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

被引：9

作者：

Liu, Yu ^{[1
,2
]}

Chai, Zhenhua ^{[1
,3
]}

Guo, Xiuya ^{[4
]}

Shi, Baochang ^{[1
,3
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Aerosp Engn, Wuhan 430074, Peoples R China

[3] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

[4] Wuhan Text Univ, Sch Math & Phys Sci, Wuhan 430200, Peoples R China

来源：

JOURNAL OF HYDROLOGY | 2021年 / 598卷

基金：

中国国家自然科学基金;

关键词：

Shallow water equations; Lattice Boltzmann model; Overland flows; Chapman-Enskog analysis; Discrete velocity Boltzmann equation; BOUNDARY-CONDITIONS; OVERLAND-FLOW; SIMULATIONS; DISPERSION; DERIVATION; SCHEME;

D O I：

10.1016/j.jhydrol.2021.126428

中图分类号：

TU [建筑科学];

学科分类号：

0813 ;

摘要：

In this paper, a lattice Boltzmann (LB) model is proposed for a class of viscous shallow water equations, in which a second-order moment of the source term is applied to recover the viscosity in the governing equation and eliminate the additional errors generated during the Chapman-Enskog analysis. There are three different schemes based on different treatments of the source term. Through numerical simulations of several classical benchmark problems, we find that the second-order moment of the source term can not only improve the accuracy of the LB model, but also ensure the conservation of the system. In addition, the influence of rainfall intensity on shallow water flow is also taken into account, and the results show that present LB model can also accurately study such problems as overland flows.

引用

页数：10

共 47 条

[1] UPWIND METHODS FOR HYPERBOLIC CONSERVATION-LAWS WITH SOURCE TERMS [J].

BERMUDEZ, A ;

VAZQUEZ, E .

COMPUTERS & FLUIDS, 1994, 23 (08) :1049-1071

[2] Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model [J].

Bresch, D ;

Desjardins, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 238 (1-2) :211-223

[3] On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models [J].

Bresch, Didier ;

Desjardins, Benoit .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2006, 86 (04) :362-368

[4] Multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: Modeling, analysis, and elements [J].

Chai, Zhenhua ;

Shi, Baochang .

PHYSICAL REVIEW E, 2020, 102 (02)

[5] A LATTICE BOLTZMANN MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA [J].

Chai, Zhenhua ;

Liang, Hong ;

Du, Rui ;

Shi, Baochang .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2019, 41 (04) :B746-B772

[6] Lattice Boltzmann model for high-order nonlinear partial differential equations [J].

Chai, Zhenhua ;

He, Nanzhong ;

Guo, Zhaoli ;

Shi, Baochang .

PHYSICAL REVIEW E, 2018, 97 (01)

[7] A Multiple-Relaxation-Time Lattice Boltzmann Model for General Nonlinear Anisotropic Convection-Diffusion Equations [J].

Chai, Zhenhua ;

Shi, Baochang ;

Guo, Zhaoli .

JOURNAL OF SCIENTIFIC COMPUTING, 2016, 69 (01) :355-390

[8] Lattice Boltzmann method for fluid flows [J].

Chen, S ;

Doolen, GD .

ANNUAL REVIEW OF FLUID MECHANICS, 1998, 30 :329-364

[9]

Cordier S., 2013, ESAIM PROCEEDING CEM, V43, P59, DOI [10.1051/proc/201343004, DOI 10.1051/PROC/201343004]

[10] A streamline diffusion finite element method for the viscous shallow water equations [J].

Dawson, Clint ;

Videman, Juha H. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 251 :1-7

← 1 2 3 4 5 →