Discrete Boltzmann model of shallow water equations with polynomial equilibria

Jianping Meng, Xiao-Jun Gu (), David R. Emerson (), Yong Peng () and Jianmin Zhang ()
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Jianping Meng: Scientific Computing Department, STFC Daresbury Laboratory, Warrington WA4 4AD, UK
Xiao-Jun Gu: Scientific Computing Department, STFC Daresbury Laboratory, Warrington WA4 4AD, UK
David R. Emerson: Scientific Computing Department, STFC Daresbury Laboratory, Warrington WA4 4AD, UK
Yong Peng: State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China
Jianmin Zhang: State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 09, 1-15

Abstract: A type of discrete Boltzmann model for simulating shallow water flows is derived by using the Hermite expansion approach. Through analytical analysis, we study the impact of truncating distribution function and discretizing particle velocity space. It is found that the convergence behavior of expansion is nontrivial while the conservation laws are naturally satisfied. Moreover, the balance of source terms and flux terms for steady solutions is not sacrificed. Further numerical validations show that the capability of simulating supercritical flows is enhanced by employing higher-order expansion and quadrature.

Keywords: Discrete Boltzmann model; shallow water equations; supercritical flows (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0129183118500808

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