An improved finite particle method for discontinuous interface problems

WANG Lu; YANG Yang; XU Fei

doi:10.11883/bzycj-2017-0390

Volume 39 Issue 2

Feb. 2019

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WANG Lu, YANG Yang, XU Fei. An improved finite particle method for discontinuous interface problems[J]. Explosion And Shock Waves, 2019, 39(2): 024202. doi: 10.11883/bzycj-2017-0390

Citation:

WANG Lu, YANG Yang, XU Fei. An improved finite particle method for discontinuous interface problems[J]. Explosion And Shock Waves, 2019, 39(2): 024202. doi: 10.11883/bzycj-2017-0390

WANG Lu, YANG Yang, XU Fei. An improved finite particle method for discontinuous interface problems[J]. Explosion And Shock Waves, 2019, 39(2): 024202. doi: 10.11883/bzycj-2017-0390

Citation:

WANG Lu, YANG Yang, XU Fei. An improved finite particle method for discontinuous interface problems[J]. Explosion And Shock Waves, 2019, 39(2): 024202. doi: 10.11883/bzycj-2017-0390

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An improved finite particle method for discontinuous interface problems

doi: 10.11883/bzycj-2017-0390

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, Shaanxi, China

Received Date: 2017-10-30
Rev Recd Date: 2018-01-10
Publish Date: 2019-02-05

Abstract

Abstract

The finite particle method(FPM) is an important improvement for the smoothed particle hydrodynamics(SPH) method, which effectively improves the calculation accuracy of boundary particles. However, when the discontinuous physical field is solved by the FPM, the accuracy in the vicinity of the discontinuous interface is greatly reduced, and the non-singularity of the matrix must be satisfied in the FPM, which requires an elaborate handling of the interface. Based on the discontinuous SPH(DSPH) method, this paper proposed an improved FPM-discontinuous special FPM(DSFPM), which considers the discontinuous interface, aiming to improve the computational accuracy at the interface and further improve the efficiency and stability of the FPM. In this paper, the estimation accuracy of the DSFPM was analyzed firstly, and then the algorithm flow diagram of the DSFPM to deal with the small deformation and large deformation problems was demonstrated. Next, the DSFPM, DSPH and FPM were used to simulate the small deformation problem-elastic aluminum blocks impact. By comparing the velocity and stress of the aluminum blocks and computational time, we verified the accuracy and computational efficiency of the DSFPM. Finally, the simulation of the large deformation problem was realized by a combining method with the DSFPM and DFPM.
- FPM,
- interface,
- DSFPM,
- accuracy,
- computational cost

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References(20)

References

[1]	MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 1994, 110:399-406. DOI: 10.1006/jcph.1994.1034.
[2]	杨秀峰, 刘谋斌.SPH方法Delaunay三角刨分与自由液面重构[J].计算力学学报, 2016, 33(4):594-598. DOI: 10.7511/jslx201604027. YANG Xiufeng, LIU Moubin. Delaunay triangulation and free surface extraction for SPH method[J]. Chinese Journal of Computational Mechanics, 2016, 33(4):594-598. DOI: 10.7511/jslx201604027.
[3]	龙厅, 胡德安, 韩旭.FE-ISPH与FE-WCSPH模拟流固耦合问题的比较研究[C]//中国计算力学大会.贵阳, 2014: 547. http://cpfd.cnki.com.cn/Article/CPFDTOTAL-AGLU201408004093.htm
[4]	刘谋斌, 宗智, 常建忠.光滑粒子动力学方法的发展与应用[J].力学进展, 2011, 41(2):219-236. DOI: 10.6052/1000-0992-2011-2-lxjzJ2010-078. LIU Moubin, ZONG Zhi, CHANG Jianzhong. Developments and applications of smoothed particle hydrodynamics[J]. Advances in Mechanics, 2011, 41(2):219-236. DOI: 10.6052/1000-0992-2011-2-lxjzJ2010-078.
[5]	傅学金, 强洪夫, 杨月诚.固体介质中SPH方法的拉伸不稳定性问题研究进展[J].力学进展, 2007, 37(3):375-388. DOI: 10.3321/j.issn:1000-0992.2007.03.005. FU Xuejin, QIANG Hongfu, YANG Yuecheng. Advances in the tensile instability of smoothed particle hydrodynamics applied to solid dynamics[J]. Advances in Mechanics, 2007, 37(3):375-388. DOI: 10.3321/j.issn:1000-0992.2007.03.005.
[6]	LIU W K, JUN S, LI S, et al. Reproducing kernel particle methods for structure dynamics[J]. International Journal for Numerical Methods in Engineering, 1995, 38(10):1655-1679. DOI: 10.1002/nme.1620381005.
[7]	CHEN J K, BERAUN J E. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problem[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 190:225-239. DOI: 10.1016/S0045-7825(99)00422-3.
[8]	章杰, 苏少卿, 郑宇, 等.改进SPH方法在陶瓷材料层裂数值模拟中的应用[J].爆炸与冲击, 2013, 33(4):401-407. DOI: 10.3969/j.issn.1001-1455.2013.04.011. ZHANG Jie, SU Shaoqing, ZHENG Yu, et al. Application of modified SPH method to numerical simulation of ceramic spallation[J]. Explosion and Shock Waves, 2013, 33(4):401-407. DOI: 10.3969/j.issn.1001-1455.2013.04.011.
[9]	LIU M B, LIU G R. Restoring particle consistency in smoothed particle hydrodynamics[J]. Applied Numerical Mathematics, 2006, 56(1):19-36. DOI: 10.1016/j.apnum.2005.02.012.
[10]	郑兴, 段文洋.K2_SPH方法及其对二维非线性水波的模拟[J].计算物理, 2011, 28(5):659-666. DOI: 10.3969/j.issn.1001-246X.2011.05.004. ZHENG Xing, DUAN Wenyang. K2_SPH Method and application for 2D nonlinear water wave simulation[J]. Chinese Journal of Computational Physics, 2011, 28(5):659-666. DOI: 10.3969/j.issn.1001-246X.2011.05.004.
[11]	刘谋斌, 杨秀峰, 邵家儒.高精度SPH方法及其在海洋工程中的应用[C]//颗粒材料计算力学会议论文集.兰州, 2014: 39-41. http://cpfd.cnki.com.cn/Article/CPFDTOTAL-AGLU201408001007.htm
[12]	ADAMI S, HU X Y, ADAMS N A. A generalized wall boundary condition for smoothed particle hydrodynamics[J]. Journal of Computational Physics, 2012, 231(21):7057-7075. DOI: 10.1016/j.jcp.2012.05.005.
[13]	LIU M B, SHAO J R, CHANG J Z. On the treatment of solid boundary in smoothed particle hydrodynamics[J]. Science China:Technological Sciences, 2012, 55(1):244-254. DOI: 10.1007/s11431-011-4663-y.
[14]	LIU M B, LIU G R, LAM K Y. A one-dimensional meshfree particle formulation for simulating shock waves[J]. Shock Wave, 2003, 13:201-211. DOI: 10.1007/s00193-003-0207-0.
[15]	XU F, ZHAO Y, YAN R, et al. Multi-dimensional discontinuous SPH method and its application to metal penetration analysis[J]. International Journal for Numerical Methods in Engineering, 2013, 93:1125-1146. DOI: 10.1002/nme.4414.
[16]	闫蕊, 徐绯, 张岳青.DSPH方法的有效性验证及应用[J].爆炸与冲击, 2013, 33(2):133-139. DOI: 10.3969/j.issn.1001-1455.2013.02.004. YAN Rui, XU Fei, ZHANG Yueqing. Validation of DSPH method and its application to physical problems[J]. Explosion and Shock Waves, 2013, 33(2):133-139. DOI: 10.3969/j.issn.1001-1455.2013.02.004.
[17]	宋俊豪, 张超英, 梁朝湘, 等.RDSPH:一种适用于一维非连续条件的新SPH方法[J].广西师范大学学报(自然科学版), 2009, 27(3):9-13. DOI: 10.3969/j.issn.1001-6600.2009.03.003. SONG Junhao, ZHANG Chaoying, LIANG Chaoxiang, et al. A new one-dimensional smoothed particle hydrodynamics method in simulating discontinuous problem[J], Journal of Guangxi Normal University (Natural Science Edition), 2009, 27(3):9-13. DOI: 10.3969/j.issn.1001-6600.2009.03.003.
[18]	YANG Yang, XU Fei, ZHANG Meng, et al. An effective improved algorithm for finite particle method[J]. International Journal of Computational Methods, 2016, 13(4):1641009. DOI: 10.1142/S0219876216410097.
[19]	MONAGHAN J J. Smoothed particle hydrodynamic[J]. Annual Review of Astronomy and Astrophysics, 1992, 30(1):543-574. DOI: 10.1146/annurev.aa.30.090192.002551.
[20]	MONAGHAN J J, KAJTAR J. SPH particle boundary forces for arbitrary boundaries[J]. Computer Physics Communications, 2009, 180(10):1811-1820. DOI: 10.1016/j.cpc.2009.05.008.