A lattice Boltzmann model for the viscous shallow water equations with source terms

Liu, Yu; Chai, Zhenhua; Guo, Xueyi; Shi, Baochang

doi:10.1016/j.jhydrol.2021.126428

Cited by 6 publications

(2 citation statements)

References 43 publications

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“…It uses the two-dimensional finite volume method to solve the shallow water equations in the simulation of two-dimensional surface diffuse flow by using the TVD excitation technique and the Riemann solver to solve the model computationally. The two-dimensional surface model can effectively and accurately simulate the flow of water on complex urban surfaces and provide support for engineering planning and design [ 31 , 33 ]. The shallow water control equations used in the simulation are as follows:

where h is the water depth,

; u is the velocity component in the x-direction, m/s; v is the velocity component in the y-direction;

is the bottom slope component in the x-direction;

is the bottom slope component in the y-direction;

is the friction component in the x-direction;

is the friction component in the y-direction;

is the outflow rate per unit area, m3/s; u 1D is the velocity component of

in the x-direction, m/s;

is the velocity component of

in the y-direction, m/s.…”

Section: Materials and Methodsmentioning

confidence: 99%

Hydrodynamic Modelling and Flood Risk Analysis of Urban Catchments under Multiple Scenarios: A Case Study of Dongfeng Canal District, Zhengzhou

Wei

Zhang

Liu

2022

IJERPH

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In recent years, urban flooding has become an increasingly serious problem, posing a serious threat to socio-economic development and personal safety. In this paper, we consider the Dongfeng Canal area in Zhengzhou City as an example and build a 1D/2D coupled urban flood model using the InfoWorks ICM. This study area uses six scenarios with rainfall return periods of 5 a, 20 a, and 50 a, corresponding to rainfall ephemeris of 1 h and 2 h to assess the flood risk. The results of the study show that (1) The flood depth, inundation duration, and extent of inundation in the study area vary with the return period and rainfall history. Generally, most of the water accumulation is concentrated in the low-lying areas adjacent to the river and near the roadbed. (2) As the rainfall recurrence period and rainfall duration increase, the proportion of overflow at the nodes becomes more pronounced and the overload from the pipe network flows mainly to the overload. (3) The high-risk areas under the different scenarios are mainly distributed on both sides of the river, and most of the low-risk areas transform into medium- and high-risk areas as the rainfall recurrence period and rainfall duration increase. This study analyses the flood risk situation under different scenarios, as well as the elements and areas that should be monitored in case of flooding, with the aim of providing a reference for flood prevention and control in the study area and formulating corresponding countermeasures. It also serves as a reference for flood risk analysis in other areas with similar situations.

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where h is the water depth,

; u is the velocity component in the x-direction, m/s; v is the velocity component in the y-direction;

is the bottom slope component in the x-direction;

is the bottom slope component in the y-direction;

is the friction component in the x-direction;

is the friction component in the y-direction;

is the outflow rate per unit area, m3/s; u 1D is the velocity component of

in the x-direction, m/s;

is the velocity component of

in the y-direction, m/s.…”

Section: Materials and Methodsmentioning

confidence: 99%

Hydrodynamic Modelling and Flood Risk Analysis of Urban Catchments under Multiple Scenarios: A Case Study of Dongfeng Canal District, Zhengzhou

Wei

Zhang

Liu

2022

IJERPH

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show abstract

“…To verify the introduced model, they examined the LBM for four different cases and demonstrated that the proposed scheme is accurate and straightforward. Liu et al 27 proposed an LBM for viscous shallow water equations with a source term to recover the viscosity and avoid errors in the Chapman-Enskog analysis. They also assessed the other two LBM approaches, and all three methods were evaluated by several known benchmarks.…”

Section: Introductionmentioning

confidence: 99%

Finite difference lattice Boltzmann method for modeling dam break debris flows

2023

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A finite difference lattice Boltzmann method (FDLBM) for the simulation of mud and debris flows for one-dimensional cases has been introduced. The proposed FDLBM recovers the generalized equations of mud and debris flows, that is, an unsteady one-dimensional Saint-Venant equation, including the effects of the non-Newtonian behavior of the mixture of water and soil, contraction–expansion losses (or large eddy loss), wind force, various geometries, and lateral inflow or outflow. The proposed FDLBM can be implemented for various non-Newtonian viscoplastic constitutive models of the studied mud and debris flows. The method is validated against previous studies for several benchmark cases, including steady-state problems, hydraulic jump tests, dam breaks with dry and wet beds, and slope dam break floods. Finally, the Anhui debris dam failure flood was investigated by this approach, and the results demonstrated a good agreement with the observed computational and field tests.

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Water-balanced inlet and outlet boundary conditions of the lattice Boltzmann method for shallow water equations

Liu

et al. 2023

Computers & Fluids

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A lattice Boltzmann model for the viscous shallow water equations with source terms

Cited by 6 publications

References 43 publications

Hydrodynamic Modelling and Flood Risk Analysis of Urban Catchments under Multiple Scenarios: A Case Study of Dongfeng Canal District, Zhengzhou

Hydrodynamic Modelling and Flood Risk Analysis of Urban Catchments under Multiple Scenarios: A Case Study of Dongfeng Canal District, Zhengzhou

Finite difference lattice Boltzmann method for modeling dam break debris flows

Water-balanced inlet and outlet boundary conditions of the lattice Boltzmann method for shallow water equations

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