Cellular Automata and Finite Volume solvers converge for 2D shallow flow modelling for hydrological modelling

Caviedes‐Voullième, Daniel; Fernández-Pato, Javier; Hinz, Christoph

doi:10.1016/j.jhydrol.2018.06.021

Cited by 26 publications

(26 citation statements)

References 39 publications

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“…This simplification is traditionally accepted based on the assumption that flooding over plain areas is characterized by slow velocity propagation. Thanks to the simplification of the governing equations, both the KWA and the DWA could reduce the computational times, although some authors have pointed out that the zero inertia approach could be computationally even more expensive than complete dynamic solvers due to a highly constraining stability requirement [5,12,13,[26][27][28][29][30][31][32][33][34][35]. Unfortunately, in areas characterized by the presence of roads, railways or channel embankments, or in urban environments, where the flooding dynamics can be strongly influenced by streets and buildings and the main flow variables change rapidly in space and time, the flood inundation simulations performed with simplified models can give rise to unacceptable approximations [13,36,37].…”

Section: Introductionmentioning

confidence: 99%

“…Conversely, a model based on the complete version of the SWEs can be adopted in any situation and with a high degree of detail (provided that the domain geometry is sufficiently well known) [38]. As many authors state, in fact, strongly hyperbolic flows, such as those characterized by moving shock waves, cannot be accurately solved by applying the zero inertia approach [13,29,30,34,39].…”

Section: Introductionmentioning

confidence: 99%

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A GPU-Accelerated Shallow-Water Scheme for Surface Runoff Simulations

Aureli

Prost

Vacondio

et al. 2020

Water

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The capability of a GPU-parallelized numerical scheme to perform accurate and fast simulations of surface runoff in watersheds, exploiting high-resolution digital elevation models (DEMs), was investigated. The numerical computations were carried out by using an explicit finite volume numerical scheme and adopting a recent type of grid called Block-Uniform Quadtree (BUQ), capable of exploiting the computational power of GPUs with negligible overhead. Moreover, stability and zero mass error were ensured, even in the presence of very shallow water depth, by introducing a proper reconstruction of conserved variables at cell interfaces, a specific formulation of the slope source term and an explicit discretization of the friction source term. The 2D shallow water model was tested against two different literature tests and a real event that recently occurred in Italy for which field data is available. The influence of the spatial resolution adopted in different portions of the domain was also investigated for the last test. The achieved low ratio of simulation to physical times, in some cases less than 1:20, opens new perspectives for flood management strategies. Based on the result of such models, emergency plans can be designed in order to achieve a significant reduction in the economic losses generated by flood events.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A GPU-Accelerated Shallow-Water Scheme for Surface Runoff Simulations

Aureli

Prost

Vacondio

et al. 2020

Water

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“…The popular, alternative strategy of cellular automata modelling involves describing the physics governing fluid flow or sediment transport by means of discrete rules that control water, air and sediment transport processes on the basis of information from surrounding model grid cells (Willgoose et al 1991;Liu and Coulthard 2017). This cellular automata strategies have made it possible to reproduce shallow-water flows for hydrological purposes (Adams et al 2017;Caviedes-Voullième et al 2018), but also to simulate the development of braided streams (Murray and Paola 2003), floodplains (Coulthard and Van De Wiel 2006), sand dunes (Zhang et al 2012), wetland landscape pattern (Williams et al 2016) and river deltas , for evaluating their response to global changes and human drivers. Aside from cellular automata, precipiton methods can be applied for simulating the evolution of a river landscape, given their ability in mimicking self-organized emerging properties of geomorphological systems, from high-resolution braided patterns to drainage network organization (Davy et al 2017).…”

Section: Introductionmentioning

confidence: 99%

On the main components of landscape evolution modelling of river systems

Nones

2020

Acta Geophys.

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Currently, the use of numerical models for reproducing the evolution of river systems and landscapes is part of the day-by-day research activities of fluvial engineers and geomorphologists. However, despite landscape evolution modelling is based on a rather long tradition, and scientists and practitioners are studying how to schematize the processes involved in the evolution of a landscape since decades, there is still the need for improving the knowledge of the physical mechanisms and their numerical coding. Updating past review papers, the present work focuses on the first aspect, discussing six main components of a landscape evolution model, namely continuity of mass, hillslope processes, water flow, erosion and sediment transport, soil properties, vegetation dynamics. The more common schematizations are discussed in a plain language, pointing out the current knowledge and possible open questions to be addressed in the future, towards an improvement of the reliability of such kind of models in describing the evolution of fluvial landscapes and river networks.

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“…When Ulam and von Neumann introduced cellular automata (CAs), they were motivated by biological applications and wanted to create a self-replicating machine, which could be analogous to the human brain and be computationally universal [1,2]. Later, CAs became of interest as models of complex phenomena in various fields of research, such as biology [3], environmental sciences [4], materials science [5], pedestrian dynamics [6], urban transport [7], hydrology [8], and agriculture [9], to name a few. This popularity is due to the fact that CAs reflect the assumption that all laws (physical, economic, sociological, and so on) must result from interactions that are strictly local.…”

Section: Introductionmentioning

confidence: 99%

All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional

Wolnik

Baets

2019

Phys. Rev. E

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A binary number-conserving cellular automaton is a discrete dynamical system that models the movement of particles in a d-dimensional grid. Each cell of the grid is either empty or contains a particle. In subsequent time steps the particles move between the cells, but in one cell there can be at most one particle at a time. In this paper, the von Neumann neighborhood is considered, which means that in each time step a particle can move to an adjacent cell only. It is proven that regardless of the dimension d, all of these cellular automata are trivial, as they are intrinsically one-dimensional. Thus, for given d, there are only 4d + 1 binary number-conserving cellular automata with the von Neumann neighborhood: the identity rule and the shift and traffic rules in each of the 2d possible directions.

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Cellular Automata and Finite Volume solvers converge for 2D shallow flow modelling for hydrological modelling

Cited by 26 publications

References 39 publications

A GPU-Accelerated Shallow-Water Scheme for Surface Runoff Simulations

A GPU-Accelerated Shallow-Water Scheme for Surface Runoff Simulations

On the main components of landscape evolution modelling of river systems

All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional

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