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 引用本文: 王志力 陆永军 耿艳芬. 一维孔隙率浅水方程及其数值离散[J]. 力学学报, 2008, 40(5): 585-592.
Zhili Wang, Yongjun Lu, Yanfen Geng. One dimensional shallow water equations with porosity and their numerical discretization scheme[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5): 585-592.
 Citation: Zhili Wang, Yongjun Lu, Yanfen Geng. One dimensional shallow water equations with porosity and their numerical discretization scheme[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5): 585-592.

## One dimensional shallow water equations with porosity and their numerical discretization scheme

• 摘要: 通过孔隙率方法来描述挡水物对过水能力的影响建立了一维孔隙率浅水方程. 采用有限体积方法和Roe格式的近似Riemann解建立了孔隙率浅水方程的离散模式. 对底坡和孔隙率源项采用特性方向分解的方法进行处理，使模型精确满足C(Conservative)特性，增加了模型的稳定性. 通过算例模拟证明了模型可以对河道中的挡水物作用进行模拟，且计算结果表明模型具有和谐、稳定、分辨率高等优点.

Abstract: In this paper, the introduction of porosity into theone-dimensional shallow water equations is investigated to lead to modifiedexpressions for the fluxes and source terms subjected to the effects ofbuildings and other structures. An extra porosity source term appears in themomentum equation. The numerical discretization scheme for shallow waterequations with porosity is presented using finite volume method and Roe-typeapproximate Riemann solver. The source terms of the bed slope and theporosity are both decomposed in the characteristic direction to make thescheme exactly satisfy the conservative property. Several cases have beenbrought, such as the dam break with variable porosity, the steady flowthrough continue porosity and the damming heights in different pier width,to show that the scheme can be used to simulate the influence of buildingsand other structures in the channel with harmonious, robust andhigh-resolution characteristics.

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