Bottom friction models for shallow water equations: Manning’s roughness coefficient and small-scale bottom heterogeneity

Dyakonova, Tatyana; Хоперсков, А. В.

doi:10.1088/1742-6596/973/1/012032

Cited by 13 publications

(11 citation statements)

References 19 publications

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“…In this approach, the Saint-Venant equations should be written in the form of the Exner equation [7,12,20] which allows simulating the dynamics of soil erosion and sediment movement due to fluid flow. Deformations of the bottom surface in weak currents are accompanied by the formation of structures in the form of ripples, ridges, dunes, etc., which are an important structural element of the bottom, having a significant effect on hydraulic flow resistance [21]. For example, strong currents lead to a significant erosion of the bottom, in particular, a channel can be formed due to the dam break and then rapidly deepens and expands under the influence of increasing of the fluid flow.…”

Section: математическая модельmentioning

confidence: 99%

Application of Graphics Processing Units for Self-Consistent Modelling of Shallow Water Dynamics and Sediment Transport

Khrapov

Хоперсков

2020

Lobachevskii J Math

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In this paper, we describe a numerical algorithm for the self-consistent simulations of surface water and sediment dynamics. The method is based on the original Lagrangian-Eulerian CSPH-TVD approach for solving the Saint-Venant and Exner equations, taking into account the physical factors essential for the understanding of the shallow water and surface soil layer motions, including complex terrain structure and its evolution due to sediment transport. Additional Exner equation for sediment transport has been used for the numerical CSPH-TVD scheme stability criteria definition. By using OpenMP-CUDA and GPUDirect technologies for hybrid computing systems (supercomputers) with several graphic coprocessors (GPUs) interacting with each other via the PCI-E / NVLINK interface we also develop a parallel numerical algorithm for the CSPH-TVD method. The developed parallel version of the algorithm demonstrates high efficiency for various configurations of Nvidia Tesla CPU + GPU computing systems. In particular, maximal speed up is 1800 for a system with four C2070 GPUs compare to the serial version for the CPU. The calculation time on the GPU V100 (Volta architecture) is reduced by 95 times compared to the GPU C2070 (Fermi architecture).

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Section: математическая модельmentioning

confidence: 99%

Application of Graphics Processing Units for Self-Consistent Modelling of Shallow Water Dynamics and Sediment Transport

Khrapov

Хоперсков

2020

Lobachevskii J Math

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“…where m f is a positive constant, and S a (W ) = (S a x (W ), S a y (W )) parameterizes the friction between the fluid and the non-erodible bottom and is given by a Manning law (Dyakonova and Khoperskov, 2018):…”

Section: Simplified Two-layer Savage-hutter-type Modelmentioning

confidence: 99%

The Lituya Bay landslide-generated mega-tsunami – numerical simulation and sensitivity analysis

González‐Vida

Macías

Castro

et al. 2019

Nat. Hazards Earth Syst. Sci.

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Abstract. The 1958 Lituya Bay landslide-generated mega-tsunami is simulated using the Landslide-HySEA model, a recently developed finite-volume Savage–Hutter shallow water coupled numerical model. Two factors are crucial if the main objective of the numerical simulation is to reproduce the maximal run-up with an accurate simulation of the inundated area and a precise recreation of the known trimline of the 1958 mega-tsunami of Lituya Bay: first, the accurate reconstruction of the initial slide and then the choice of a suitable coupled landslide–fluid model able to reproduce how the energy released by the landslide is transmitted to the water and then propagated. Given the numerical model, the choice of parameters appears to be a point of major importance, which leads us to perform a sensitivity analysis. Based on public domain topo-bathymetric data, and on information extracted from the work of Miller (1960), an approximation of Gilbert Inlet topo-bathymetry was set up and used for the numerical simulation of the mega-event. Once optimal model parameters were set, comparisons with observational data were performed in order to validate the numerical results. In the present work, we demonstrate that a shallow water type of model is able to accurately reproduce such an extreme event as the Lituya Bay mega-tsunami. The resulting numerical simulation is one of the first successful attempts (if not the first) at numerically reproducing, in detail, the main features of this event in a realistic 3-D basin geometry, where no smoothing or other stabilizing factors in the bathymetric data are applied.

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“…Such an approach can essentially simplify solutions to complex real-world case study tasks of hydrodynamics [13]. Some additional examples of recent pieces of literature relating to the use of 1D and 2D flow models of shallow water are also highlighted in [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Data arrangements to train an artificial neural network within solving the tasks for calculating the Chézy roughness coefficient under uncertainty of parameters determining the hydraulic resistance to flow in river channels

Khodnevych¹,

Stefanyshyn²

2022

esanr

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Hydraulic calculations and mathematical modelling of open flows in river channels keep still being among the most topical hydro-engineering today’s problems in terms of practice. While solving them, independently on the research topic and purpose, and methods used, a number of simplifications and assumptions are usually accepted and applied. Moreover, there is a range of methodological, structural, and parametric uncertainties, which to be overcome require complex empirical pre-researches. First of all, these uncertainties relate to assessing hydraulic resistances and establishing numerical characteristics of them, which depend on many factors varying spatially and temporally.One of the most frequently used integral empirical characteristics expressing the hydraulic resistance to open flows in river channels is the Chézy roughness coefficient C. However, despite a large number of empirical and semi-empirical formulas and dependencies to calculate the Chézy coefficient, there is no ideal way or method to determine this empirical characteristic unambiguously. On the one hand, while opting for an appropriate formula to calculate the Chézy coefficient, we need to take into account practical experience based on comprehensive options analysis considering different empirical equations used alternatively to represent the hydraulic resistance to open flows. On the other hand, the fullness and comprehensiveness of field researches of numerous hydro-morphological factors and parameters characterizing various aspects of the hydraulic resistance to open flows can also have an essential role. In particular, the accuracy assessment of the Chézy coefficient computing based on field data, despite methods and formulas, indicates that the accuracy of field measurements of the parameters included in selected formulas largely determines the relative error of such calculations.This paper deals with the problem of data arrangements and the development of general rules for the formation of training and test samples of data to train artificial neural networks being elaborated to compute the Chézy coefficient taking into account the parametric uncertainty of data on the hydro-morphological factors and parameters characterizing the hydraulic resistance in river channels. The problem is solved on the example of an artificial neural network of direct propagation with one hidden layer and a sigmoid logistic activation function.

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Bottom friction models for shallow water equations: Manning’s roughness coefficient and small-scale bottom heterogeneity

Cited by 13 publications

References 19 publications

Application of Graphics Processing Units for Self-Consistent Modelling of Shallow Water Dynamics and Sediment Transport

Application of Graphics Processing Units for Self-Consistent Modelling of Shallow Water Dynamics and Sediment Transport

The Lituya Bay landslide-generated mega-tsunami – numerical simulation and sensitivity analysis

Data arrangements to train an artificial neural network within solving the tasks for calculating the Chézy roughness coefficient under uncertainty of parameters determining the hydraulic resistance to flow in river channels

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