| 一维双曲守恒律的龙格-库塔控制体积间断有限元方法 |
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| 引用本文： | 陈大伟,蔚喜军. 一维双曲守恒律的龙格-库塔控制体积间断有限元方法[J]. 计算物理, 2009, 26(4): 501-509 |
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| 作者姓名： | 陈大伟 蔚喜军 |
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| 作者单位： | 中国工程物理研究院研究生部,北京,100088;北京应用物理与计算数学研究所,计算物理实验室,北京,100088 |
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| 摘 要： | 给出数值求解一维双曲守恒律方程的新方法——龙格-库塔控制体积间断有限元方法(RKCVDFEM),其中空间离散基于控制体积有限元方法,时间离散基于二阶TVB Runge-Kutta技术,有限元空间选取为分段线性函数空间.理论分析表明,格式具有总变差有界(TVB)的性质,而且空间和时间离散形式上具有二阶精度.数值算例表明,数值解收敛到熵解并且对光滑解的收敛阶是最优的,优于龙格-库塔间断Galerkin方法(RKDGM)的计算结果.
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| 关 键 词： | 双曲守恒律 龙格.库塔技术 控制体积有限元方法 |
| 收稿时间： | 2008-03-12 |
| 修稿时间： | 2008-07-29 |
RKCVDFEM for One-dimensional Hyperbolic Conservation Laws |
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| CHEN Dawei,YU Xijun. RKCVDFEM for One-dimensional Hyperbolic Conservation Laws[J]. Chinese Journal of Computational Physics, 2009, 26(4): 501-509 |
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| Authors: | CHEN Dawei YU Xijun |
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| Affiliation: | 1. Graduate School of China Academy of Engineering Physics, Beijing 100088, China;2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China |
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| Abstract: | Runge-Kutta control volume discontinuous finite element method(RKCVDFEM) is proposed to solve numerically hyperbolic conservation laws,in which space discretization is based on control volume finite element method(CVFEM) while time discretization is based on a second order accurate TVB Runge-Kutta technique.Piecewise linear function space is chosen as finite element space.The scheme is total variation bounded(TVB) and is formally second order accurate in space and time.Numerical examples show that numerical... |
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| Keywords: | hyperbolic conservation laws Runge-Kutta technique control volume finite element method |
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