Three-dimensional shallow water system: A relaxation approach

Liu, Xin; Mohammadian, Abdolmajid; Sedano, Julio ngel Infante; Kurganov, Alexander

doi:10.1016/j.jcp.2016.12.030

Cited by 6 publications

(3 citation statements)

References 53 publications

(109 reference statements)

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“…This has been observed in multiple studies like Liang and Marche 44 and Liu et al. 27 The vertical variation of the horizontal velocity at a section x = 22 m, for temporal instances of 3, 10, 40, and, 60 s are shown in Figure 13.…”

Section: Scenario Ivasupporting

confidence: 64%

“…This has been usually attributed to the process of downstream moving front colliding with a wave falling upstream from the top of the sill, and thus the hydrostatic assumption may not be exactly satisfied. This has been observed in multiple studies like Liang and Marche 44 and Liu et al 27 . The vertical variation of the horizontal velocity at a section

x=22

m, for temporal instances of

3,\kern0.3em 10,\kern0.3em 40,\kern0.3em \mathrm{and},\kern0.3em 60\;\mathrm{s}

are shown in Figure 13.…”

Section: Model Testssupporting

confidence: 64%

“…However, the validation of the models with the experimental data is limited. Specific comparison with the full‐scale models has been done for numerical tests in Audusse et al 2 and limited experimental comparison has been made in Liu et al 27 . The testing of benchmark experimental cases for the occurrence of specialized flow features needs to be performed extensively to highlight the capabilities of the approach in field‐scale modeling of environmental phenomena.…”

Section: Introductionmentioning

confidence: 99%

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Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

Bhat,

Pahar

2023

Numerical Methods in Fluids

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The study of multilayered shallow water equations has developed from a consideration of immiscible layers as a vertical mesh to the layer bounds as imaginary extremes for vertical integration of the flow equations. In the current work, a quasi three‐dimensional flow model has been developed with the consideration of the spatiotemporal flexibility/variability of the pervious vertical discretization/layer ratios. Thus, in principle, vertical layering offers a nonuniform grid with a temporal variation. The system of equations thus formulated comprises a conservative part and the appended source/sink terms. These source/sink terms pertain to the inter‐layer interactions such as mass/momenta transfer and interfacial stress, which have been treated in a novel implicit form alongwith the subgrid‐scale eddy‐viscosity for interlayer shear. They are integrated into the system through different physical considerations so as to arrive at a well‐balanced numerical scheme in a regular finite volume grid. The model has been validated through the standard test‐cases highlighting the conservation properties and the model's adaptability to uniform and nonuniform vertical meshes alongwith the spatiotemporal transitions of layer ratios, with a specific interest in limiting cases of wet/dry fronts. The increase in layer ratios tends to nearly replicate the full‐scale model results in experimental scenarios at a lesser computational overhead.

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Section: Scenario Ivasupporting

confidence: 64%