中文版 | English
Title

奇异值分解-广义差分在热流固多场耦合中的算法应用

Alternative Title
ALGORITHM APPLICATION OF SINGULAR VALUE DECOMPOSITION-GENERALIZED FINITE DIFFERENCE FOR THERMAL FLUID-STRUCTURE INTERACTION
Author
Name pinyin
HUANG Tao
School number
11749305
Degree
博士
Discipline
080103 流体力学
Subject category of dissertation
08 工学
Supervisor
余鹏
Mentor unit
力学与航空航天工程系
Publication Years
2022-05-19
Submission date
2022-07-26
University
哈尔滨工业大学
Place of Publication
哈尔滨
Abstract
热流固多场耦合现象在人们的日常生活、工业应用以及自然环境中十分常见。传统的 ALE 方法在处理热流固耦合问题时需要重构网格,流行的浸没边界法在处理绝热边界时精度较低。基于奇异值分解(Singular Value Decomposition)的广义差分(Generalized Finite Difference)方法,简称 SVD-GFD,在处理运动体时不需要重构网格,而且交界面处具备至少二阶精度。因此,研究发展 SVD-GFD 热流固多场耦合算法能够拓宽热流固耦合的数值研究手段,为某些热流固耦合物理问题的研究提供更加稳定且高效的数值研究工具,例如复杂几何体或者高普朗特数下的热流固多场耦合问题。同时,对热流固多场耦合问题的探讨研究不仅能够增强我们对大自然的认识,还能有助于工业技术的发展,例如河沙沉淀、化学反应器中的固体颗粒的流化以及血液中药物输送等。
现今依然比较缺乏可靠的 CFD 工具来模拟复杂几何体或高普朗特数下的热流固耦合问题。于是本文将 SVD-GFD 方法拓展成热流固多场耦合算法。通过引入布辛涅斯克假设处理热浮力,并通过热浮力项将流场与温度场进行耦合。SVD-GFD 方法所采用的是由笛卡尔网格与无网格点组成的混合网格,且控制方程在背景笛卡尔网格与无网格点上分别采用标准差分格式与 SVD-GFD 求解。同时,笛卡尔网格与无网格点之间也采用 SVD-GFD 进行耦合衔接。在时间推进上,N-S 方程采用投影法进行求解,其中的热浮力项被当作源项处理,而对流传热方程则采用二阶半隐式克兰克-尼科尔森格式,固体的运动则依然采用二阶精度的休恩方法。于是,SVD-GFD 热流固多场耦合算法在时间上二阶、空间上至少二阶,且具备较高的几何适应性。
为了检测 SVD-GFD 热流固多场耦合算法的适用性,本文利用该算法对各类热流问题进行了数值模拟,如固体不动的强迫对流与混合对流问题,涉及动边界的热流问题,以及二维和三维的热流固耦合问题。结果表明,SVD-GFD 方法处理热流中的复杂固体时比较灵活,同时保证了较高的精度和良好的稳定性。本文较为创新的将 SVD-GFD 方法拓展用于数值求解复杂几何体或者高普朗特数下的热流固多场耦合问题。
目前大部分关于颗粒沉降的研究均聚焦于几何构型简单的球体、圆柱粒子或者方形粒子。于是本文利用 SVD-GFD 多场耦合算法程序对较为复杂的几何体圆环在低雷诺数下的沉降进行了三维数值研究,探讨分析了圆环初始倾斜角(θ0)与雷诺数(ReT)对其运动过程以及流场的影响。研究表明,圆环的运动终态由 ReT 决定,不由 θ0 决定。圆环在沉降过程中最初伴随着“之”字形平动与自转,且这种运动形式随着 ReT 与 θ0 的增加而更加明显,但最终将达到倾斜角为 0 的直线稳态下落。当 ReT 与 θ0 较高时,流场中更容易产生涡街,圆环内侧附着的回流区长度随着雷诺数的增大而增加,且在下落过程中回流区的长度先增加达到最大值而后逐渐缩减至定值。此外,压力项对于圆环的阻力以及侧向升力的产生起到了主导作用,也是圆环下落速度出现减速段的原因,且这种现象随着 ReT 与 θ0 的增大而更加明显。
本文对两个大小尺寸不同的圆柱粒子在槽道中的沉降进行了数值研究,分析了不同雷诺数(Re)与尺寸差异(β)对两粒子沉降的影响。结果发现,在 Re与 β 的共同影响下,两个粒子系统在槽道中沉降的终态存在三种模式,即稳定状态、周期振荡与倍周期分岔。稳定状态包括惯性力不起主导作用的 SSI(Re ≈ 10)与惯性力起主导作用的 SSII。周期振荡又包括不受尾迹影响的周期性运动PMI 与受尾迹影响的周期性运动 PMII。PMI 与 PMII 所对应的极限环方向分别是逆时针与顺时针。出现在 8 ≤ Re ≤ 9 的 PMI 所对应的极限环随着 β 的增加而减小,而出现在 12 ≤ Re < 70 的 PMI 所对应的极限环随着 β 的增加而增大。PMII 所对应的极限环随着 β 的增加而增大。倍周期分岔主要出现在 14 ≤ Re ≤ 30,其极限环存在两个分支。
关于高普朗特数(Pr)下颗粒沉降的研究在一定程度上比较缺乏。因此,本文利用 SVD-GFD 热流固多场耦合算法对冷态粒子在非等温流体中的沉降进行了数值模拟,分析了 Pr 与格拉晓夫数(Gr)对粒子沉降与传热的影响。研究发现,在 Pr 与 Gr 的共同作用下,粒子的沉降终态呈现出沿着槽道中心线稳态下落(模态 A)、小幅周期振荡下落(模态 B)与靠近壁面处的稳态下落(模态 C)。传热由 Pr 起决定性作用且随着 Pr 增加而增强。Gr 对传热的影响较小,但在高Pr 下,这种影响会被放大。随着 Pr 的增大,冷态粒子在槽道中沉降的终态更倾向于模态 B。较高 Pr 下的粒子运动随 Pr 变化规律与较低 Pr 下的粒子运动随 Pr变化规律截然不同。例如,模态 B 下的粒子终态雷诺数(ReT)与振幅在较低 Pr范围内随着 Pr 增加而快速增加,在较高 Pr 范围下随着 Pr 增加而缓慢减小。同时,研究还发现,模态 C 下,在距离粒子较远的尾迹中存在分离点,且分离点随着 Pr 增加而逐渐靠近粒子。
Keywords
Language
Chinese
Training classes
联合培养
Enrollment Year
2017
Year of Degree Awarded
2022-07
References List

[1] Yu S, Yu P, Tang T. Effect of thermal buoyancy on flow and heat transfer around a permeable circular cylinder with internal heat generation[J]. International Journal of Heat and Mass Transfer, 2018, 126: 1143–1163.
[2] Wu Z, Ren Y, Ou G, et al. Influence of special water properties variation on the heat transfer of supercritical water flow around a sphere[J]. Chemical Engineering Science, 2020, 222: 115698.
[3] Walayat K, Zhang Z, Usman K, et al. Dynamics of elliptic particle sedimentation with thermal convection[J]. Physics of Fluids, 2018, 30(10): 103301.
[4] Majlesara M, Abouali O, Kamali R, et al. Numerical study of hot and cold spheroidal particles in a viscous fluid[J]. International Journal of Heat and Mass Transfer, 2020, 149: 119206.
[5] Yu C, Wang Y, Zhang H, et al. Numerical investigation on turbulent thermal performance of parallel flow heat exchanger with a novel polyhedral longitudinal vortex generator in shell side[J]. International Journal of Thermal Sciences, 2021, 166: 106962.
[6] Maddahi M H, Hatamipour M S, Jamialahmadi M. A model for the prediction of thermal resistance of calcium sulfate crystallization fouling in a liquid–solid fluidized bed heat exchanger with cylindrical particles[J]. International Journal of Thermal Sciences, 2019, 145: 106017.
[7] Wang X Y. A SVD-GFD Method to simulate 3D Moving Boundary Flow Problems[D]. 2008.
[8] Chew C S, Yeo K S, Shu C. A generalized finite-difference (GFD) ALE scheme for incompressible flows around moving solid bodies on hybrid meshfree–Cartesian grids[J]. Journal of Computational Physics, 2006, 218(2): 510–548.
[9] Yu P, Yeo K S, Shyam Sundar D, et al. A three-dimensional hybrid meshfree￾Cartesian scheme for fluid-body interaction[J]. International Journal for Numerical Methods in Engineering, 2011, 88(4): 385–408.
[10] Wang X Y, Yeo K S, Chew C S, et al. A SVD-GFD scheme for computing 3D incompressible viscous fluid flows[J]. Computers & Fluids, 2008, 37(6): 733–746.
[11] Yeo K S, Ang S J, Shu C. Simulation of fish swimming and manoeuvring by an SVD-GFD method on a hybrid meshfree-Cartesian grid[J]. Computers & Fluids, 2010, 39(3): 403–430.
[12] Ang S J, Yeo K S, Chew C S, et al. A singular-value decomposition (SVD)-based generalized finite difference (GFD) method for close-interaction moving boundary flow problems[J]. International Journal for Numerical Methods in Engineering, 2008, 76(12): 1892–1929.
[13] Tian F-B, Wang L. Numerical Modeling of Sperm Swimming[J]. Fluids, 2021, 6(2): 73.
[14] Hagstrom C A, Leckie D A, Smith M G. Point bar sedimentation and erosion produced by an extreme flood in a sand and gravel-bed meandering river[J]. Sedimentary Geology, 2018, 377: 1–16.
[15] Harris A D, Baumgardner S E, Sun T, et al. A Poor Relationship Between Sea Level and Deep-Water Sand Delivery[J]. Sedimentary Geology, 2018, 370: 42–51.
[16] Bruno L, Fransos D, Lo Giudice A. Solid barriers for windblown sand mitigation: Aerodynamic behavior and conceptual design guidelines[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 173: 79–90.
[17] Bruno L, Coste N, Fransos D, et al. Shield for Sand: An Innovative Barrier for Windblown Sand Mitigation[J]. Recent Patents on Engineering, 2018, 12(3): 237–246.
[18] Luo Z, Zhao Y, Lv B, et al. Dry coal beneficiation technique in the gas–solid fluidized bed: a review[J]. International Journal of Coal Preparation and Utilization, 2019: 1–29.
[19] Nie C, Pei H, Jiang L, et al. Growth of large-cell and easily-sedimentation microalgae Golenkinia SDEC-16 for biofuel production and campus sewage treatment[J]. Renewable Energy, 2018, 122: 517–525.
[20] Sakalova H, Malovanyy M, Vasylinych T, et al. The Research of Ammonium Concentrations in City Stocks and Further Sedimentation of Ion-Exchange Concentrate[J]. Journal of Ecological Engineering, 2019, 20(1): 158–164.
[21] Eggleton C D, Popel A S. Large deformation of red blood cell ghosts in a simple shear flow[J]. Physics of Fluids, 1998, 10(8): 1834–1845.
[22] Matsunaga D, Imai Y, Wagner C, et al. Reorientation of a single red blood cell during sedimentation[J]. Journal of Fluid Mechanics, 2016, 806: 102–128.
[23] Lawrence J J, Coenen W, Sánchez A L, et al. On the dispersion of a drug delivered intrathecally in the spinal canal[J]. Journal of Fluid Mechanics, 2019, 861: 679–720.
[24] Coclite A, Pascazio G, de Tullio M D, et al. Predicting the vascular adhesion of deformable drug carriers in narrow capillaries traversed by blood cells[J]. Journal of Fluids and Structures, 2018, 82: 638–650.
[25] Glowinski R, Pan T-W, Periaux J. A fictitious domain method for Dirichlet problem and applications[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 111(3–4): 283–303.
[26] Glowinski R, Pan T-W, Periaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 112(1–4): 133–148.
[27] Glowinski R, Pan T-W, Periaux J. A Lagrange multiplier/fictitious domain method for the Dirichlet problem—Generalization to some flow problems[J]. Japan Journal of Industrial and Applied Mathematics, 1995, 12(1): 87–108.
[28] Glowinski R, Pan T-W, Periaux J. A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies: (I) case where the rigid body motions are known a priori[J]. Comptes Rendus de l’Académie des Sciences-Series I-Mathematics, 1997, 324(3): 361–369.
[29] Glowinski R. A distributed Lagrange multiplier/fictitious domain method for particulate flows[J]. International Journal of Multiphase Flow, 1999: 40.
[30] Sharma N, Patankar N A. A fast computation technique for the direct numerical simulation of rigid particulate flows[J]. Journal of Computational Physics, 2005, 205(2): 439–457.
[31] Yu Z, Shao X. A direct-forcing fictitious domain method for particulate flows[J]. Journal of Computational Physics, 2007, 227(1): 292–314.
[32] Yu Z, Shao X. Direct numerical simulation of particulate flows with a fictitious domain method[J]. International Journal of Multiphase Flow, 2010, 36(2): 127–134.
[33] Xia Y, Yu Z, Deng J. A fictitious domain method for particulate flows of arbitrary density ratio[J]. Computers & Fluids, 2019, 193: 104293.
[34] Yu Z, Shao X, Wachs A. A fictitious domain method for particulate flows with heat transfer[J]. Journal of Computational Physics, 2006, 217(2): 424–452.
[35] Dan C, Wachs A. Direct Numerical Simulation of particulate flow with heat transfer[J]. International Journal of Heat and Fluid Flow, 2010, 31(6): 1050–1057.
[36] Wachs A. Rising of 3D catalyst particles in a natural convection dominated flow by a parallel DNS method[J]. Computers & Chemical Engineering, 2011, 35(11): 2169–2185.
[37] Shao X, Shi Y, Yu Z. Combination of the fictitious domain method and the sharp interface method for direct numerical simulation of particulate flows with heat transfer[J]. International Journal of Heat and Mass Transfer, 2012, 55(23–24): 6775–6785.
[38] Haeri S, Shrimpton J S. A new implicit fictitious domain method for the simulation of flow in complex geometries with heat transfer[J]. Journal of Computational Physics, 2013, 237: 21–45.
[39] Thirumalaisamy R, Patankar N A, Bhalla A P S. Handling Neumann and Robin boundary conditions in a fictitious domain volume penalization framework[J]. Journal of Computational Physics, 2022, 448: 110726.
[40] 宫兆新, 鲁传敬, 黄华雄. 浸入边界法及其应用[J]. 力学季刊, 2007, 28(3): 353–362.
[41] 杨明, 刘巨保, 岳欠杯, 等.基于浸入边界-有限元法的流固耦合碰撞数值模拟方法[J]. 应用数学与力学, 2019, 40(8): 880–892.
[42] Griffith B E, Patankar N A. Immersed Methods for Fluid–Structure Interaction[J]. Annual Review of Fluid Mechanics, 2020, 52(1): 421–448.
[43] Peskin C S. Flow patterns around heart valves a numerical method[J]. Journal of Computational Physics, 1972, 10(2): 252–271.
[44] Peskin C S. Numerical analysis of blood flow in the heart[J]. Journal of Computational Physics, 1977, 25(3): 220–252.
[45] Höfler K, Schwarzer S. Navier-Stokes simulation with constraint forces: Finite￾difference method for particle-laden flows and complex geometries[J]. Physical Review E, 2000, 61(6): 7146–7160.
[46] Mohd-Yusof J. For simulations of flow in complex geometries[J]. Annual research briefs, 1997, 317: 35.
[47] 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.
[48] Feng Z-G, Michaelides E E. Proteus: a direct forcing method in the simulations of particulate flows[J]. Journal of Computational Physics, 2005, 202(1): 20–51.
[49] Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows[J]. Journal of Computational Physics, 2005, 209(2): 448–476.
[50] Colonius T, Taira K. A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(25–28): 2131–2146.
[51] Kim J, Choi H. An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries[J]. KSME International Journal, 2004, 18(6): 1026–1035.
[52] Wang Z, Fan J, Luo K, et al. Immersed boundary method for the simulation of flows with heat transfer[J]. International Journal of Heat and Mass Transfer, 2009, 52(19–20): 4510–4518.
[53] Feng Z-G, Michaelides E E. Inclusion of heat transfer computations for particle laden flows[J]. Physics of Fluids, 2008, 20(4): 040604.
[54] Feng Z-G, Michaelides E E. Heat transfer in particulate flows with Direct Numerical Simulation (DNS)[J]. International Journal of Heat and Mass Transfer, 2009, 52(3–4): 777–786.
[55] Ren W, Shu C, Yang W. An efficient immersed boundary method for thermal flow problems with heat flux boundary conditions[J]. International Journal of Heat and Mass Transfer, 2013, 64: 694–705.
[56] Luo K, Zhuang Z, Fan J, et al. A ghost-cell immersed boundary method for simulations of heat transfer in compressible flows under different boundary conditions[J]. International Journal of Heat and Mass Transfer, 2016, 92: 708–717.
[57] Luo K, Mao C, Zhuang Z, et al. A ghost-cell immersed boundary method for the simulations of heat transfer in compressible flows under different boundary conditions Part-II: Complex geometries[J]. International Journal of Heat and Mass Transfer, 2017, 104: 98–111.
[58] Das S, Panda A, Deen N G, et al. A sharp-interface Immersed Boundary Method to simulate convective and conjugate heat transfer through highly complex periodic porous structures[J]. Chemical Engineering Science, 2018, 191: 1–18.
[59] Liu S, Jiang L, Chong K L, et al. From Rayleigh–Bénard convection to porous￾media convection: how porosity affects heat transfer and flow structure[J]. Journal of Fluid Mechanics, 2020, 895: A18.
[60] Ge M Y, Chua K J, Shu C, et al. Analytical and numerical study of tissue cryofreezing via the immersed boundary method[J]. International Journal of Heat and Mass Transfer, 2015, 83: 1–10.
[61] Tang Y, Mu L, He Y. Numerical Simulation of Fluid and Heat Transfer in a Biological Tissue Using an Immersed Boundary Method Mimicking the Exact Structure of the Microvascular Network[J]. Fluid Dynamics & Materials Processing, 2020, 16(2): 281–296.
[62] Favre F, Antepara O, Oliet C, et al. An immersed boundary method to conjugate heat transfer problems in complex geometries. Application to an automotive antenna[J]. Applied Thermal Engineering, 2019, 148: 907–928.
[63] Lee S, Hwang W. Development of an efficient immersed-boundary method with subgrid-scale models for conjugate heat transfer analysis using large eddy simulation[J]. International Journal of Heat and Mass Transfer, 2019, 134: 198–208.
[64] Aidun C K, Clausen J R. Lattice-Boltzmann Method for Complex Flows[J]. Annual Review of Fluid Mechanics, 2010, 42(1): 439–472.
[65] Ziegler D P. Boundary conditions for lattice Boltzmann simulations[J]. Journal of Statistical Physics, 1993, 71(5–6): 1171–1177.
[66] Chen S, Martínez D, Mei R. On boundary conditions in lattice Boltzmann methods[J]. Physics of Fluids, 1996, 8(9): 2527–2536.
[67] Zou Q, He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model[J]. Physics of Fluids, 1997, 9(6): 1591–1598.
[68] Zhao-Li G, Chu-Guang Z, Bao-Chang S. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method[J]. Chinese Physics, 2002, 11(4): 366–374.
[69] Guo Z, Zheng C, Shi B. An extrapolation method for boundary conditions in lattice Boltzmann method[J]. Physics of Fluids, 2002, 14(6): 2007–2010.
[70] Wang L, Zhao Y, Yang X, et al. A lattice Boltzmann analysis of the conjugate natural convection in a square enclosure with a circular cylinder[J]. Applied Mathematical Modelling, 2019, 71: 31–44.
[71] Fattahi E, Farhadi M, Sedighi K. Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus[J]. International Journal of Thermal Sciences, 2010, 49(12): 2353–2362.
[72] Tiwari A, Vanka S P. A ghost fluid Lattice Boltzmann method for complex geometries[J]. International Journal for Numerical Methods in Fluids, 2012, 69(2): 481–498.
[73] Khazaeli R, Mortazavi S, Ashrafizaadeh M. Application of a ghost fluid approach for a thermal lattice Boltzmann method[J]. Journal of Computational Physics, 2013, 250: 126–140.
[74] Mozafari-Shamsi M, Sefid M, Imani G. Developing a ghost fluid lattice Boltzmann method for simulation of thermal Dirichlet and Neumann conditions at curved boundaries[J]. Numerical Heat Transfer, Part B: Fundamentals, 2016, 70(3): 251–266.
[75] Mozafari-Shamsi M, Sefid M, Imani G. Application of the ghost fluid lattice Boltzmann method to moving curved boundaries with constant temperature or heat flux conditions[J]. Computers & Fluids, 2018, 167: 51–65.
[76] Yin X, Zhang J. An improved bounce-back scheme for complex boundary conditions in lattice Boltzmann method[J]. Journal of Computational Physics, 2012, 231(11): 4295–4303.
[77] Zhang T, Shi B, Guo Z, et al. General bounce-back scheme for concentration boundary condition in the lattice-Boltzmann method[J]. Physical Review E, 2012, 85(1): 016701.
[78] Chen Q, Zhang X, Zhang J. Improved treatments for general boundary conditions in the lattice Boltzmann method for convection-diffusion and heat transfer processes[J]. Physical Review E, 2013, 88(3): 033304.
[79] Li L, Mei R, Klausner J F. Lattice Boltzmann models for the convection￾diffusion equation: D2Q5 vs D2Q9[J]. International Journal of Heat and Mass Transfer, 2017, 108: 41–62.
[80] Li L, Mei R, Klausner J F. Boundary conditions for thermal lattice Boltzmann equation method[J]. Journal of Computational Physics, 2013, 237: 366–395.
[81] Tao S, Xu A, He Q, et al. A curved lattice Boltzmann boundary scheme for thermal convective flows with Neumann boundary condition[J]. International Journal of Heat and Mass Transfer, 2020, 150: 119345.
[82] Hirt C W, Amsden A A, Cook J L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics, 1974, 14(3): 227–253.
[83] Hughes T J R, Liu W K, Zimmermann T K. Lagrangian-Eulerian finite element formulation for incompressible viscous flows[J]. Computer Methods in Applied Mechanics and Engineering, 1981, 29(3): 329–349.
[84] Donea J, Giuliani S, Halleux J P. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions[J]. Computer Methods in Applied Mechanics and Engineering, 1982, 33(1–3): 689–723.
[85] Hu H H, Joseph D D, Crochet M J. Direct simulation of fluid particle motions[J]. Theoretical and Computational Fluid Dynamics, 1992, 3(5): 285–306.
[86] Hu H H, Patankar N A, Zhu M Y. Direct Numerical Simulations of Fluid–Solid Systems Using the Arbitrary Lagrangian–Eulerian Technique[J]. Journal of Computational Physics, 2001, 169(2): 427–462.
[87] Gan H, Chang J, Feng J J, et al. Direct numerical simulation of the sedimentation of solid particles with thermal convection[J]. Journal of Fluid Mechanics, 2003, 481: 385–411.
[88] Falcone M, Bothe D, Marschall H. 3D direct numerical simulations of reactive mass transfer from deformable single bubbles: An analysis of mass transfer coefficients and reaction selectivities[J]. Chemical Engineering Science, 2018, 177: 523–536.
[89] Jia H, Xiao X, Kang Y. Investigation of a free rising bubble with mass transfer by an arbitrary Lagrangian–Eulerian method[J]. International Journal of Heat and Mass Transfer, 2019, 137: 545–557.
[90] Ismael M A. Forced convection in partially compliant channel with two alternated baffles[J]. International Journal of Heat and Mass Transfer, 2019, 142: 118455.
[91] Mehryan S A M, Ghalambaz M, Feeoj R K, et al. Free convection in a trapezoidal enclosure divided by a flexible partition[J]. International Journal of Heat and Mass Transfer, 2020: 149: 119186.
[92] Nguyen V-T. An arbitrary Lagrangian–Eulerian discontinuous Galerkin method for simulations of flows over variable geometries[J]. Journal of Fluids and Structures, 2010, 26(2): 312–329.
[93] Zhou J, Yang X, Ye J, et al. Arbitrary Lagrangian-Eulerian method for computation of rotating target during microwave heating[J]. International Journal of Heat and Mass Transfer, 2019, 134: 271–285.
[94] Liszka T, Orkisz J. The finite difference method at arbitrary irregular grids and its application in applied mechanics[J]. Computers & Structures, 1980, 11(1–2): 83–95.
[95] Liszka T. An interpolation method for an irregular net of nodes[J]. International Journal for Numerical Methods in Engineering, 1984, 20(9): 1599–1612.
[96] Duarte C A, Oden J T. H-p clouds—an h-p meshless method[J]. Numerical Methods for Partial Differential Equations: An International Journal, 1996, 12(6): 673–705.
[97] Liszka T J, Duarte C A M, Tworzydlo W W. hp-Meshless cloud method[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1–4): 263–288.
[98] Ding H, Shu C, Yeo K S, et al. Development of least-square-based two￾dimensional finite-difference schemes and their application to simulate natural convection in a cavity[J]. Computers & Fluids, 2004, 33(1): 137–154.
[99] Ding H, Shu C, Yeo K S, et al. Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(9–11): 727–744.
[100] Trefethen L N, Bau I D. Numerical linear algebra[M]. Siam, 1997.
[101] Hämmerlin G, Hoffmann K H. Numerical mathematics[M]. Springer Science & Business Media, 2012.
[102] Zhao Y, Yeo K S, Yu P, et al. Simulation of C-Start and S-Start of Fishes by an ALE-GFD Method and a Curvature-Wave Backbone Model[J]. Structural Longevity, 2010, 4(1): 31–38.
[103] Wang X Y, Yu P, Yeo K S, et al. SVD–GFD scheme to simulate complex moving body problems in 3D space[J]. Journal of Computational Physics, 2010, 229(6): 2314-2338.
[104] Wu D, Yeo K S, Lim T T. A numerical study on the free hovering flight of a model insect at low Reynolds number[J]. Computers & Fluids, 2014, 103: 234–261.
[105] Yao Y, Yeo K S. Longitudinal free flight of a model insect flyer at low Reynolds number[J]. Computers & Fluids, 2018, 162: 72–90.
[106] Nguyen T T, Shyam Sundar D, Yeo K S, et al. Modeling and analysis of insect￾like flexible wings at low Reynolds number[J]. Journal of Fluids and Structures, 2016, 62: 294–317.
[107] Yao Y, Yeo K S, Nguyen T T. A numerical study on free hovering fruit-fly with flexible wings[C]//IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics. Springer, Cham, 2019: 15–25.
[108] Jie Y, Seng Y K. Numerical Study of Flapping-Wing Flight of Hummingbird Hawkmoth during Hovering: Longitudinal Dynamics[J]. 2016, 10(12): 8.
[109] Yao J, Yeo K S. A simplified dynamic model for controlled insect hovering flight and control stability analysis[J]. Bioinspiration & Biomimetics, 2019, 14(5): 056005.
[110] Yao J, Yeo K S. Free hovering of hummingbird hawkmoth and effects of wing mass and wing elevation[J]. Computers & Fluids, 2019, 186: 99–127.
[111] Yao J, Yeo K S. Forward flight and sideslip manoeuvre of a model hawkmoth[J]. Journal of Fluid Mechanics, 2020, 896: A22.
[112] Yu P, Lu R, He W, et al. Steady flow around an inclined torus at low Reynolds numbers: Lift and drag coefficients[J]. Computers & Fluids, 2018, 171: 53–64.
[113] Fortes A F, Joseph D D, Lundgren T S. Nonlinear mechanics of fluidization of beds of spherical particles[J]. Journal of Fluid Mechanics, 1987, 177: 467–483.
[114] ten Cate A, Nieuwstad C H, Derksen J J, et al. Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity[J]. Physics of Fluids, 2002, 14(11): 4012–4025.
[115] Zhang Y, Muller S J. Unsteady sedimentation of a sphere in wormlike micellar fluids[J]. Physical Review Fluids, 2018, 3(4): 043301.
[116] Chu C R, Wu T R, Tu Y F, et al. Interaction of two free-falling spheres in water[J]. Physics of Fluids, 2020, 32(3): 033304.
[117] Feng J, Hu H H, Joseph D D. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation[J]. Journal of Fluid Mechanics, 1994, 261: 95–134.
[118] Dash S M, Lee T S. Two spheres sedimentation dynamics in a viscous liquid column[J]. Computers & Fluids, 2015, 123: 218–234.
[119] Lee H, Fouxon I, Lee C. Sedimentation of a small sphere in stratified fluid[J]. Physical Review Fluids, 2019, 4(10): 104101.
[120] Sobhani S M J, Bazargan S, Sadeghy K. Sedimentation of an elliptic rigid particle in a yield-stress fluid: A Lattice-Boltzmann simulation[J]. Physics of Fluids, 2019, 31(8): 081902.
[121] Ardekani M N, Costa P, Breugem W P, et al. Numerical study of the sedimentation of spheroidal particles[J]. International Journal of Multiphase Flow, 2016, 87: 16–34.
[122] Gan H, Feng J J, Hu H H. Simulation of the sedimentation of melting solid particles[J]. International Journal of Multiphase Flow, 2003, 29(5): 751–769.
[123] Chorin A J. Numerical Solution of the Navier-Stokes Equations[J]. 1968, 22(104): 745–762.
[124] Chorin A J. On the Convergence of Discrete Approximations to the Navier￾Stokes Equations[J]. 1969, 23(106): 341–353.
[125] Clift R, Grace J R, Weber M E. Bubbles, Drops, and Particles[M]. Academic Press, New York, 1978.
[126] Kang Y-S, Kim J, Sohn D, et al. A new three-dimensional variable-node finite element and its application for fluid–solid interaction problems[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 281: 81–105.
[127] Kim J, Lee C, Kim H-G, et al. The surrounding cell method based on the S-FEM for analysis of FSI problems dealing with an immersed solid[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 341: 658–694.
[128] Nie D, Lin J, Gao Q. Settling behavior of two particles with different densities in a vertical channel[J]. Computers & Fluids, 2017, 156: 353–367.
[129] Aidun C K, Ding E-J. Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state[J]. Physics of Fluids, 2003, 15(6): 1612.
[130] Bharti R P, Chhabra R P, Eswaran V. A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder[J]. Heat and Mass Transfer, 2007, 43(7): 639–648.
[131] Zhang N, Zheng Z C, Eckels S. Study of heat-transfer on the surface of a circular cylinder in flow using an immersed-boundary method[J]. International Journal of Heat and Fluid Flow, 2008, 29(6): 1558–1566.
[132] Ren W W, Shu C, Wu J, et al. Boundary condition-enforced immersed boundary method for thermal flow problems with Dirichlet temperature condition and its applications[J]. Computers & Fluids, 2012, 57: 40–51.
[133] Pan D. A General Boundary Condition Treatment in Immersed Boundary Methods for Incompressible Navier-Stokes Equations with Heat Transfer[J]. Numerical Heat Transfer, Part B: Fundamentals, 2012, 61(4): 279–297.
[134] Wang Y, Shu C, Yang L M. Boundary condition-enforced immersed boundary￾lattice Boltzmann flux solver for thermal flows with Neumann boundary conditions[J]. Journal of Computational Physics, 2016, 306: 237–252.
[135] Hu Y, Li D, Shu S, et al. An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems[J]. Communications in Computational Physics, 2016, 20(5): 1210–1257.
[136] Guo T, Shen E, Lu Z, et al. Implicit heat flux correction-based immersed boundary-finite volume method for thermal flows with Neumann boundary conditions[J]. Journal of Computational Physics, 2019, 386: 64–83.
[137] Khanafer K, Aithal S M. Laminar mixed convection flow and heat transfer characteristics in a lid driven cavity with a circular cylinder[J]. International Journal of Heat and Mass Transfer, 2013, 66: 200–209.
[138] Khanafer K, Aithal S M, Vafai K. Mixed convection heat transfer in a differentially heated cavity with two rotating cylinders[J]. International Journal of Thermal Sciences, 2019, 135: 117–132.
[139] Xu A, Shi L, Zhao T S. Thermal effects on the sedimentation behavior of elliptical particles[J]. International Journal of Heat and Mass Transfer, 2018, 126: 753–764.
[140] Wang Z, Fan J, Luo K. Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles[J]. International Journal of Multiphase Flow, 2008, 34(3): 283–302.
[141] Yang B, Chen S, Cao C, et al. Lattice Boltzmann simulation of two cold particles settling in Newtonian fluid with thermal convection[J]. International Journal of Heat and Mass Transfer, 2016, 93: 477–490.
[142] Yu Z, Phan-Thien N, Tanner R I. Dynamic simulation of sphere motion in a vertical tube[J]. Journal of Fluid Mechanics, 2004, 518: 61–93.
[143] Loisel V, Abbas M, Masbernat O, et al. The effect of neutrally buoyant finite￾size particles on channel flows in the laminar-turbulent transition regime[J]. Physics of Fluids, 2013, 25(12): 123304.
[144] Lashgari I, Picano F, Breugem W P, et al. Channel flow of rigid sphere suspensions: Particle dynamics in the inertial regime[J]. International Journal of Multiphase Flow, 2016, 78: 12–24.
[145] Sheard G J, Thompson M C, Hourigan K. From spheres to circular cylinders: non-axisymmetric transitions in the flow past rings[J]. Journal of Fluid Mechanics, 2004, 506: 45–78.
[146] Sheard G J, Thompson M C, Hourigan K. From spheres to circular cylinders: the stability and flow structures of bluff ring wakes[J]. Journal of Fluid Mechanics, 2003, 492: 147–180.
[147] Sheard G J, Thompson M C, Hourigan K. Asymmetric structure and non-linear transition behaviour of the wakes of toroidal bodies[J]. European Journal of Mechanics - B/Fluids, 2004, 23(1): 167–179.
[148] Roshko A. On the development of turbulent wakes from vortex streets[R]. 1954: 1191.
[149] Monson D R. The Effect of Transverse Curvature on the Drag and Vortex Shedding of Elongated Bluff Bodies at Low Reynolds Number[J]. Journal of Fluids Engineering, 1983, 105(3): 308–318.
[150] Leweke T, Provansal M. The flow behind rings: bluff body wakes without end effects[J]. Journal of Fluid Mechanics, 1995, 288: 265–310.
[151] Leweke T, Provansal M, Boyer L. Stability of vortex shedding modes in the wake of a ring at low Reynolds numbers[J]. Physical Review Letters, 1993, 71(21): 3469–3472.
[152] Yu P. Steady flow past a torus with aspect ratio less than 5[J]. Journal of Fluids and Structures, 2014, 48: 393–406.
[153] Majumdar S R, O’Neill M E. On axisymmetric stokes flow past a torus[J]. Zeitschrift für angewandte Mathematik und Physik ZAMP, 1977, 28(4): 541–550.
[154] Goren S L, O’Neill M E. Asymmetric creeping motion of an open torus[J]. Journal of Fluid Mechanics, 1980, 101(1): 97–110.
[155] Johnson R E, Wu T Y. Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus[J]. Journal of Fluid Mechanics, 1979, 95(2): 263–277.
[156] Amarakoon A M D. Drag measurements for axisymmetric motion of a torus at low Reynolds number[J]. Physics of Fluids, 1982, 25(9): 1495.
[157] Sheard G J, Hourigan K, Thompson M C. Computations of the drag coefficients for low-Reynolds-number flow past rings[J]. Journal of Fluid Mechanics, 2005, 526: 257–275.
[158] Inoue Y, Yamashita S, Kumada M. An experimental study on a wake behind a torus using the UVP monitor[J]. Experiments in Fluids, 1999, 26(3): 197–207.
[159] Johnson T A, Patel V C. Flow past a sphere up to a Reynolds number of 300[J]. Journal of Fluid Mechanics, 1999, 378: 19–70.
[160] Wang L, Guo Z L, Mi J C. Drafting, kissing and tumbling process of two particles with different sizes[J]. Computers & Fluids, 2014, 96: 20–34.
[161] Daniel W B, Ecke R E, Subramanian G, et al. Clusters of sedimenting high￾Reynolds-number particles[J]. Journal of Fluid Mechanics, 2009, 625: 371–385.
[162] Uhlmann M, Doychev T. Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion[J]. Journal of Fluid Mechanics, 2014, 752: 310–348.
[163] Verjus R, Guillou S, Ezersky A, et al. Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: Multiple states and routes to chaos[J]. Physics of Fluids, 2016, 28(12): 123303.
[164] Zhang Y, Zhang Y, Pan G, et al. Numerical study of the particle sedimentation in a viscous fluid using a coupled DEM-IB-CLBM approach[J]. Journal of Computational Physics, 2018, 368: 1–20.
[165] Nie D, Lin J. Discontinuity in the sedimentation system with two particles having different densities in a vertical channel[J]. Physical Review E, 2019, 99(5): 053112.
[166] Nie D, Lin J. Simulation of sedimentation of two spheres with different densities in a square tube[J]. Journal of Fluid Mechanics, 2020, 896: A12.
[167] Nie D, Guan G, Lin J. Interaction between two unequal particles at intermediate Reynolds numbers: A pattern of horizontal oscillatory motion[J]. Physical Review E, 2021, 103(1): 013105.
[168] Fendell F E. Laminar natural convection about an isothermally heated sphere at small Grashof number[J]. Journal of Fluid Mechanics, 1968, 34(1): 163–176.
[169] Hieber C A, Gebhart B. Mixed convection from a sphere at small Reynolds and Grashof numbers[J]. Journal of Fluid Mechanics, 1969, 38(1): 137–159.
[170] Feng Z-G, Michaelides E E. Unsteady Heat Transfer From a Sphere at Small Peclet Numbers[J]. Journal of Fluids Engineering, 1996, 118(1): 96–102.
[171] Bar-Ziv E, Zhao B, Mograbi E, et al. Experimental validation of the Stokes law at nonisothermal conditions[J]. Physics of Fluids, 2002, 14(6): 2015–2018.
[172] Hashemi Z, Abouali O, Kamali R. Three dimensional thermal Lattice Boltzmann simulation of heating/cooling spheres falling in a Newtonian liquid[J]. International Journal of Thermal Sciences, 2014, 82: 23–33.

Academic Degree Assessment Sub committee
力学与航空航天工程系
Domestic book classification number
O359.1
Data Source
人工提交
Document TypeThesis
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/356277
DepartmentDepartment of Mechanics and Aerospace Engineering
Recommended Citation
GB/T 7714
黄涛. 奇异值分解-广义差分在热流固多场耦合中的算法应用[D]. 哈尔滨. 哈尔滨工业大学,2022.
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