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龙格库塔间断有限元方法在计算爆轰问题中的应用
  • 期刊名称：计算物理，Vol. 27, No.4,509-517 (2010) (EI)
  • 时间：0
  • 分类：O241.82[理学—计算数学;理学—数学]
  • 作者机构：[1]中国科学院数学与系统科学研究院计算数学所,科学与工程计算国家重点实验室,北京100190, [2]中国矿业大学（北京）理学院,北京100083
  • 相关基金：国家973计划（2005CB321703）; 国家自然科学基金（10531080 10729101）资助项目
  • 相关项目：初边值问题数值解法及应用
关键词： 龙格库塔间断有限元方法, 爆轰波, 反应Euler方程, 刚性源项, Runge-Kutta discontinuous Galerkin method, detonation wave, reactive Euler equations, stiff source term
中文摘要：

构造求解带源项守恒律方程组的龙格库塔间断有限元（RKDG）方法,并分别结合源项的Strang分裂法和无分裂法数值求解模型守恒律方程和反应欧拉方程.为了和有限体积型WENO方法进行比较,设计计算源项的WENO重构格式.对一维带源项守恒律的计算表明,对于非刚性问题,RKDG方法比有限体积型WENO方法的误差更小;对于刚性问题,RKDG方法对于间断面位置的捕捉更为精确.对于一二维爆轰波问题的计算结果表明,RKDG方法对爆轰波结构的分辨和爆轰波位置的捕捉能力更强.

英文摘要：

A Runge-Kutta discontinuous Galerkin（RKDG） method for conservation law with source term is shown.The method is implemented with Strang split or unsplit methods,and is applied to solve one-dimensional conservation law with source term as well as one and two-dimensional detonation wave problems.In order to compare with the fifth-order finite volume WENO method,a special reconstruction method is proposd to calculate integration of the source term with high-order spatial accuracy.Numerical tests in one dimension show that the RKDG method has smaller errors than WENO method for nonstiff problems and is more accurate in capturing position of discontinuity in stiff problems.Numerical simulations of detonation waves demonstrate that the RKDG method is more effcient in resolving detailed structure of detonation waves and location of detonation front.

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若干非线性问题的数值解法
期刊论文 78 会议论文 13 获奖 1
初边值问题数值解法及应用
期刊论文 11 著作 1
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