マルチモーメント制約を用いた高解像度数値解法の一般化と実用化

• 研究課題/領域番号: 24560187
• 研究種目: 基盤研究(C)
• 配分区分: 基金
• 応募区分: 一般
• 研究分野: 流体工学
• 研究機関: 東京工業大学
• 研究代表者: 肖 鋒 東京工業大学, 総合理工学研究科(研究院), 准教授 (50280912)
• 研究期間 (年度): 2012-04-01 – 2015-03-31
• 研究課題ステータス: 完了 (2014年度)
• 配分額: 5,330千円 (直接経費: 4,100千円、間接経費: 1,230千円); 2014年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円); 2013年度: 1,950千円 (直接経費: 1,500千円、間接経費: 450千円); 2012年度: 2,080千円 (直接経費: 1,600千円、間接経費: 480千円)
• キーワード: 高精度数値解法 / 圧縮性流体 / 浅水波モデル / 保存解法 / マルチ・モーメント制約 / WENO再構築 / 衝撃波 / 数値振動 / 数値流体力学 / 高精度解法 / 実用性 / 流束再構築 / 非構造格子 / 圧縮性流れ / 数値解法 / 高精度スキーム / 多相流 / 国際研究者交流 / 台湾：中国

研究成果の概要

(１）マルチモーメント制約高精度数値解法の一般的な定式化を提案し，制約条件の数値的性質について理論解析と数値実験による検討を行い，実問題の数値モデルを構築する際に制約条件の選び方における指針を見出すことができた。(２）マルチモーメント制約条件を用い，高い実用性を有する4次精度高解像度数値解法MCV-WENO4法を提案し，検証した。(３）Gauss-Legendre点を用いたラグランジュ補間関数に基づく高精度数値解法（GLPCC）を提案し，DG法と同等の数値性質を有することを示した。(４）非構造格子へ拡張し，任意形状メッシュ要素におけるマルチモーメント有限体積法のフレームワークを構築した。

研究成果

• [雑誌論文] A high-order conservative collocation scheme and its application to global shallow water equations (2015)
  • 著者名/発表者名: C. G. Chen, X.L. Li, X.S. Shen and F. Xiao
  • 雑誌名: Geosci. Model Dev. 巻: 8 号: 2 ページ: 221-233
  • DOI: 10.5194/gmd-8-221-2015
  • 査読あり / オープンアクセス / 謝辞記載あり
• [雑誌論文] Global shallow water models based on multi-moment constrained finite volume method and three quasi-uniform spherical grids (2014)
  • 著者名/発表者名: C.G. Chen, X.L. Li, X.S. Shen and F. Xiao
  • 雑誌名: J. Comp. Phys. 巻: 271 ページ: 191-223
  • DOI: 10.1016/j.jcp.2013.10.026
  • 査読あり / 謝辞記載あり
• [雑誌論文] An interface capturing method with a continuous function: The THINC method on unstructured triangular and tetrahedral meshes (2014)
  • 著者名/発表者名: K.M. Shyue and F. Xiao
  • 雑誌名: Journal of Computational Physics 巻: 268 ページ: 326-354
  • DOI: 10.1016/j.jcp.2014.03.010
  • 査読あり
• [雑誌論文] An interface capturing method with a continuous function: The THINC method on unstructured triangular and tetrahedral meshes (2014)
  • 著者名/発表者名: S. Ii, B. Xie and F. Xiao
  • 雑誌名: J. Comput. Phys. 巻: 259 ページ: 260-269
  • DOI: 10.1016/j.jcp.2013.11.034
  • 査読あり / 謝辞記載あり
• [雑誌論文] A global shallow-water model on an icosahedral hexagonal grid by a multi-moment constrained finite-volume scheme (2014)
  • 著者名/発表者名: C.G. Chen, J.Z. Bin, F. Xiao, X.L. Li, X.S. Shen
  • 雑誌名: Q. J. R. Meteorol. Soc. 巻: 140 号: 679 ページ: 639-650
  • DOI: 10.1002/qj.2157
  • 査読あり / 謝辞記載あり
• [雑誌論文] Simulation and mitigation of the magneto-Rayleigh-Taylor instabilities in Z-pinch gas discharge extreme ultraviolet plasma radiation sources (2013)
  • 著者名/発表者名: B. Huang, T. Tomizuka, B. Xie, Y. Sakai, Q. Zhu, I. Song, A. Okino, F. Xiao, M. Watanabe and E. Hotta
  • 雑誌名: Physics of Plasmas 巻: 20 号: 11
  • DOI: 10.1063/1.4835275
  • NAID: 120006582289
  • 査読あり
• [雑誌論文] An accurate multi-moment constrained finite volume transport model on Yin-Yang grid (2013)
  • 著者名/発表者名: X.L. Li, X.S. Shen, X.D. Peng, F.Xiao, Z.R. Zhuang and C.G. Chen
  • 雑誌名: Advances in Atmospheric Sciences 巻: 30 号: 5 ページ: 1320-1330
  • DOI: 10.1007/s00376-013-2217-x
  • 査読あり
• [雑誌論文] A note on the general multi-moment constrained flux reconstruction formulation for high order schemes (2013)
  • 著者名/発表者名: F. Xiao, S. Ii, C.G. Chen and X.L. Li
  • 雑誌名: Applied Mathematical Modelling 巻: 37 号: 7 ページ: 5092-5108
  • DOI: 10.1016/j.apm.2012.10.050
  • 査読あり
• [雑誌論文] A Multimoment Constrained Finite-Volume Model for Nonhydrostatic Atmospheric Dynamics (2013)
  • 著者名/発表者名: X.L. Li, C.G. Chen, X.S. Shen and F. Xiao
  • 雑誌名: Mon. Wea. Rev. 巻: 141 号: 4 ページ: 1216-1240
  • DOI: 10.1175/mwr-d-12-00144.1
  • 査読あり
• [学会発表] A Robust and Efficient Solver for Interfacial Multi-phase Flows on Unstructured Grids (2015)
  • 著者名/発表者名: F.Xiao, B. Xie, Z.Y. Sun
  • 学会等名: 2015 SIAM Conference on Computational Science and Engineering
  • 発表場所: Salt lake city, Utah, USA
  • 年月日: 2015-03-14 – 2015-03-18
• [学会発表] A WENO derivative constrained 4th order flux reconstruction method (2014)
  • 著者名/発表者名: Z.Y. Sun and F. Xiao
  • 学会等名: International Conference on Progress in Fluid Dynamics and Simulation
  • 発表場所: Taipei, Taiwan
  • 年月日: 2014-10-25 – 2014-10-27
  • 招待講演
• [学会発表] Development of accurate and robust CFD solvers for complex flows in complex geometries (2014)
  • 著者名/発表者名: F. Xiao
  • 学会等名: 7th Taiwan-Japan Workshop on Mechanical and Aerospace Engineering
  • 発表場所: Taipei, Taiwan
  • 年月日: 2014-09-12 – 2014-09-15
  • 招待講演
• [学会発表] Accurate and robust multi-moment finite volume solver on unstructured grids for incompressible flows (2014)
  • 著者名/発表者名: Feng Xiao and Bin Xie
  • 学会等名: 11th. World Congress on Computational Mechanics (WCCM XI)/ 5th. European Conference on Computational Mechanics (ECCM V)/ 6th. European Conference on Computational Fluid Dynamics (ECFD VI)
  • 発表場所: Barcelona, Spain.
  • 年月日: 2014-07-20 – 2014-07-25
• [学会発表] A high-order scheme by multi-moment constrained flux reconstruction and its application on global modeling (2014)
  • 著者名/発表者名: C.G. Chen, R.X. Zhai and F. Xiao
  • 学会等名: 11th. World Congress on Computational Mechanics (WCCM XI)/ 5th. European Conference on Computational Mechanics (ECCM V)/ 6th. European Conference on Computational Fluid Dynamics (ECFD VI)
  • 発表場所: Barcelona, Spain.
  • 年月日: 2014-07-20 – 2014-07-25
• [学会発表] A multi-moment finite volume method for incompressible Navier-Stokes equations on unstructured grids (2014)
  • 著者名/発表者名: B. Xie and F. Xiao
  • 学会等名: 8th International Conference on Computational Fluid Dynamics (ICCFD8)
  • 発表場所: Chengdu, China
  • 年月日: 2014-07-14 – 2014-07-18
• [学会発表] An algebriac VOF method for unstructured grids: The THINC scheme (2014)
  • 著者名/発表者名: F. Xiao, S. Ii and B. Xie
  • 学会等名: 2nd International Conference on Numerical Methods in Multiphase Flows (ICNMMF-II)
  • 発表場所: Darmstadt, Germany
  • 年月日: 2014-06-30 – 2014-07-02
• [学会発表] An Accurate and Robust Numerical Model for Interfacial Multiphase Flows on Arbitrary Unstructured Grids (2014)
  • 著者名/発表者名: F.Xiao, B.Xie, S.Ii and A.Ikebata:
  • 学会等名: The 1st International Conference on Computational Engineering and Science for Safety and Environmental Problems
  • 発表場所: Sendai, Japan
  • 年月日: 2014-04-13 – 2014-04-16
• [学会発表] Multiphase Fluid Simulations for Water Saving Products (2014)
  • 著者名/発表者名: A.Ikebata, S. Yoshida and F. Xiao
  • 学会等名: The 1st International Conference on Computational Engineering and Science for Safety and Environmental Problems
  • 発表場所: Sendai, Japan
  • 年月日: 2014-04-13 – 2014-04-16
• [学会発表] A Simple Eulerian THINC Scheme for Compressible Two-Phase Flows (2014)
  • 著者名/発表者名: K.M.Shyue and F. Xiao
  • 学会等名: The 1st International Conference on Computational Engineering and Science for Safety and Environmental Problems
  • 発表場所: Sendai, Japan
  • 年月日: 2014-04-13 – 2014-04-16
  • 招待講演
• [学会発表] Interface Capturing Schemes on Arbitrary Unstructured Grids: the THINC Formulations (2014)
  • 著者名/発表者名: B.Xie, S.Ii and F.Xiao
  • 学会等名: The 1st International Conference on Computational Engineering and Science for Safety and Environmental Problems
  • 発表場所: Sendai, Japan
• [学会発表] Accurate and Robust Multi-Moment Finite Volume Fluid Solver for Arbitrary Unstructured Grids (2014)
  • 著者名/発表者名: F.Xiao
  • 学会等名: Advances in Computational Fluid–Structure Interaction and Flow Simulation (A Conference Celebrating the 60th Birthday of Tayfun E. Tezduyar)
  • 発表場所: Tokyo, Japan
  • 招待講演
• [学会発表] A robust and practical multi-moment finite volume model for computational fluid dynamics (2013)
  • 著者名/発表者名: F.Xiao and B.Xie
  • 学会等名: The 2nd International Conference on Advances in Computational Modeling and Simulation (ACMS 2013)
  • 発表場所: Kunming, China
  • 招待講演
• [学会発表] 3D numerical model for free interfacial flows and applications to offshore waves with submerged obstacles (2013)
  • 著者名/発表者名: B.Xie and F.Xiao
  • 学会等名: The 2nd International Conference on Advances in Computational Modeling and Simulation (ACMS 2013)
  • 発表場所: Kunming, China
• [学会発表] THINC method: An accurate and efficient algebraic approach for capturing free interfaces (2013)
  • 著者名/発表者名: F. Xiao, S. Ii and B. Xie
  • 学会等名: The V Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED 2013)
  • 発表場所: Ibiza, Spain
• [学会発表] Development of numerical model toward DNS and modeled simulations of gas/liquid interfacial flows (2013)
  • 著者名/発表者名: F.Xiao
  • 学会等名: International Workshop on Numerical simulations of Particle/droplet/bubble-laden Multiphase flows
  • 発表場所: Tokyo, Japan
  • 招待講演
• [学会発表] Numerical Framework for Atmospheric Modeling on Cubed Sphere by Multi-Moment Scheme (2013)
  • 著者名/発表者名: C.G. Chen, F. Xiao, X.L. Li, X.S. Shen
  • 学会等名: 2013 SIAM Conference on Computational Science and Engineering
  • 発表場所: Boston, MA, USA
• [学会発表] Construct high-order schemes using multi-moments or multi-moment constraints (2012)
  • 著者名/発表者名: F.Xiao
  • 学会等名: The 1st International Conference on Frontiers in Computational Physics: Modeling the Earth System
  • 発表場所: Boulder, CO, USA
  • 招待講演
• [学会発表] High order multi-moment method for geophysical flows on unstructured grids (2012)
  • 著者名/発表者名: S. Ii, S. Wada, R. Akoh, F. Xiao
  • 学会等名: The 1st International Conference on Frontiers in Computational Physics: Modeling the Earth System
  • 発表場所: Boulder, CO, USA
• [学会発表] Global shallow water model on icosahedral-hexagonal grid by multi-moment constrained finite volume method (2012)
  • 著者名/発表者名: C.G. Chen, X.L. Li, X.S. Shen, F. Xiao
  • 学会等名: The 1st International Conference on Frontiers in Computational Physics: Modeling the Earth System
  • 発表場所: Boulder, CO, USA
• [学会発表] Development of non-hydrostatic atmospheric model by multi-moment constrained finite volume method (2012)
  • 著者名/発表者名: X.L. Li, F. Xiao, C.G. Chen, X.S. Shen
  • 学会等名: The 1st International Conference on Frontiers in Computational Physics: Modeling the Earth System
  • 発表場所: Boulder, CO, USA
• [学会発表] A multi-moment constrained finite volume model for non-hydrostatic atmospheric dynamics (2012)
  • 著者名/発表者名: X.L. Li, C.G. Chen, X.S. Shen and F. Xiao
  • 学会等名: The 2012 workshop on the solution of partial differential equations on the sphere
  • 発表場所: Cambridge, UK