Analysis of Heat and Fluid Flow Problems in a Multiply-Connected Region, using a Conformal Mapping

2011 Fiscal Year Final Research Report

• Project/Area Number: 20540108
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: MOCHIMARU Yoshihiro 東京工業大学, 大学院・理工学研究科, 教授 (90092577)
• Project Period (FY): 2008 – 2011
• Keywords: 数理物理 / 数理工学 / シミュレーション工学 / 流体工学

Research Abstract

Extension and applicability of conformal mapping used in a finite difference scheme is investigated. Univalence of conformal mapping required is searched in a family of functions possessing parameters, whereas an explicit condition for multiply-connectedness is clearly introduced and several concrete conformal mapping functions for a multiply-connected domain are proposed, supplemented with a transform of a variable if any, since such a conformal mapping function is not uniquely determined as long as only corresponding boundary configurations are specified a priori.

Research Products

• [Journal Article] Basic Idea for Numerical Analysis of Heat and Fluid Flow Problems, using A Spectral Finite Difference Scheme (2011)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: Journal of Analytical & Bioanalytical Techniques Volume: 2 Pages: 33
  • Peer Reviewed
• [Journal Article] Spectral Finite Difference Analysis of Natural Convection in a Triply-Connected Region of a Nearly Parallel Enclosure (2011)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: Second International Conference on Computational Methods for Thermal Problems Pages: 151-154
  • Peer Reviewed
• [Journal Article] Spectral Finite Difference Analysis of Natural Convection in a Multiply-Connected Region with Sudden Expansion (2011)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: International Journal of Pure and Applied Mathematics Volume: 70 Pages: 765-774
  • Peer Reviewed
• [Journal Article] Spectral Finite Difference Analysis of Natural Convection in a Multiply-Connected Region (2010)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: International Electronic Journal of Pure and Applied Mathematics Volume: 2 Pages: 7-15
  • Peer Reviewed
• [Journal Article] Spectral Finite Difference Analysis for Natural Convection in a Multiply-connected Region (2010)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: Thermal and Environmental Issues in Energy Systems Volume: 2 Pages: 1097-1100
  • Peer Reviewed
• [Journal Article] Conformal Mapping from a Rectangular to a Circular Region (2010)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: Using Special Functions, Int. J. Pure and Applied Mathematics Volume: 62 Pages: 185-193
  • Peer Reviewed
• [Journal Article] Numerical Analysis of Natural Convection Heat Transfer from a Fin in a Parallel Enclosure (2009)
  • Author(s): Y. Mochimaru & M-W. Bae
  • Journal Title: ISME Busan 2009 Proceedings Volume: (CD-ROM) Pages: 153. 1-153. 5
• [Journal Article] Spectral Finite Difference Analysis in a Doubly-Connected Region (2009)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: First International Conference on Computational Methods for Thermal Problems Pages: 191-194
  • Peer Reviewed
• [Journal Article] Natural Convection Heat Transfer from Near Pentagon-like Configuration, using a Mathieu Function Expansion (2009)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: Proceedings of ICCHMT' 09 Pages: 105-110
• [Journal Article] Precise Estimation of Conformal Mapping in Heat and Fluid Flow Problems (2008)
  • Author(s): Y. Mochimaru & M-w. Bae
  • Journal Title: KSAE2008 Annual Conf. And Exhibition Pages: 148
• [Journal Article] Existence/Non-Existence of Conformal Mapping in Some Family of Functions (2008)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: International J. Pure and Applied Math. Volume: 49 Pages: 497-503
  • Peer Reviewed
• [Journal Article] Existence Non-Existence of Conformal Mapping in Some Family of Functions (2008)
  • Author(s): Yoshihiro Mochimaru
  • Journal Title: Fifth International Conf. Applied Math. Comp. Volume: 2 Pages: 307-308
• [Presentation] Basic Idea for Numerical Analysis of Heat and Fluid Flow Problems, using a Spectral Finite Difference Scheme (2011)
  • Author(s): Yoshihiro Mochimaru
  • Organizer: Second International Conference on Analytical and Bioanalytical Techniques
  • Place of Presentation: San Francisco, U. S. A.
  • Year and Date: 2011-12-16
• [Presentation] Spectral Finite Difference Analysis for Natural Convection in a Multiply-connected Region (2010)
  • Author(s): Yoshihiro Mochimaru
  • Organizer: Thermal and Environmental Issues in Energy Systems
  • Place of Presentation: Sorrento, Italy
  • Year and Date: 2010-05-19
• [Presentation] Precise Estimation of Conformal Mapping in Heat and Fluid Flow Problems (2008)
  • Author(s): Yoshihiro Mochimaru
  • Organizer: KSAE2008 Annual Conf. And Exhibition
  • Place of Presentation: Taejon, Korea
  • Year and Date: 2008-11-20
• [Presentation] Existence Non-Existence of Conformal Mapping in Some Family of Functions (2008)
  • Author(s): Yoshihiro Mochimaru
  • Organizer: Fifth International Conf. Applied Math. Comp.
  • Place of Presentation: Plovdiv, Bulgaria
  • Year and Date: 2008-08-13