基于反距离加权插值重构的沉浸式边界方法研究

王鑫鑫; 赵万东; 梁剑寒

doi:10.21656/1000-0887.440360

基于反距离加权插值重构的沉浸式边界方法研究

doi: 10.21656/1000-0887.440360

国防科技大学空天科学学院，长沙 410073

我刊青年编委寇家庆来稿

基金项目:

国家留学基金委基金 202206110008

湖南省自然科学基金 2024JJ6454

详细信息

作者简介:
王鑫鑫(1996—)，男，博士生(E-mail: wazedxwxx@gmail.com)

梁剑寒(1973—)，男，教授，博士生导师

通讯作者:
赵万东(1993—)，男，助理研究员(通讯作者. E-mail: zhaowandong19@nudt.edu.cn)

中图分类号: O242
计量
- 文章访问数: 49
- HTML全文浏览量: 11
- PDF下载量: 20
- 被引次数: 0
出版历程
- 收稿日期: 2023-12-19
- 修回日期: 2024-11-12
- 刊出日期: 2025-06-01

Investigation of the Immersed Boundary Method Based on the Inverse Distance Weighted Interpolation Reconstruction

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, P.R.China

Recommended by KOU Jiaqing, M.AMM Youth Editorial Board

摘要

摘要: 提出了一种自适应的幂参数反距离加权(adaptive power parameter inverse distance weighted, AIDW)的重构方法，旨在提高虚拟网格法在处理沉浸边界问题时的精确性. AIDW利用了反距离加权插值的特性，结合插值节点的物理量分布与局部流动特性的综合信息，以自动调整幂参数的值，从而在各种流场条件下提升重构精度. 该方法尤其在处理复杂边界附近的间断界面时存在优势. 通过倾斜激波管和圆柱Couette流动两个算例的数值模拟，AIDW展现出了其在修正间断界面的扭曲和提高流场物理量分布精度方面的优势.
- 沉浸式边界法 /
- 虚拟网格法 /
- 反距离加权插值 /
- Descartes网格
Abstract: An adaptive power parameter inverse distance weighted (AIDW) reconstruction method to enhance the accuracy of the ghost cell method, was proposed for handling of immersed boundary. The AIDW utilizes the characteristics of the inverse distance weighted interpolation, integrating comprehensive information from the distribution of physical parameters at interpolation nodes with local flow properties to automatically adjust the power parameter value, to improve the reconstruction precision across various flow conditions, particularly in the cases of discontinuities near complex boundaries. Numerical simulations of 2 examples of an inclined shock tube and a cylindrical Couette flow demonstrate advantages of the AIDW in correcting distortions at discontinuous interfaces and in enhancing the accuracy of the physical parameter distribution.
- immersed boundary method /
- ghost cell method /
- inverse distance weighted interpolation /
- Cartesian grid
edited-by

edited-by
注释:

1) 我刊青年编委寇家庆来稿

HTML全文

图 1 二维虚拟网格法

Figure 1. The 2D ghost-cell methods

下载: 全尺寸图片幻灯片

图 2 间断界面的IDW插值

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. Inverse distance weighted interpolations for discontinuous interfaces

下载: 全尺寸图片幻灯片

图 3 Test 1和test 2的密度等值线

Figure 3. Density contours of test 1 and test 2

下载: 全尺寸图片幻灯片

图 4 Test 1和test 2中的质量损失对比

Figure 4. Comparison of mass losses in 2 tests

下载: 全尺寸图片幻灯片

图 5 圆柱Couette流测试算例的物理构型

Figure 5. The configuration of the stationary rotating vortex Couette flow case

下载: 全尺寸图片幻灯片

图 6 四种插值方法精度的比较

Figure 6. Comparison of 4 interpolation method

下载: 全尺寸图片幻灯片

表 1 倾斜激波管流动参数

Table 1. Inclined shock tube flow parameters

test	ρ_L	u_L	p_L	ρ_R	u_R	p_R	time
1	1.0	0.0	1.0	0.125	0.0	0.1	0.2
2	1.0	0.0	1.0	0.1	0.0	1.0	5.0

下载: 导出CSV

参考文献(24)

[1]	PESKIN C S. The immersed boundary method[J]. Acta Numerica, 2002, 11: 479-517. doi: 10.1017/S0962492902000077
[2]	MITTAL R, IACCARINO G. Immersed boundary methods[J]. Annual Review of Fluid Mechanics, 2005, 37: 239-261. doi: 10.1146/annurev.fluid.37.061903.175743
[3]	CLARKE D K, SALAS M D, HASSAN H A. Euler calculations for multielement airfoils using Cartesian grids[J]. AIAA Journal, 1986, 24(3): 353-358. doi: 10.2514/3.9273
[4]	UDAYKUMAR H S, SHYY W, RAO M M. ELAFINT: a mixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries[J]. International Journal for Numerical Methods in Fluids, 1996, 22(8): 691-712. doi: 10.1002/(SICI)1097-0363(19960430)22:8<691::AID-FLD371>3.0.CO;2-U
[5]	YE T, MITTAL R, UDAYKUMAR H S, et al. An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries[J]. Journal of Computational Physics, 1999, 156(2): 209-240. doi: 10.1006/jcph.1999.6356
[6]	FADLUN E A, VERZICCO R, ORLANDI P, et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations[J]. Journal of Computational Physics, 2000, 161(1): 35-60. doi: 10.1006/jcph.2000.6484
[7]	LUO H, MITTAL R, ZHENG X, et al. An immersed-boundary method for flow-structure interaction in biological systems with application to phonation[J]. Journal of Computational Physics, 2008, 227(22): 9303-9332. doi: 10.1016/j.jcp.2008.05.001
[8]	TSENG Y H, FERZIGER J H. A ghost-cell immersed boundary method for flow in complex geometry[J]. Journal of Computational Physics, 2003, 192(2): 593-623. doi: 10.1016/j.jcp.2003.07.024
[9]	KIM J, KIM D, CHOI H. An immersed-boundary finite-volume method for simulations of flow in complex geometries[J]. Journal of Computational Physics, 2001, 171(1): 132-150. doi: 10.1006/jcph.2001.6778
[10]	GHIAS R, MITTAL R, DONG H. A sharp interface immersed boundary method for compressible viscous flows[J]. Journal of Computational Physics, 2007, 225(1): 528-553. doi: 10.1016/j.jcp.2006.12.007
[11]	GILMANOV A, SOTIROPOULOS F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies[J]. Journal of Computational Physics, 2005, 207(2): 457-492. doi: 10.1016/j.jcp.2005.01.020
[12]	KIM D, CHOI H. Immersed boundary method for flow around an arbitrarily moving body[J]. Journal of Computational Physics, 2006, 212(2): 662-680. doi: 10.1016/j.jcp.2005.07.010
[13]	SCHNEIDERS L, HARTMANN D, MEINKE M, et al. An accurate moving boundary formulation in cut-cell methods[J]. Journal of Computational Physics, 2013, 235: 786-809. doi: 10.1016/j.jcp.2012.09.038
[14]	FAVIER J, REVELL A, PINELLI A. A lattice Boltzmann-immersed boundary method to simulate the fluid interaction with moving and slender flexible objects[J]. Journal of Computational Physics, 2014, 261: 145-161. doi: 10.1016/j.jcp.2013.12.052
[15]	MITTAL R, DONG H, BOZKURTTAS M, et al. A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries[J]. Journal of Computational Physics, 2008, 227(10): 4825-4852. doi: 10.1016/j.jcp.2008.01.028
[16]	TORO E F. Riemann Solvers and Numerical Methods for Fluid Dynamics: a Practical Introduction[M]. Berlin, Heidelberg: Springer, 2013.
[17]	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
[18]	HARTEN A, LAX P D, VAN LEER B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws[J]. SIAM Review, 1983, 25(1): 35-61. doi: 10.1137/1025002
[19]	OSHER S, FEDKIW R, PIECHOR K. Level set methods and dynamic implicit surfaces[J]. Applied Mechanics Reviews, 2004, 57(3): B15. http://scans.hebis.de/10/87/16/10871634_toc.pdf
[20]	李慧玲, 胡晓磊, 余子寒, 等. 玻璃微珠液滴碰撞分离过程数值研究[J]. 应用数学和力学, 2023, 44(12): 1512-1521. LI Huiling, HU Xiaolei, YU Zihan, et al. Numerical study on the collision-separation process of glass bead droplets[J]. Applied Mathematics and Mechanics, 2023, 44(12): 1512-1521. (in Chinese)
[21]	SHEPARD D. A two-dimensional interpolation function for irregularly-spaced data[C]//Proceedings of the 1968 23 rd ACM National Conference. 1968: 517-524.
[22]	FRANKE R, NIELSON G. Smooth interpolation of large sets of scattered data[J]. International Journal for Numerical Methods in Engineering, 1980, 15(11): 1691-1704. doi: 10.1002/nme.1620151110
[23]	MAJUMDAR S, IACCARINO G, DURBIN P. RANS solvers with adaptive structured boundary non-conforming grids[J]. Annual Research Briefs, 2001, 1: 179. http://www.stanford.edu/group/ctr/ResBriefs01/sekhar.pdf
[24]	徐维铮, 吴卫国. 三阶WENO-Z格式精度分析及其改进格式[J]. 应用数学和力学, 2018, 39(8): 946-960. XU Weizheng, WU Weiguo. Precision analysis of the 3rd-order WENO-Z scheme and its improved scheme[J]. Applied Mathematics and Mechanics, 2018, 39(8): 946-960. (in Chinese)