| 激波结构的研究--用立方样条数值模拟Kdv-Burgers激波结构的发展 |
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| 引用本文： | 王恩涌.激波结构的研究--用立方样条数值模拟Kdv-Burgers激波结构的发展[J].甘肃高师学报,2004,9(5):18-22. |
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| 作者姓名： | 王恩涌 |
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| 作者单位： | 兰州师范高等专科学校,甘肃兰州,730070 |
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| 摘 要： | 使用王璞和R·Kahawita教授在河口动力学的数值模拟研究中得到的化简后的立方样条求解偏微分方程的 3× 3矩阵系统求解方法 (1- 3)数值模拟求解了一维的非线性Kdv -Burgers模型方程 ,讨论了耗散与弥散对此激波结构的影响 ,结果和文献4] 一致。说明了对于Kdv方程不存在扭型弧立波 ;对于Burgers方程不存在钟型孤立波 ;对于Kdv -Burgers方程则兼有二者特点存在扭钟型 (振荡型 )弧立激波 ;这个结论对于文献5] 是一个数值上的支持。在计算过程中 ,再次显示了立方样条在求解偏微分方程 (特别是流体力学问题 )中所具有的 :(1)任选网格保持高精度 ;(2 )极易处理边条 ;(3)具有的三对角型方程组计算快捷等优点。
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| 关 键 词： | Kdv-Burgers激波 激波结构 数值模拟 |
| 文章编号： | 1008-9020(2004)05-018-05 |
| 修稿时间： | 2004年4月10日 |
Study on shock wave structure |
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| Wang Enyong.Study on shock wave structure[J].Journal of Gansu Normal College,2004,9(5):18-22. |
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| Authors: | Wang Enyong |
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| Abstract: | This paper uses the 3*3matrix system solution(1-3)of partial differential equation that is obtained from the study of numerical simulation using cubic splint predigested by professor wang pu and R.Kahawita in bayou dynamics to figure out the mono-dimension nonlinear KDV-Burgers Matrix Equation and discuss the effect of dissipation and dispersion on the shock wave structure.The result meets with literature 4,which shows there is no existence of twisting isolated wave for KDV Equation;no existence of campaniform isolated wave for Burgers Equation;existence of twisting and campaniform isolated wave for KDV-Burgers Matrix Equation;stand a numerical side for literature 5.On the course of working out,some advantages that exist in figuring out the partial differential equation especially in hydrodynamics by using cubic splints are showed again:(1)freely choose grids and keep high accuracy;(2)deal with regulas easily;(3)quick to work out the three diagonalmatrix. |
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| Keywords: | KDV-Burgers shock wave shock wave structure numerical simulation |
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