| Runge-Kutta间断有限元格式在一维浅水方程中的应用 |
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| 引用本文： | 赵张益,张庆河,李世森.Runge-Kutta间断有限元格式在一维浅水方程中的应用[J].水科学进展,2012,23(5):695-701. |
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| 作者姓名： | 赵张益 张庆河 李世森 |
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| 作者单位： | 1. 天津大学建筑工程学院, 天津 300072;2. 天津大学水利工程仿真与安全国家重点实验室, 天津 300072 |
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| 基金项目： | 天津市自然科学基金重点资助项目(12JCZDJC30200);国家高技术研究发展计划(863)资助项目(2012AA112509)~~ |
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| 摘 要： | 针对一维浅水方程组建立了考虑源项离散的Runge-Kutta间断有限元格式,该格式具有通量与源项的和谐性,可以用于求解任意非棱柱体明渠浅水流动问题。所建立的数值模式分别应用于复杂地形下非棱柱体明渠跨临界流浅水流动算例和水跃问题,模拟结果表明,数值解与解析解以及实测值吻合良好,数值格式具有捕捉间断问题中锐利波形的能力。
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| 关 键 词： | 一维浅水方程组 间断有限元 Runge-Kutta时间离散 源项 和谐格式 |
| 收稿时间： | 2011-12-20 |
Application of Runge-Kutta discontinuous Galerkin scheme for one-dimensional shallow water equations |
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| ZHAO Zhang-yi
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ZHANG Qing-he
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LI Shi-sen.Application of Runge-Kutta discontinuous Galerkin scheme for one-dimensional shallow water equations[J].Advances in Water Science,2012,23(5):695-701. |
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| Authors: | ZHAO Zhang-yi ZHANG Qing-he LI Shi-sen |
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| Institution: | 1. School of Civil Engineering, Tianjin University, Tianjin 300072, China;2. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China |
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| Abstract: | The Runge-Kutta discontinuous Galerkin scheme(RKDG),which maintains balance of flux and source terms,is formulated to solve one-dimensional shallow water flows in non-prismatic channel.To validate the numerical model,a transcritical flow over a hump in a non-prismatic channel and a hydraulic jump were simulated.The simulated results from RKDG agree well with the analytical solution and measured values.It is shown that the RKDG scheme developed in the present paper has proven its capability of capturing sharp waveform in discontinuous flows. |
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| Keywords: | one-dimensional shallow water equations discontinuous Galerkin scheme Runge-Kutta scheme source terms well-balanced scheme |
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