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“…( 2019 ) conclude that numerical issues in these problematic regions may originate from simplifying the shallow water equations (SWEs) while discretizations of the full SWEs are not subject to these limitations. Second‐order finite‐volume (FV) schemes (Audusse & Bristeau, 2005 ; Hou et al., 2015 ; Murillo et al., 2008 ) or discontinuous Galerkin (DG) schemes (Kesserwani et al., 2008 ; Shaw et al., 2021 ; Vater et al., 2017 ) offer additional accuracy, however at the cost of higher runtimes. For large‐scale river flooding, the usage of a second‐order scheme instead of its first‐order counterpart may be preferrable in view of the workload–accuracy tradeoff (Horváth et al., 2020 ).…”

Section: Introductionmentioning

confidence: 99%

Locally Relevant High‐Resolution Hydrodynamic Modeling of River Floods at the Regional Scale

Buttinger‐Kreuzhuber

Waser

Cornel

et al. 2022

Water Resources Research

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This paper deals with the simulation of inundated areas for a region of 84,000 km 2 from estimated flood discharges at a resolution of 2 m. We develop a modeling framework that enables efficient parallel processing of the project region by splitting it into simulation tiles. For each simulation tile, the framework automatically calculates all input data and boundary conditions required for the hydraulic simulation on‐the‐fly. A novel method is proposed that ensures regionally consistent flood peak probabilities. Instead of simulating individual events, the framework simulates effective hydrographs consistent with the flood quantiles by adjusting streamflow at river nodes. The model accounts for local effects from buildings, culverts, levees, and retention basins. The two‐dimensional full shallow water equations are solved by a second‐order accurate scheme for all river reaches in Austria with catchment sizes over 10 km 2 , totaling 33,380 km. Using graphics processing units (GPUs), a single NVIDIA Titan RTX simulates a period of 3 days for a tile with 50 million wet cells in less than 3 days. We find good agreement between simulated and measured stage–discharge relationships at gauges. The simulated flood hazard maps also compare well with local high‐quality flood maps, achieving critical success index scores of 0.6–0.79.

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Comparison of Wetting and Drying Between a RKDG2 Method and Classical FV Based Second-Order Hydrostatic Reconstruction

Cited by 5 publications

References 17 publications

Coupled, Physics-Based Modeling Reveals Earthquake Displacements are Critical to the 2018 Palu, Sulawesi Tsunami

Coupled, Physics-Based Modeling Reveals Earthquake Displacements are Critical to the 2018 Palu, Sulawesi Tsunami

A limiter‐based well‐balanced discontinuous Galerkin method for shallow‐water flows with wetting and drying: Triangular grids

Locally Relevant High‐Resolution Hydrodynamic Modeling of River Floods at the Regional Scale

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