1995 年度実績報告書

Navier-Stokes 方程式の解析と数値計算の総合的研究

研究課題

研究課題/領域番号	07304019
研究種目	総合研究(A)
研究機関	京都大学
研究代表者	岡本久京都大学, 数理解析研究所, 教授 (40143359)
研究分担者	大木谷耕司広島大学, 総合科学部, 助教授 (70211787) 池田栄雄富山大学, 理学部, 助教授 (60115128) 東海林まゆみ日本大学, 理工学部, 講師 (10216161) 西浦康政北海道大学, 電子科学研究所, 教授 (00131277) 今井仁司徳島大学, 工学部, 助教授 (80203298)
キーワード	流体力学 / 数値解析 / モデリング / 渦法 / 反応拡散系
研究概要	Navier-Stokes方程式への応用に関し,岡本久は同方程式の新しい厳密解を発見し,その流体力学的な性質を解明した.流体の数値シミュレーションに関しては,渦法による数値実験を岡本久が行なった.せん断流と渦層の相互作用,あるいは2枚の渦層の相互作用による複雑な運動,特に特異点の発生とその構造に関して、これまで漠然と想像されてきたこととは違うメカニズムが存在することがわかった. 東海林まゆみは非粘性,非圧縮流体の2次元渦なし流れ問題における進行波解の分岐現象を調べた.数値シミュレーションにより分岐解形状や分岐構造を具体的に決定した.渦あり流れの場合にも数値シミュレーションを実行しつつある.中木達幸は多孔質媒体を流体が蒸発を伴いながら流れるときに,流体の存在範囲が複数になるための十分条件を見い出した.また,その条件の有用性を数値実験で確認した. 今井仁司は自由境界がある場合のNavier-Stokes方程式の解の数値計算を,「スペクトル法+写像関数」で数値計算する方法を開発した.大木谷耕司は2次元の非圧縮流体の方程式の解の特異構造を数値的方法で研究した.特に,準地衡近似方程式の場合に,有限時間で解が爆発するという従来の解釈を覆す数値実験結果を得た.中村正彰は電磁流体系の解の一意存在及びアトラクターの有限性の解析を行なった. 西浦兼政は高次元空間における,非線形非平衡系に現れる界面パターンの存在と安定性を研究し,スケーリング則の存在・非存在のルールを明らかにした.池田栄雄は双安定な2成分のactivator-inhibitor系において,あるパラメーターに関する進行波解・定在波の大域的な構造と安定性を,特異摂動理論と分岐理論を用いて決定した.國府寛司はorbit-flipと呼ばれる余次元2のホモクリニック軌道の倍分岐が無限回引き続いて起こるような大域的分岐現象を,ある種区分線形ベクトル場を数学的・数値的に調べることによって発見した.

研究成果
(23件)

すべてその他

すべて文献書誌 (23件)

[文献書誌] Hisashi Okamoto: "Axisymmetric stagnation flow converging obliquely on a cylinder" J. Phys. Soc. Japan. 64. 2714-2717 (1995)
[文献書誌] T. Sakajo and Hisashi Okamoto: "Numerical computation of vortex sheet roll-up in the background shear flow" to appear in Fluid Dynam. Res.17. (1996)
[文献書誌] M. Katsurada and H. Okamoto: "On the collocation points of the fundamental solution method for the potential problem" Int. J. Comp. Math. Appl.31. 123-137 (1996)
[文献書誌] H. Okamoto and M. Shoji: "Two Dimensional, Periodic, Capillary-Gravity Waves With Negative Surfase Tension" Proc. IUTAM Conf. Structure and Dynamics of Nonlinear Waves in Fluids. 363-369 (1995)
[文献書誌] 東海林まゆみ: "進行波解-渦ありながれと渦なしながれ" 京大数理解析研究所講究録891. 891. 54-63 (1995)
[文献書誌] Y. Nishiura and I. Ohnishi: "Some mathematical aspects of micro-phase separation in diblock copolymers" Physica. D84. 31-39 (1995)
[文献書誌] K. Ohkitani: "Some Mathematical Aspects in 2D Vortex Dynamics" Proceedings of a conference “Partial Differential Equations and Applications", June 1995.
[文献書誌] Freddy Dumortier, Hiroshi Kokubu, et al.: "A degenerate singularity generating geometric Lorenz attractors" Ergodic Theory and Dynamical Systems. 15. 833-856 (1995)
[文献書誌] Hiroshi Kokubu, M. Komuro, and et al.: "Multiple homolinic bifurcations from orbit-flip, I : Successive homoclinic doublings" to appear in International Journal of Bifurcations and Chaos, the special issue, 1996.
[文献書誌] H. Imai, and et al.: "On Spectral Collocation Methods in Space and Time for Free Boundary Problems" Computational Mechanics '95 (Proc. of ICES '95). 1. 798-803 (1995)
[文献書誌] Hitoshi Imai: "On Validity of a Fuzzy Approach for an III-Posed Shape Design Problem" Proc. of Japan-Russia Joint Seminar on “Integral Equations in Problems of Mathematical Physics". (to appear).
[文献書誌] H. Imai, N. Ishimura and Masa Aki Nakamura: "Convergence of attractors for the simplified magnetic Benard equations" to appear in European Journal of Applied Mathematics. 7. (1996)
[文献書誌] Y. Nishiura and I. Ohnishi: "Spectral comparison result and morphology for diblock copolymer problems" Lecture Notes in Num. Appl. Anal.14. 253-256 (1995)
[文献書誌] T. Takaishi, M. Mimura and Y. Nishiura: "Pattern formation in coupled reaction-diffusion systems" Japan J. of Industrial and Applied Math.12. 385-424 (1995)
[文献書誌] Y. Nishiura, et al.: "Dynamics of inhibitory pulse-coupled oscillators" Applicable Analysis“Dynamical Systems and applications". 4. 549-562 (1995)
[文献書誌] M. taniguchi and Y. Nishiura: "Stability and Characteristic wavelength of Planar interfaces in the large diffusion limit of the inhibitor" to appear in Proc. Roy. Soc. Edingburgh.
[文献書誌] Y. Nishiura and I. Ohnishi: "Nonlocal effects in phase separation dynamics" to appear in the Proc. of ICIAM95, Humberg 1995.
[文献書誌] Y. Nishiura and D. Ueyama: "The dynamics of self-replicating patterns and spiral patterns in an oscillatory field" to appear in the Proc. of NOLTA '95, Las Vegas, '95.
[文献書誌] 今井仁司,石村直之,中村正彰: "磁気ベナ-ル問題のカオス" 日本物理学会学会誌. 50. 697-703 (1995)
[文献書誌] H. Imai, N. Ishimura and Masa Aki Nakamura: "Magnetic Benard system and its simplified model" Advances in Numberical Matheamtics ; Proc. Second Japan-China Seminar on Numerical Math., Leture Notes in Numerical and Applied Analysis. 14. 79-92 (1995)
[文献書誌] N. Ishimura and Masa Aki Nakamura: "A note on uniqueness for the classical slution of the MHD equations in R^3" to appear in Proceedings of the Fourth MSJ Intl. Res. Inst. on Nonlinear Waves, Hokkaido Univ. '96.
[文献書誌] T. Nakaki and K. Tomoeda: "Numerical approximations to some nonlinear diffusion equation with strong absorption" :Proceeding of The 4th Intl. Colloquium on Numerical Analysis, Plovdiv, Bulgaria, August 1995. (in press).
[文献書誌] 藤井宏・岡本久: "非線型力学" 岩波書店, 165 (1995)

1995 年度 実績報告書

Navier-Stokes 方程式の解析と数値計算の総合的研究

研究代表者

岡本 久 京都大学, 数理解析研究所, 教授 (40143359)

研究成果

[文献書誌] Hisashi Okamoto: "Axisymmetric stagnation flow converging obliquely on a cylinder" J. Phys. Soc. Japan. 64. 2714-2717 (1995)

[文献書誌] T. Sakajo and Hisashi Okamoto: "Numerical computation of vortex sheet roll-up in the background shear flow" to appear in Fluid Dynam. Res.17. (1996)

[文献書誌] M. Katsurada and H. Okamoto: "On the collocation points of the fundamental solution method for the potential problem" Int. J. Comp. Math. Appl.31. 123-137 (1996)

[文献書誌] H. Okamoto and M. Shoji: "Two Dimensional, Periodic, Capillary-Gravity Waves With Negative Surfase Tension" Proc. IUTAM Conf. Structure and Dynamics of Nonlinear Waves in Fluids. 363-369 (1995)

[文献書誌] 東海林まゆみ: "進行波解-渦ありながれと渦なしながれ" 京大数理解析研究所講究録891. 891. 54-63 (1995)

[文献書誌] Y. Nishiura and I. Ohnishi: "Some mathematical aspects of micro-phase separation in diblock copolymers" Physica. D84. 31-39 (1995)

[文献書誌] K. Ohkitani: "Some Mathematical Aspects in 2D Vortex Dynamics" Proceedings of a conference “Partial Differential Equations and Applications", June 1995.

[文献書誌] Freddy Dumortier, Hiroshi Kokubu, et al.: "A degenerate singularity generating geometric Lorenz attractors" Ergodic Theory and Dynamical Systems. 15. 833-856 (1995)

[文献書誌] Hiroshi Kokubu, M. Komuro, and et al.: "Multiple homolinic bifurcations from orbit-flip, I : Successive homoclinic doublings" to appear in International Journal of Bifurcations and Chaos, the special issue, 1996.

[文献書誌] H. Imai, and et al.: "On Spectral Collocation Methods in Space and Time for Free Boundary Problems" Computational Mechanics '95 (Proc. of ICES '95). 1. 798-803 (1995)

[文献書誌] Hitoshi Imai: "On Validity of a Fuzzy Approach for an III-Posed Shape Design Problem" Proc. of Japan-Russia Joint Seminar on “Integral Equations in Problems of Mathematical Physics". (to appear).

[文献書誌] H. Imai, N. Ishimura and Masa Aki Nakamura: "Convergence of attractors for the simplified magnetic Benard equations" to appear in European Journal of Applied Mathematics. 7. (1996)

[文献書誌] Y. Nishiura and I. Ohnishi: "Spectral comparison result and morphology for diblock copolymer problems" Lecture Notes in Num. Appl. Anal.14. 253-256 (1995)

[文献書誌] T. Takaishi, M. Mimura and Y. Nishiura: "Pattern formation in coupled reaction-diffusion systems" Japan J. of Industrial and Applied Math.12. 385-424 (1995)

[文献書誌] Y. Nishiura, et al.: "Dynamics of inhibitory pulse-coupled oscillators" Applicable Analysis“Dynamical Systems and applications". 4. 549-562 (1995)

[文献書誌] M. taniguchi and Y. Nishiura: "Stability and Characteristic wavelength of Planar interfaces in the large diffusion limit of the inhibitor" to appear in Proc. Roy. Soc. Edingburgh.

[文献書誌] Y. Nishiura and I. Ohnishi: "Nonlocal effects in phase separation dynamics" to appear in the Proc. of ICIAM95, Humberg 1995.

[文献書誌] Y. Nishiura and D. Ueyama: "The dynamics of self-replicating patterns and spiral patterns in an oscillatory field" to appear in the Proc. of NOLTA '95, Las Vegas, '95.

[文献書誌] 今井仁司,石村直之,中村正彰: "磁気ベナ-ル問題のカオス" 日本物理学会学会誌. 50. 697-703 (1995)

[文献書誌] H. Imai, N. Ishimura and Masa Aki Nakamura: "Magnetic Benard system and its simplified model" Advances in Numberical Matheamtics ; Proc. Second Japan-China Seminar on Numerical Math., Leture Notes in Numerical and Applied Analysis. 14. 79-92 (1995)

[文献書誌] N. Ishimura and Masa Aki Nakamura: "A note on uniqueness for the classical slution of the MHD equations in R^3" to appear in Proceedings of the Fourth MSJ Intl. Res. Inst. on Nonlinear Waves, Hokkaido Univ. '96.

[文献書誌] T. Nakaki and K. Tomoeda: "Numerical approximations to some nonlinear diffusion equation with strong absorption" :Proceeding of The 4th Intl. Colloquium on Numerical Analysis, Plovdiv, Bulgaria, August 1995. (in press).

[文献書誌] 藤井宏・岡本久: "非線型力学" 岩波書店, 165 (1995)

1995 年度実績報告書

岡本久京都大学, 数理解析研究所, 教授 (40143359)