基于B样条物质点法的溃坝流模拟研究

徐云卿; 周晓敏; 赵世一; 徐聖飞; 孙政

doi:10.21656/1000-0887.430363

基于B样条物质点法的溃坝流模拟研究

doi: 10.21656/1000-0887.430363

徐云卿^1,,
周晓敏^{1, 2},
赵世一¹,
徐聖飞¹,
孙政^{1, 2, ,}

1.
江西理工大学土木与测绘工程学院，江西赣州 341000
2.
江西理工大学江西省环境岩土与工程灾害控制重点实验室，江西赣州 341000

基金项目:

国家自然科学基金项目 12262013

国家自然科学基金项目 11902127

江西省主要学科学术和技术带头人-青年项目 20225BCJ23022

国家级大学生创新创业训练项目 202010407006

江西省大学生创新创业训练项目 S202210407026

详细信息

作者简介:
徐云卿(1999—)，男，硕士(E-mail: xuyunqing@mail.jxust.edu.cn)

通讯作者:
孙政(1986—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: sunzheng@jxust.edu.cn)

中图分类号: O35
计量
- 文章访问数: 405
- HTML全文浏览量: 137
- PDF下载量: 51
- 被引次数: 0
出版历程
- 收稿日期: 2022-11-10
- 修回日期: 2023-03-20
- 刊出日期: 2023-08-01

Simulation Study on Dam Break Flow Based on the B-Spline Material Point Method

XU Yunqing^1
,,
ZHOU Xiaomin^{1, 2},
ZHAO Shiyi¹,
XU Shengfei¹,
SUN Zheng^{1, 2
, ,}

1.
School of Civil and Surveying Engineering, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, P.R.China
2.
Jiangxi Provincial Key Laboratory of Environmental Geotechnical Engineering and Disaster Control, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, P.R.China

摘要

摘要: 溃坝流是水利工程中常见的一种自由表面流动问题，准确模拟溃坝流问题具有重要的工程意义. B样条物质点法(BSMPM)作为一种物质点法(material point method，MPM)的改进算法，其提高了物质点的计算精度和收敛性，且在自由表面流动问题中有独特的算法优势. 基于B样条物质点法，通过引入人工状态方程，发展了一种弱可压缩B样条物质点法(WC-BSMPM)；开展溃坝流问题的模拟研究，分析B样条插值基函数阶数对模拟结果的影响. 结果表明：模拟所得流体波前位置、波前流速及给定位置处的高程变化与已有实验结果吻合较好；同时，随着B样条基函数阶数的增加，模拟结果与试验结果吻合度逐渐提高. 随着基函数阶数的增加，计算耗时呈约1.5倍增长；不同阶次B样条物质点法的计算耗时随背景网格尺寸的增长率基本一致，约呈线性增长. 验证了弱可压缩B样条物质点法模拟溃坝流问题的有效性，为模拟溃坝流问题提供了一种新的思路和方法.
- 溃坝流 /
- B样条物质点法 /
- 自由表面流 /
- 人工状态方程
Abstract: The dam break flow poses a common free surface flow problem in hydraulic engineering, and its accurate simulation is of great engineering significance. The B-spline material point method (BSMPM), as an improved algorithm of the material point method (MPM), has optimized accuracy and convergence in material point calculations and unique algorithmic advantages in free surface flow problems. Based on the BSMPM, a weakly compressible BSMPM (WC-BSMPM) was developed through introduction of an artificial equation of state. The simulation of the dam break flow problem was carried out, with the effects of the order of the B-spline interpolation basis function on the simulation results analyzed. The results show that, the simulated fluid wavefront position, the wavefront velocity and the elevation variation at a given position are basically consistent with the existing experimental results. As the order of the basis function increases, the computation time will lengthen for about 1.5 times. However, the computation times of the BSMPM of different orders will uniformly increase approximately linearly with the background grid size. The validity of the WC-BSMPM simulation of the dam break flow problem was verified. The research provides a new idea and method for the simulation of dam break flow problems.
- dam break flow /
- B-spline material point method /
- free surface flow /
- artificial equation of state

HTML全文

图 1 Cox-de Boor递归示意图

Figure 1. Schematic diagram of the Cox-de Boor recursion

下载: 全尺寸图片幻灯片

图 2 网格空间示意图

Figure 2. Illustration of grid spaces

下载: 全尺寸图片幻灯片

图 3 溃坝流问题示意图

Figure 3. Illustration of the dam break flow problem

下载: 全尺寸图片幻灯片

图 4 溃坝流体波前位置随时间的变化

Figure 4. Variation of the dam-break fluid wavefront position with time

下载: 全尺寸图片幻灯片

图 5 初始水位高度h₀=0.3 m，(a)、(b)、(c)和(d)分别为给定位置h₁，h₂，h₃和h₄水位高程随时间的变化

Figure 5. Initial water level height h₀=0.3 m, (a), (b), (c) and (d) denoting the changes of the water level elevation at given positions h₁, h₂, h₃ and h₄ with time, respectively

下载: 全尺寸图片幻灯片

图 6 初始水位高度h₀=0.3 m，(a)、(b)、(c)和(d)分别为BSMPM 1阶、2阶、3阶的模拟结果和实验结果在t=0.32 s(T^*=1.83)，t=0.41 s(T^*=2.34)，t=0.46 s(T^*=2.63)下的速度云图

Figure 6. Initial water level height h₀=0.3 m, (a), (b), (c) and (d) denoting the velocity profiles of the BSMPM 1st-order, 2nd-order and 3rd-order simulation results and experimental results at t=0.32 s(T^*=1.83), t=0.41 s(T^*=2.34), t=0.46 s(T^*=2.63), respectively

下载: 全尺寸图片幻灯片

图 7 单步CPU计算耗时随网格尺寸和基函数阶数的变化

Figure 7. Variation of the single-step CPU computation time with the grid size and the order of basis functions

下载: 全尺寸图片幻灯片

表 1 不同网格尺寸下，1阶、2阶和3阶基函数下B样条物质点法的求解耗时

Table 1. Solution time costs of the BSMPM for the 1st-order, 2nd-order and 3rd-order basis functions with different grid sizes

grid size Δ/m	CPU time per step t_CPU/ms
grid size Δ/m	1st order	2nd order	3rd order
0.01	15.802	24.296	36.592
0.02	3.590	5.890	9.032
0.04	0.949	1.636	2.070

下载: 导出CSV

参考文献(27)

[1]	谢任之. 溃坝水力学[M]. 济南: 山东科学技术出版社, 1989. XIE Renzhi. Dam Failure Hydraulics[M]. Jinan: Shandong Science and Technology Press, 1989. (in Chinese)
[2]	RITTER A. Die fortpflanzung de wasserwellen[J]. Zeitschrift Verein Deutscher Ingenieure, 1892, 36 (33): 947-954.
[3]	IKNI T, BERREKSI A, BELHOCINE M. Numerical study of shallow-water equations using three explicit schemes-application to dam break flood wave[J]. International Journal of Hydrology Science and Technology, 2021, 12 (2): 101-115. doi: 10.1504/IJHST.2021.116662
[4]	郑素佩, 李霄, 赵青宇, 等. 求解二维浅水波方程的旋转混合格式[J]. 应用数学和力学, 2022, 43 (2): 176-186. doi: 10.21656/1000-0887.420063 ZHENG Supei, LI Xiao, ZHAO Qingyu, et al. A rotated mixed scheme for solving 2D shallow water equations[J]. Applied Mathematics and Mechanics, 2022, 43 (2): 176-186. (in Chinese) doi: 10.21656/1000-0887.420063
[5]	BUKREEV V, GUSEV A, MALYSHEVA A, et al. Experimental verification of the gas-hydraulic analogy with reference to the dam-break problem[J]. Fluid Dynamics, 2004, 39 (5): 801-809. doi: 10.1007/s10697-005-0014-7
[6]	LOBOVSKÝ L, BOTIA-VERA E, CASTELLANA F, et al. Experimental investigation of dynamic pressure loads during dam break[J]. Journal of Fluids and Structures, 2014, 48: 407-434. doi: 10.1016/j.jfluidstructs.2014.03.009
[7]	鲍远林, 陈秀荣, 程冰, 等. 有限体积KFVS方法在二维溃坝中的应用[J]. 应用数学, 2004, 17 (S1): 156-159. https://www.cnki.com.cn/Article/CJFDTOTAL-YISU2004S1037.htm BAO Yuanlin, CHEN Xiurong, CHENG Bing, et al. The application of KFVS finite volume method in the two-dimensional dam breaking[J]. Mathematica Applicata, 2004, 17 (S1): 156-159. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YISU2004S1037.htm
[8]	HAN K Y, LEE J T, PARK J H. Flood inundation analysis resulting from Levee-break[J]. Journal of Hydraulic Research, 1998, 36 (5): 747-759. doi: 10.1080/00221689809498600
[9]	胡四一, 谭维炎. 用TVD格式预测溃坝洪水波的演进[J]. 水利学报, 1989(7): 1-11. doi: 10.13243/j.cnki.slxb.1989.07.001 HU Siyi, TAN Weiyan. Prediction of dam-break flood wave evolution with TVD scheme[J]. Journal of Hydraulic Engineering, 1989(7): 1-11. (in Chinese) doi: 10.13243/j.cnki.slxb.1989.07.001
[10]	王大国, THAM Leslie George, 水庆象, 等. 基于CBOS有限元溃坝流数值模型[J]. 工程力学, 2013, 30 (3): 451-458. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201303066.htm WANG Daguo, THAM Leslie George, SHUI Qingxiang, et al. Numerical model of dam breaking flow with CBOS finite element method[J]. Engineering Mechanics, 2013, 30 (3): 451-458. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201303066.htm
[11]	张建伟, 杜宇, 陈海舟. 溃坝水流冲击水垫塘的SPH模拟[J]. 水电能源科学, 2021, 39 (3): 41-44. https://www.cnki.com.cn/Article/CJFDTOTAL-SDNY202103011.htm ZHANG Jianwei, DU Yu, CHEN Haizhou. SPH simulation of dam-break flow impacting plunge pool[J]. Water Resources and Power, 2021, 39 (3): 41-44. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SDNY202103011.htm
[12]	SULSKY D, CHEN Z, SCHREYR H. A particle method for history-dependent materials[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 118 (1): 179-196.
[13]	MA S, ZHANG X, QIU X. Comparison study of MPM and SPH in modeling hypervelocity impact problems[J]. International Journal of Impact Engineering, 2009, 36 (2): 272-282.
[14]	SUN Z, LI H, GAN Y, et al. Material point method and smoothed particle hydrodynamics simulations of fluid flow problems: a comparative study[J]. Progress in Computational Fluid Dynamics, 2018, 18: 1-18.
[15]	王宇新, 李晓杰, 王小红, 等. 炸药爆轰物质点法三维数值模拟[J]. 应用数学和力学, 2015, 36 (2): 198-206. doi: 10.3879/j.issn.1000-0887.2015.02.009 WANG Yuxin, LI Xiaojie, WANG Xiaohong, et al. 3D simulation of explosive detonation with the material point method[J]. Applied Mathematics and Mechanics, 2015, 36 (2): 198-206. (in Chinese) doi: 10.3879/j.issn.1000-0887.2015.02.009
[16]	张雄, 刘岩, 张帆, 等. 极端变形问题的物质点法研究进展[J]. 计算力学学报, 2017, 34 (1): 1-16. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201701001.htm ZHANG Xiong, LIU Yan, ZHANG Fan, et al. Recent progress of material point method for extreme deformation problems[J]. Chinese Journal of Computational Mechanics, 2017, 34 (1): 1-16. (in Chinese)) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201701001.htm
[17]	马上, 张雄, 邱信明. 超高速碰撞问题的三维物质点法[J]. 爆炸与冲击, 2006, 26 (3): 273-278. https://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ200603013.htm MA Shang, ZHANG Xiong, QIU Xinming. Three-dimensional matter point method for hypervelocity impact[J]. Explosion and Shock Waves, 2006, 26 (3): 273-278. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ200603013.htm
[18]	郑勇刚, 顾元宪, 陈震. 薄膜破坏过程数值模拟的MPM方法[J]. 力学学报, 2006, 38 (3): 347-355. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200603009.htm ZHENG Yonggang, GU Yuanxian, CHEN Zhen. Numerical simulation of thin film failure with MPM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38 (3): 347-355. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200603009.htm
[19]	周晓敏, 孙政. 非Newton流体的物质点法模拟研究[J]. 应用数学和力学, 2019, 40 (10): 1135-1146. doi: 10.21656/1000-0887.390349 ZHOU Xiaomin, SUN Zheng. Simulation of non-Newtonian fluid flows with the material point method[J]. Applied Mathematics and Mechanics, 2019, 40 (10): 1135-1146. (in Chinese) doi: 10.21656/1000-0887.390349
[20]	GAN Y, SUN Z, CHEN Z, et al. Enhancement of the material point method using B-spline basis functions[J]. International Journal for Numerical Methods in Engineering, 2018, 113 (3): 411-431
[21]	TIELEN R, WOBBES E, MÖLLER M, et al. A high order material point method[J]. Procedia Engineering, 2017, 175: 265-272.
[22]	SONG Y, LIU Y, ZHANG X. A transport point method for complex flow problems with free surface[J]. Computational Particle Mechanics, 2020, 7 (2): 377-391.
[23]	ZHOU X, SUN Z. Numerical investigation of non-Newtonian power law flows using B-spline material point method[J]. Journal of Non-Newtonian Fluid Mechanics, 2021, 298: 104678.
[24]	SUN Z, HUANG Z, ZHOU X. Benchmarking the material point method for interaction problems between the free surface flow and elastic structure[J]. Progress in Computational and Fluid Dynamics, 2019, 19 (1): 1-11.
[25]	DE BOOR C. A Practical Guide to Spline[M]. New York: Springer, 1978.
[26]	孙政, 周晓敏. 物质点法改进算法及其工程应用[M]. 长沙: 中南大学出版社, 2021. SUN Zheng, ZHOU Xiaomin. Improved Material Point Method and Its Engineering Application[M]. Changsha: Central South University Press, 2021. (in Chinese)
[27]	周光坰, 严宗毅, 许世雄, 等. 流体力学(上)[M]. 北京: 高等教育出版社, 2001. ZHOU Guangjiong, YAN Zongyi, XU Shixiong, et al. The Fluid Mechanics(I)[M]. Beijing: Higher Education Press, 2001. (in Chinese)