Computational Time Improvement for Some Shallow Water Finite Volume Models Applying Parallelization and Optimized Small Matrix Computations.

Author(s):  
M. J. Castro ◽  
J. A. García ◽  
J. M. González ◽  
C. Parés
Atmosphere ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 179 ◽  
Author(s):  
Yuanfu Xie

Z-grid finite volume models conserve all-scalar quantities as well as energy and potential enstrophy and yield better dispersion relations for shallow water equations than other finite volume models, such as C-grid and C-D grid models; however, they are more expensive to implement. During each time integration, a Z-grid model must solve Poisson equations to convert its vorticity and divergence to a stream function and velocity potential, respectively. To optimally utilize these conversions, we propose a model in which the stability and possibly accuracy on the sphere are improved by introducing more stencils, such that a generalized Z-grid model can utilize longer time-integration steps and reduce computing time. Further, we analyzed the proposed model’s dispersion relation and compared it to that of the original Z-grid model for a linearly rotating shallow water equation, an important property for numerical models solving primitive equations. The analysis results suggest a means of balancing stability and dispersion. Our numerical results also show that the proposed Z-grid model for a shallow water equation is more stable and efficient than the original Z-grid model, increasing the time steps by more than 1.4 times.


Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 750
Author(s):  
Antonio Pasculli ◽  
Jacopo Cinosi ◽  
Laura Turconi ◽  
Nicola Sciarra

The current climate change could lead to an intensification of extreme weather events, such as sudden floods and fast flowing debris flows. Accordingly, the availability of an early-warning device system, based on hydrological data and on both accurate and very fast running mathematical-numerical models, would be not only desirable, but also necessary in areas of particular hazard. To this purpose, the 2D Riemann–Godunov shallow-water approach, solved in parallel on a Graphical-Processing-Unit (GPU) (able to drastically reduce calculation time) and implemented with the RiverFlow2D code (version 2017), was selected as a possible tool to be applied within the Alpine contexts. Moreover, it was also necessary to identify a prototype of an actual rainfall monitoring network and an actual debris-flow event, beside the acquisition of an accurate numerical description of the topography. The Marderello’s basin (Alps, Turin, Italy), described by a 5 × 5 m Digital Terrain Model (DTM), equipped with five rain-gauges and one hydrometer and the muddy debris flow event that was monitored on 22 July 2016, were identified as a typical test case, well representative of mountain contexts and the phenomena under study. Several parametric analyses, also including selected infiltration modelling, were carried out in order to individuate the best numerical values fitting the measured data. Different rheological options, such as Coulomb-Turbulent-Yield and others, were tested. Moreover, some useful general suggestions, regarding the improvement of the adopted mathematical modelling, were acquired. The rapidity of the computational time due to the application of the GPU and the comparison between experimental data and numerical results, regarding both the arrival time and the height of the debris wave, clearly show that the selected approaches and methodology can be considered suitable and accurate tools to be included in an early-warning system, based at least on simple acoustic and/or light alarms that can allow rapid evacuation, for fast flowing debris flows.


2021 ◽  
Vol 594 ◽  
pp. 125924
Author(s):  
Janice Lynn Ayog ◽  
Georges Kesserwani ◽  
James Shaw ◽  
Mohammad Kazem Sharifian ◽  
Domenico Bau

2014 ◽  
Vol 55 (13) ◽  
pp. 3587-3612 ◽  
Author(s):  
Rattandeep Singh ◽  
Sandeep Gupta ◽  
S. Raman ◽  
Prodyut Chakraborty ◽  
Puneet Sharma ◽  
...  

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