| 避免核函数导数的二阶导数核近似方法的修正 |
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| 引用本文： | 热合买提江&#;依明,阿合买提江&#;依明江.避免核函数导数的二阶导数核近似方法的修正[J].计算力学学报,2018,35(4):494-499. |
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| 作者姓名： | 热合买提江&#;依明 阿合买提江&#;依明江 |
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| 作者单位： | 新疆大学 数学与系统科学学院, 乌鲁木齐 830046,新疆大学 数学与系统科学学院, 乌鲁木齐 830046 |
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| 基金项目： | 国家自然科学基金（51565054）；新疆大学博士毕业生科研启动基金（BS150210）资助项目. |
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| 摘 要： | 采用核近似光滑粒子流体力学SPH（Smooth Particle Hydrodynamics）方法计算一元函数二阶导数和多元函数二阶偏导数，对避免核函数导数算法进行了改进，提出了对核函数光滑长度处处具有o（h）精度的算法，并分别推导出一元和多元函数的修正公式。用不同的粒子间距和不同的光滑长度进行了二阶导数的计算和热传导问题的模拟，进行了修正方法与原方法的误差分析。结果表明，本文提出的修正措施在提高精度、减少误差及加快收敛速度等方面起到很大的作用。
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| 关 键 词： | SPH核近似方法 避免核函数导数 修正 精度 |
| 收稿时间： | 2017/4/16 0:00:00 |
| 修稿时间： | 2017/8/26 0:00:00 |
Corrective scheme for derivative free method to compute Second Order Derivatives |
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| Rahmatjan Imin,Ahmatjan Iminjan.Corrective scheme for derivative free method to compute Second Order Derivatives[J].Chinese Journal of Computational Mechanics,2018,35(4):494-499. |
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| Authors: | Rahmatjan Imin Ahmatjan Iminjan |
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| Institution: | School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China and School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China |
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| Abstract: | New corrective schemes for Second Order Derivative Free Smoothed Particle Hydrodynamics method (SODF-SPH) are proposed.The corrective schemes are deduced in one-variable and multivariate functions which have o(h) accuracy everywhere.Then selecting different particle distances and setting different smooth lengths the second order derivatives of the one-variable and the multivariate functions are computed to simulated heat conduction errors between SODF-SPH methods and corrective scheme are compared and analyzed.The results show that the corrective schemes greatly improve the accuracy and convergence speed. |
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| Keywords: | SPH kernel approximation SODF-SPH method corrective accuracy |
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