粘弾性流体に特有な渦の数理解析

• Project/Area Number: 18H01135
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Kanazawa University
• Principal Investigator: 野津 裕史 金沢大学, 数物科学系, 教授 (00588783)
• Co-Investigator(Kenkyū-buntansha): 中澤 嵩 大阪大学, 数理・データ科学教育研究センター, 准教授 (20726765) ; 米田 剛 東京大学, 大学院数理科学研究科, 准教授 (30619086) ; SHEN Amy 沖縄科学技術大学院大学, マイクロ・バイオ・ナノ流体ユニット, 教授 (70740314) ; 佐藤 勝彦 北海道大学, 電子科学研究所, 准教授 (90513622)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Project Status: Granted (Fiscal Year 2020)
• Budget Amount: ¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000); Fiscal Year 2021: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2020: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2019: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2018: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
• Keywords: 粘弾性流体 / 渦

Outline of Annual Research Achievements

本研究において、粘弾性流体に特有な渦が現れる理由を解明する。円柱周りの流れを考える。例えば水などの粘性流体では、（流体の粘度と速度に関する無次元数である）レイノルズ数がある程度大きいときに円柱の下流方向においてカルマン渦が発生する。これはよく知られている事実であり、非圧縮ナヴィエ・ストークス方程式の数値シミュレーションによって再現できる。一方、粘弾性流体では、レイノルズ数が小さく（緩和時間と剪断速度に関する無次元数である）ワイゼンベルグ数が大きいときに円柱の上流方向において、渦が発生することが物理実験によって確認されている。これが、粘弾性流体に特有な渦である。粘弾性流体に特有な渦を偏微分方程式の数値シミュレーションによって再現することが本研究の目的である。そのために、適切な偏微分方程式の選択あるいはモデリングおよび数値シミュレーション手法の構築とその実行が必要である。本年度、数値シミュレーション手法について重点的に検討を行い、エネルギーに基づく数値シミュレーション手法の構築および上対流マックスウェル微分を流れの軌跡に沿って取り扱う手法の時間２次精度化を行った。特に、上対流マックスウェル微分の時間２次精度化は、差分法と有限要素法のどちらでも利用可能な汎用的な数学的結果を与えている。一方で、空間２、３次元のアダプティブ・メッシュ・リファインメントの開発も進めた。粘弾性流体のためのアダプティブ・メッシュ・リファインメントを用いた高精度な数値計算スキームの開発に向けて、今後の発展が期待できる。

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

粘弾性流体を扱うための知見および数値シミュレーション手法の高精度化のための理論と実装技術を蓄積できている。

Strategy for Future Research Activity

様々な粘弾性流体モデルの高ワイゼンベルグ数の粘弾性流体モデルの数値シミュレーションを行い、粘弾性流体に特有な渦が発生するメカニズムを解明する。

Research Products

• [Journal Article] GENERALIZED FLOW FIELD SHAPE OPTIMIZATION WITH SNAPSHOT POD (2020)
  • Author(s): T. Nakazawa
  • Journal Title: A2 Volume: 75 Issue: 2 Pages: I_135-I_143
  • DOI: 10.2208/jscejam.75.2_i_135 10.2208/jscejam.75.2_I_135
  • ISSN: 2185-4661
  • Year and Date: 2020-02-06
  • Peer Reviewed
• [Journal Article] Particle trapping in merging flow junctions by fluid-solute-colloid-boundary interactions (2020)
  • Author(s): S. Shin, J.T. Ault, K. Toda-Peters, A.Q. Shen
  • Journal Title: Physical Review Fluids Volume: 5
  • DOI: 10.1103/physrevfluids.5.024304
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Intracellular nanomaterial delivery via spiral hydroporation (2020)
  • Author(s): Kang, Carlson, Kang, Lee, Haward, Choi, Shen, Chung
  • Journal Title: ACS Nano Volume: 14 Pages: 3048-3058
  • DOI: 10.1021/acsnano.9b07930
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Analysis of a projection method for the Stokes problem using an ε-Stokes approach (2019)
  • Author(s): M. Kimura, K. Matsui, A. Muntean, H. Notsu
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 36 Pages: 959-985
  • DOI: 10.1007/s13160-019-00373-3
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Chaos in nanomagnet via feedback current (2019)
  • Author(s): T. Taniguchi, N. Akashi, H. Notsu, M. Kimura, H. Tsukahara, K. Nakajima
  • Journal Title: Physical Review B Volume: 100 Pages: 174425-174425
  • DOI: 10.1103/physrevb.100.174425
  • Peer Reviewed
• [Journal Article] Theoretical and numerical studies for energy estimates of the shallow water equations with a transmission boundary condition (2019)
  • Author(s): M.M. Murshed, K. Futai, M. Kimura, H. Notsu
  • Journal Title: Discrete & Continuous Dynamical Systems - S Volume: -
  • DOI: 10.3934/dcdss.2020230
  • Peer Reviewed
• [Journal Article] Stability estimates and a Lagrange-Galerkin scheme for a Navier-Stokes type model of flow in non-homogeneous porous media (2019)
  • Author(s): I. Wijaya, H. Notsu
  • Journal Title: Discrete & Continuous Dynamical Systems - S Volume: -
  • DOI: 10.3934/dcdss.2020234
  • Peer Reviewed
• [Journal Article] Substrate stiffness affects particle distribution pattern in a drying suspension droplet (2019)
  • Author(s): R. Iqbal, A. Matsumoto, A. Sudeepthi, A.Q. Shen, A.K. Sen
  • Journal Title: Applied Physics Letters Volume: 114 Pages: 253701-253701
  • DOI: 10.1063/1.5097620
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Rheological scaling of ionic-liquid-based polyelectrolytes in ionic liquid solutions (2019)
  • Author(s): A. Matsumoto, F. Del Giudice, R. Rotrattanadumrong, A.Q. Shen
  • Journal Title: Macromolecules Volume: 52 Pages: 2759-2771
  • DOI: 10.1021/acs.macromol.8b02544
  • Peer Reviewed / Open Access
• [Journal Article] Heterogeneous flow inside threads of low viscosity fluids leads to anomalous long filament lifetimes (2019)
  • Author(s): S.M. Recktenwald, S.J. Haward, A.Q. Shen, N. Willenbacher
  • Journal Title: Scientific Reports Volume: 9 Pages: 7110-7121
  • DOI: 10.1038/s41598-019-43590-z
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Microfluidic analog of an opposed-jets device (2019)
  • Author(s): Haward, Hopkins, Toda-Peters, Shen
  • Journal Title: Applied Physics Letters Volume: 114 Pages: 223701-223701
  • DOI: 10.1063/1.5097850
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Coupling of vortex breakdown and stability in a swirling flow (2019)
  • Author(s): Chan, Ault, Haward, Meiburg, Shen
  • Journal Title: Physical Review Fluids Volume: 4 Pages: 084701-084701
  • DOI: 10.1103/physrevfluids.4.084701
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Purely elastic fluid-structure interactions in microfluidics: Implications for mucociliary flows (2019)
  • Author(s): C.C. Hopkins, S.J. Haward, A.Q. Shen
  • Journal Title: Small Volume: 16 Pages: 1903872-1903872
  • DOI: 10.1002/smll.201903872
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Shape optimization problem based on the generalized J integral considering RANS and Snapshot POD (2019)
  • Author(s): T. Nakazawa
  • Journal Title: JFST Volume: 14 Issue: 3 Pages: JFST0015-JFST0015
  • DOI: 10.1299/jfst.2019jfst0015
  • ISSN: 1880-5558
  • Peer Reviewed / Open Access
• [Journal Article] Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition (2019)
  • Author(s): Takashi Nakazawa and Chihiro Nakajima
  • Journal Title: IIS Volume: 25 Issue: 2 Pages: 147-160
  • DOI: 10.4036/iis.2019.b.02 10.4036/iis.2019.B.02
  • NAID: 130007705282
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access
• [Journal Article] The Gradient Flow Structure of an Extended Maxwell Viscoelastic Model and a Structure-Preserving Finite Element Scheme (2019)
  • Author(s): Kimura Masato、Notsu Hirofumi、Tanaka Yoshimi、Yamamoto Hiroki
  • Journal Title: Journal of Scientific Computing Volume: 78 Pages: 1111-1131
  • DOI: 10.1007/s10915-018-0799-2
  • Peer Reviewed
• [Journal Article] Controlled symmetry breaking and vortex dynamics in intersecting flows (2019)
  • Author(s): Burshtein Noa、Shen Amy Q.、Haward Simon J.
  • Journal Title: Physics of fluids Volume: 31 Pages: 034104-034104
  • DOI: 10.1063/1.5087732
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A local instability mechanism of the Navier-Stokes flow with swirl on the no-slip flat boundary (2019)
  • Author(s): L. Lichtenfelz, T. Yoneda
  • Journal Title: Journal of Mathematical Fluid Mechanics Volume: 21
  • DOI: 10.1007/s00021-019-0424-7
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Applications of Campanato spaces with variable growth condition to the Navier-Stokes equation (2019)
  • Author(s): E. Nakai, T. Yoneda
  • Journal Title: Hokkaido Mathematical Journal Volume: 48 Pages: 99-140
  • Peer Reviewed
• [Journal Article] Apical Junctional Fluctuations Lead to Cell Flow while Maintaining Epithelial Integrity (2019)
  • Author(s): Okuda Satoru、Kuranaga Erina、Sato Katsuhiko
  • Journal Title: Biophysical Journal Volume: 116 Pages: 1159-1170
  • DOI: 10.1016/j.bpj.2019.01.039
  • Peer Reviewed / Open Access
• [Journal Article] Flow control by the fusion between mathematical and data sciences (2019)
  • Author(s): T. Nakazawa
  • Journal Title: JAXA Special Publication: Proceedings of the 50th Fluid Dynamics Conference / the 36th Aerospace Numerical Simulation Symposium Volume: JAXA-SP-18-005 Pages: 131-134
  • Peer Reviewed / Open Access
• [Journal Article] Multi-axial non-contact in situ micromanipulation by steady streaming around two oscillating cylinders on holonomic miniature robots (2018)
  • Author(s): O. Fuchiwaki, Y. Tanaka, H. Notsu, T. Hyakutake
  • Journal Title: Microfluidics and Nanofluidics Volume: 22
  • DOI: 10.1007/s10404-018-2098-5
  • Peer Reviewed
• [Journal Article] “Phase diagram” for viscoelastic Poiseuille flow over a wavy surface (2018)
  • Author(s): Haward Simon J.、Page Jacob、Zaki Tamer A.、Shen Amy Q.
  • Journal Title: Physics of Fluids Volume: 30 Pages: 113101-113101
  • DOI: 10.1063/1.5057392
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Evaporation and morphological patterns of bi-dispersed colloidal droplets on hydrophilic and hydrophobic surfaces (2018)
  • Author(s): R. Iqbal, B. Majhy, A.Q. Shen, A.K. Sen
  • Journal Title: Soft Matter Volume: 14 Pages: 9901-9909
  • DOI: 10.1039/c8sm01915k
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Fluid Viscoelasticity Drives Self-Assembly of Particle Trains in a Straight Microfluidic Channel (2018)
  • Author(s): Del Giudice Francesco、D’Avino Gaetano、Greco Francesco、Maffettone Pier Luca、Shen Amy Q.
  • Journal Title: Physical Review Applied Volume: 10
  • DOI: 10.1103/physrevapplied.10.064058
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Continuity of the solution map of the Euler equations in Holder spaces and weak norm inflation in Besov spaces (2018)
  • Author(s): Misiolek Gerard、Yoneda Tsuyoshi
  • Journal Title: Transactions of the American Mathematical Society Volume: 370 Pages: 4709-4730
  • DOI: 10.1090/tran/7101
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Global well posedness for a two-fluid model (2018)
  • Author(s): Y. Giga, S. Ibrahim, S. Shen, T. Yoneda
  • Journal Title: Differential Integral Equations Volume: 31 Pages: 187-214
  • NAID: 120006459752
  • Peer Reviewed / Int'l Joint Research
• [Presentation] 界面をもつポリマー流体の３次元挙動の数理解析 (2020)
  • Author(s): 野津裕史
  • Organizer: 数学パワーが世界を変える2020
  • Invited
• [Presentation] 移流拡散方程式のための質量保存時間２次精度 Lagrange-Galerkin スキームとその２流体問題への応用 (2020)
  • Author(s): 野津裕史, 二井滉太
  • Organizer: 日本応用数理学会 第16回研究部会連合発表会
• [Presentation] The gradient flow structure of an extended Maxwell viscoelastic model (2019)
  • Author(s): H. Notsu
  • Organizer: MAFELAP 2019: The Mathematics of Finite Elements and Applications 2019
  • Int'l Joint Research / Invited
• [Presentation] A Lagrange-Galerkin scheme with adaptive mesh refinement for two-fluid flow problems (2019)
  • Author(s): H. Notsu
  • Organizer: AFSI 2019: Advances in Computational Fluid-Structure Interaction and Flow Simulation
  • Int'l Joint Research / Invited
• [Presentation] Lagrange-Galerkin schemes for flow problems (2019)
  • Author(s): H. Notsu
  • Organizer: The 142nd Everest Forum
  • Int'l Joint Research / Invited
• [Presentation] An extended Maxwell viscoelastic model: Derivation and FEM (2019)
  • Author(s): H. Notsu
  • Organizer: Karlstad Applied Analysis Seminar
  • Int'l Joint Research / Invited
• [Presentation] Numerical analysis of the stabilized Lagrange-Galerkin method (2019)
  • Author(s): H. Notsu
  • Organizer: Karlstad Applied Analysis Seminar
  • Int'l Joint Research / Invited
• [Presentation] 移流拡散問題のための時間２次精度質量保存アダプティブ Lagrange-Galerkin スキームとその応用 (2019)
  • Author(s): 野津裕史, 二井滉太
  • Organizer: 第24回計算工学講演会
• [Presentation] ラグランジュ-ガレルキン法(特性曲線有限要素法)の数値解析 (2019)
  • Author(s): 野津裕史
  • Organizer: 東京大学大学院数理科学研究科, 集中講義
  • Invited
• [Presentation] Maxwell 型粘弾性モデルの勾配流構造 (2019)
  • Author(s): 野津裕史, 木村正人, 田中良巳, 山本大輝
  • Organizer: RIMS 研究集会: 諸科学分野を結ぶ基礎学問としての数値解析学
  • Invited
• [Presentation] Reservoir computing を用いた流体の情報処理能力の解析とその応用 (2019)
  • Author(s): 後藤健, 中嶋浩平, 野津裕史
  • Organizer: 2019年度応用数学合同研究集会
• [Presentation] Numerical studies of viscoelastic droplets (2019)
  • Author(s): D. de O. Medeiros, H. Notsu, C.M. Oishi
  • Organizer: 2019年度応用数学合同研究集会
• [Presentation] The gradient flow structure of the Maxwell viscoelastic model and a structure-preserving finite element scheme (2018)
  • Author(s): H. Notsu
  • Organizer: Conference on Mathematical Fluid Dynamics
  • Int'l Joint Research / Invited
• [Presentation] The gradient flow structure of the Maxwell viscoelastic model and a structure-preserving finite element scheme (2018)
  • Author(s): H. Notsu
  • Organizer: KSIAM 2018 Spring Conference
  • Int'l Joint Research / Invited
• [Presentation] A mass-conservative Lagrange-Galerkin scheme of second-order in time with adaptive mesh refinement for convection problems (2018)
  • Author(s): H. Notsu
  • Organizer: CoMFoS18
  • Int'l Joint Research / Invited
• [Presentation] Numerical analysis of Lagrange-Galerkin schemes for flow problems (2018)
  • Author(s): H. Notsu
  • Organizer: International Workshop on Computational Science 2018
  • Int'l Joint Research / Invited
• [Presentation] A mass-conservative Lagrange-Galerkin scheme of second-order in time with AMR for convection problems (2018)
  • Author(s): H. Notsu
  • Organizer: CJK2018: The Seventh China-Japan-Korea Joint Conference on Numerical Mathematics
  • Int'l Joint Research / Invited
• [Presentation] 特性曲線を用いた流れ問題のための有限要素スキームの開発 (2018)
  • Author(s): 野津裕史
  • Organizer: 山形大学グリーンマテリアル成形加工研究センター 第４２回合同セミナー
  • Invited
• [Presentation] アダプティブ Lagrange-Galerkin スキームによる３次元移流問題の数値計算 (2018)
  • Author(s): 二井滉太, 野津裕史
  • Organizer: 第23回計算工学講演会
• [Presentation] Development of an accurate Lagrange-Galerkin scheme with adaptive mesh refinement (2018)
  • Author(s): H. Notsu
  • Organizer: Extended Kanazawa Analysis Seminar
  • Invited
• [Presentation] 時間2次精度質量保存アダプティブ Lagrange-Galerkin スキームと2流体問題への応用 (2018)
  • Author(s): 二井滉太, 野津裕史
  • Organizer: 2018年度応用数学合同研究集会
• [Presentation] 2, 3次元 ALBERTA 型アダプティブ・メッシュ・リファインメントアルゴリズム (2018)
  • Author(s): 二井滉太, 野津裕史
  • Organizer: 日本応用数理学会環瀬戸内応用数理研究部会第22回シンポジウム
• [Book] 数理流体力学への招待 (2020)
  • Author(s): 米田剛
  • Total Pages: 114
  • Publisher: サイエンス社
  • ISBN: 9784781914688
• [Remarks] Scheme.HN
  • URL: http://scheme.hn/
• [Funded Workshop] CoMFoS19: Mathematical Aspects of Continuum Mechanics (2019)