| 低浓度颗粒流Boltzmann方程的同伦分析方法解 |
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| 引用本文： | 张丽,王光谦,傅旭东,孙其诚.低浓度颗粒流Boltzmann方程的同伦分析方法解[J].科学通报,2009,54(11):1518-1523. |
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| 作者姓名： | 张丽 王光谦 傅旭东 孙其诚 |
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| 作者单位： | ① 中南大学数学科学与计算技术学院, 长沙 410075;
② 清华大学水沙科学与水利水电工程国家重点实验室, 北京 100084 |
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| 基金项目： | 国家自然科学基金(批准号: 50679032)、国家重点基础研究发展计划(编号: 2007CB714101)和清华大学水沙科学与水利水电工程国家重点实验室自主课题(编号: 2008-ZY-6)资助项目 |
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| 摘 要： | 同伦分析方法(homotopy analysis method, HAM)是求解强非线性问题的有力手段. 针对颗粒流的动理学理论中的非线性微分积分方程——?Boltzmann方程, 采用 HAM方法选取局域Maxwell速度分布函数作为初始猜测解, 得到了低浓度颗粒流的Boltzmann方程的一阶近似解, 与传统的Chapman-Enskog方法得到的一阶近似解表达式的结构一致, 初步显示了HAM方法求解Boltzmann方程的有效性, 为一般Boltzmann方程的HAM方法求解奠定了基础.
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| 关 键 词： | 低浓度颗粒流 Boltzmann方程 同伦方法 Maxwell速度分布函数 |
| 收稿时间： | 2009-01-13 |
| 修稿时间： | 2009-03-17 |
A new solution to Boltzmann equation of dilute granular flow with homotopy analysis method |
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| ZHANG Li,WANG GuangQian,FU XuDong & SUN QiCheng School of Mathematical Sciences , Computing Technology,Central South University,Changsha ,China, State Key Laboratory for Hydroscience , Engineering,Tsinghua University,Beijing.A new solution to Boltzmann equation of dilute granular flow with homotopy analysis method[J].Chinese Science Bulletin,2009,54(11):1518-1523. |
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| Authors: | ZHANG Li WANG GuangQian FU XuDong & SUN QiCheng School of Mathematical Sciences Computing Technology Central South University Changsha China State Key Laboratory for Hydroscience Engineering Tsinghua University Beijing |
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| Institution: | ZHANG Li1,2,WANG GuangQian2,FU XuDong2 & SUN QiCheng2 1 School of Mathematical Sciences , Computing Technology,Central South University,Changsha 410075,China,2 State Key Laboratory for Hydroscience , Engineering,Tsinghua University,Beijing 100084 |
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| Abstract: | Homotopy analysis method is a new and efficient way to nonlinear problems.The nonlinear Boltzmann equation with differential and integral terms is discussed.The local Maxwell velocity distribution function is chosen as the initial conjecture solution in the Boltzmann equation of dilute granular flow.The concrete expression of the first-order approximate solution to Boltzmann equation with collision term being BGK model,which is consistent to the solution by Chapman-Enskog method,is given.It does not rely on... |
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| Keywords: | dilute granular flow Boltzmann equation homotopy analysis method Maxwell velocity distribution function |
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