| 辐射流体力学Lagrange方程组一类人为解构造方法 |
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| 引用本文： | 余云龙,林忠,王瑞利,刘全,陈星玎.辐射流体力学Lagrange方程组一类人为解构造方法[J].应用数学和力学,2015,36(1):110-118. |
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| 作者姓名： | 余云龙 林忠 王瑞利 刘全 陈星玎 |
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| 作者单位： | 1北京应用物理与计算数学研究所, 北京 100094;2北京工商大学 理学院, 北京 100037 |
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| 基金项目： | 国家自然科学基金（11372051；11201035；11401015）；北京市教委科研计划面上项目（KM20130011006）；北京市教师队伍建设青年英才计划（YETP1445） |
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| 摘 要： | 针对一维Lagrange辐射流体力学方程组，基于物理量在Euler空间和Lagrange空间的微分关系，提出了一种人为解构造方法，并构造了一类一维Lagrange辐射流体力学方程组人为解.构造的人为解在整个计算区域光滑可微，质量方程无源项.将构造的人为解应用至二维辐射流体力学Lagrange程序中，从数值误差、收敛阶方面验证了程序的正确性，展示了人为解的可行性和适用性.
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| 关 键 词： | 辐射流体力学方程组 人为解 Lagrange(拉格朗日)坐标 程序验证 |
| 收稿时间： | 2014-03-27 |
A Method of Manufacturing Solutions for Verification of Lagrangian Radiation Hydrodynamic Codes |
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| Institution: | 1Institute of Applied Physics and Computational Mathematics, Beijing 100094, P.R.China;2School of Science, Beijing Technology and Business University, Beijing 100037, P.R.China |
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| Abstract: | According to the derivative relation of physic variables between the Lagrangian space and Eulerian space, a new method of manufacturing solutions was proposed for the verification of Lagrangian radiation hydrodynamic codes. With this method, the manufactured solutions to the 1D Lagrangian radiation hydrodynamic equations were given to be smooth and differentiable in the whole computional domain, without source term in the mass equation. Then the manufactured solutions were applied to verify the correctness of the 2D Lagrangian radiation hydrodynamic codes. The numerical results show the effectiveness of the presented method. |
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