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对于一类含源的高阶非线性波动方程Boussinesq方程的初边值问题,利用D1Q5模型的格子Boltzmann方程,通过选取不同的演化方程和局部平衡态分布函数及修正函数,应用ChapmanEnskog多尺度技术和Taylor展开技术,提出了具有五阶高精度带修正函数的非标准格子Boltzmann模型.应用所提出的模型,仿真模拟了几个具有精确解的Boussinesq方程初边值系统,并与传统的修正有限差分法(MFDM)进行了对比,结果表明该文模型所得的数值解与精确解吻合,其模误差小于MFDM.此外,还针对精确解未知的Boussinesq方程初边值系统进行了数值仿真,并与MFDM进行了对比.数值结果表明,两种计算格式的数值解比较吻合,进一步证明了文中所构造模型的有效性和稳定性. 相似文献
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关于非线性不等式组Levenberg-Marquardt算法的收敛性(英文) 总被引:2,自引:1,他引:1
本文研究了一类非线性不等式组的求解问题.利用一列目标函数两次可微的参数优化问题来逼近非线性不等式组的解,光滑Levenberg-Marquardt方法来求解参数优化问题,在一些较弱的条件下证明了文中算法的全局收敛性,数值实例显示文中算法效果较好. 相似文献
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通过Chapman-Enskog展开技术和多尺度分析,建立了一种新的D1Q4带修正项的四阶格子Boltzmann模型,一类非线性偏微分方程从连续的Boltzmann方程得到正确恢复.统一了KdV和Burgers等已知方程类型的格子BGK模型,还首次给出了组合KdV-Burgers,广义Burgers—Huxley等方程... 相似文献
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Analysis of composite material interface crack face contact and friction effects using a new node-pairs contact algorithm 下载免费PDF全文
A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem(e.g., resistant coating and thermal barrier coatings) subjected to complicated load conditions.To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors(SIFs) and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors K?IIfor the friction coefficient decrease by 16% when f changes from 1 to 0. 相似文献