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与传统网格法相比, 光滑粒子流体动力学方法不能直接施加壁面边界条件, 这就限制了该方法在工程中的应用.为此, 本文基于Galerkin加权余量法并结合传统排斥力方法, 推导出一种新的排斥力公式来施加壁面边界条件.该方法不含未知参数, 能在不减小边界粒子尺寸的情形下有效地防止流体粒子穿透壁面, 同时可避免邻近边界的流体粒子的速度及压力振荡. 分别通过静止液柱算例、液柱坍塌算例、容器中液体静止算例及溃坝算 例来验证本文方法的有效性, 并与传统边界处理方法进行对比, 结果表明: 本文方法克服了传统方法存在的缺陷, 是一种有效的固壁边界处理方法.
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关键词:
- 光滑粒子流体动力学法 /
- 固壁边界 /
- 排斥力 /
- 加权余量法
Compared with traditional mesh method the smoothed particle hydrodynamics (SPH) is unable to directly implement the solid boundary conditions, which hinders its further application to engineering. Therefore, a new repulsive model is deduced based on the Galerkin method of weighted residuals and traditional repulsive methods. Compared with traditional repulsive models, this model does not include unknown parameters; it can avoid fluid particles penetrating wall surface effectively without reducing the size of boundary particle, and also it avoids the oscillation of fluid particles around the boundary in speed and pressure. The new method is examined and compared with traditional methods using four numerical examples including static dam on a fixed boundary, a dam-break flow on a fixed boundary because of gravity, fluid still gradually in a tank because of gravity, dam-break. It is demonstrated that SPH with this new method overcomes the disadvantages in traditional methods, and that this method is an effective method for solid boundary condition.-
Keywords:
- smoothed particle hydrodynamics method /
- solid boundary /
- repulsive force /
- method of weighted residuals
[1] Lucy L B 1977 Astron. J. 82 1013
[2] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[3] Zhang A M 2008 Chin. Phys. B 17 927
[4] Sun Z H, Han R J 2008 Chin. Phys. B 17 3185
[5] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫, 姚熊亮 2008物理学报 57 339]
[6] Monaghan J J 2005 Rep. Prog. Phys. 68 1703
[7] Monaghan J J 1994 J. Comput. Phys. 110 399
[8] Libersky L D, Petscheck A G, Carney T C 1993 J. Comput. Phys. 109 67
[9] Randles P W, Libersky L D 1996 Comput. Methods Appl. Mech. Eng. 138 375
[10] Gotoh H, Sakai T 1999 Coast. Eng. 41 303
[11] Liu G R, Gu Y T 2001 Struct. Eng. Mech. 246 29
[12] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠2010物理学报 59 3654]
[13] Rogers B, Dalrymple R 2007 Adv. Num. Model Simul. Tsun. Wave Runup. 10 75
[14] Qiang H F, Han Y W, Wang K P, Gao W R 2011 Eng. Mech. 28 245 (in Chinese) [强洪夫, 韩亚伟, 王坤鹏, 高巍然2011工程力学 28 245]
[15] Monaghan J J, Kajtar J B 2009 Comput. Phys. Commun. 180 1811
[16] Liu M B, Shao J R 2011 Sci. China: Technol. Sci. 10 1
[17] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛2008物理学报 57 3954]
[18] Koshizuka S, Oka Y 1996 Nucl. Sci. Eng. 123 421
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[1] Lucy L B 1977 Astron. J. 82 1013
[2] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[3] Zhang A M 2008 Chin. Phys. B 17 927
[4] Sun Z H, Han R J 2008 Chin. Phys. B 17 3185
[5] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫, 姚熊亮 2008物理学报 57 339]
[6] Monaghan J J 2005 Rep. Prog. Phys. 68 1703
[7] Monaghan J J 1994 J. Comput. Phys. 110 399
[8] Libersky L D, Petscheck A G, Carney T C 1993 J. Comput. Phys. 109 67
[9] Randles P W, Libersky L D 1996 Comput. Methods Appl. Mech. Eng. 138 375
[10] Gotoh H, Sakai T 1999 Coast. Eng. 41 303
[11] Liu G R, Gu Y T 2001 Struct. Eng. Mech. 246 29
[12] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠2010物理学报 59 3654]
[13] Rogers B, Dalrymple R 2007 Adv. Num. Model Simul. Tsun. Wave Runup. 10 75
[14] Qiang H F, Han Y W, Wang K P, Gao W R 2011 Eng. Mech. 28 245 (in Chinese) [强洪夫, 韩亚伟, 王坤鹏, 高巍然2011工程力学 28 245]
[15] Monaghan J J, Kajtar J B 2009 Comput. Phys. Commun. 180 1811
[16] Liu M B, Shao J R 2011 Sci. China: Technol. Sci. 10 1
[17] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛2008物理学报 57 3954]
[18] Koshizuka S, Oka Y 1996 Nucl. Sci. Eng. 123 421
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