領域分割法による数値シミュレーション手法の開発とその数学的検証

2001 Fiscal Year Annual Research Report

• Project/Area Number: 13555021
• Research Institution: Nihon University
• Principal Investigator: 中村 正彰 日本大学, 理工学部, 教授 (00017419)
• Co-Investigator(Kenkyū-buntansha): 田端 正久 九州大学, 数理学研究科, 教授 (30093272) ; 池田 勉 竜谷大学, 理工学部, 教授 (50151296) ; 今井 仁司 徳島大学, 工学部, 教授 (80203298) ; 張 紹良 東京大学, 工学系研究科, 助教授 (20252273) ; 森 正武 東京電機大学, 工学部, 教授 (20010936)
• Keywords: numerical simulation / computation mechanics / domain decomposition / precondition / fluid dynamics / spinodal decomposition / numerical integration / infinnite precision

Research Abstract

本年度の研究計画に基づき研究を実施し,次のような成果を得た.
・数値シミュレーションの新手法のための計算法開発
高速高精度計算手法の開発と応用。
高精度数値シミュレーションの逆問題への応用に成功した。
大型計算の前処理法の解析
数値積分法の解析.
・以下の非線形問題の数学的および数値解約解析に成功した.
相分離系を記述する江口・沖松村方程式の1次元非自明定常解の存在を予測し証明した。
地球マントル対流の数値シミュレーション用有限要素コードを作成した。
燃焼合成反応の数理モデルの数値シミュレーションの解析.
Navier-Stokes方程式の摩擦型境界条件問題.
・有限要素法,差分法を用いた各種流体問題の解析に成果をあげた.
各種風車の数値シミュレーション
多相流れの解析

Research Products

• [Publications] Takao Hanada, N.Ishimura, Masa Aki Nakamura: "Numerical analysis of Eguchi-Oki-Matsumura equations II"the proceedings of the fifth China-China joint-seminar on numerical mathematics. (to appear). (2002)
• [Publications] T.Hanada, H.Imai, N.Ishimura, M.Nakamura: "Eguchi-Oki-Matsumura equations for phase separation: Numerically guided approach"the proceedings of international conference on inverse problems. (to appear). (2002)
• [Publications] H.Suito, H.Kawarada: "Shape Optimization for an Acoustic Problem"Proceedings of 12th International Conference on Domain Decomposition Methods in Science and Engineering. 445-453 (2001)
• [Publications] H.Kawarada, H.Suito: "Multi-phase flow reaction"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 39-56 (2001)
• [Publications] M.Mori, M.Sugihara: "The double exponential transformation in numerical analysis"Journal of Comput.Appl.Math.. 127. 287-296 (2001)
• [Publications] M.Mori: "Optimality of the double exponential transformation in numerical analysis"Sugaku Exposition. 14,No.1. 103-1* (2001)
• [Publications] M.Tabata: "Uniform solvability of finite element solutions in approximate domains"Japan Journal of Industrial and Applied Mathematics. 18. 567-585 (2001)
• [Publications] Y.Mizuyama, M.Tabata: "Lagrangian finite element analysis of the free surface of an incompressible dielect liquid under an electric field"Theoretical Applied Mechanics. 50. 403-410 (2001)
• [Publications] M.Tabata, S.Fujima: "Numerical analysis of flow problems by finite element methods"Sugaku Expositions. 14. 155-174 (2001)
• [Publications] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. (to appear). (2002)
• [Publications] M.Tabata, A.Suzuki: "Mathematical modeling and numerical simulation of Earth's mantle convection"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 219-231 (2001)
• [Publications] 池田勉, 長山雅晴: "燃焼合成反応におけるヘリカル波"応用数理. 11,No.2. 40-48 (2001)
• [Publications] M.Nagayama, T.Ikeda, T.Ishiwata, N.Tamura, M.Ohyanagi: "Three-dimensional numerical simulation of helically propagating combustion waves"J.of Material Synthesis and Processing. 9,No.3. 153-163 (2001)
• [Publications] T.Nishida, T.Ikeda, H.Yoshihara: "Pattern formation of heat convection problems"Mathematical Modeling and Numerical Simulation in Continuum Mechanics,Lecture Notes in Computational Science and Engineering. 19. 209-218 (2001)
• [Publications] M.Kan, T.Kawamura, K.Kuwahara: "Numerical Study of the Sand Movement around a Cylindrical Body Standing on the Sand"JSME International Journal Series B. 44,No.3. 427-433 (2001)
• [Publications] M.Iwata, T.Kawamura, N.I.Wakayama: "Three-Dimensional Numerical Study of the Magnetic Effect on the Air Flow at an Intake"Theoretical and AppliedMechanics. 50. 289-294 (2001)
• [Publications] T.Hayashi, S.Yamashita, H.Yamada, T.Kawamura: "Experimental and Numerical Study of the Flow around the Rotating Savonius Rotor"Proceedings of Europian Wind Energy Conference. 398-401 (2001)
• [Publications] S.Saitoh, M.Mori: "representation of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. 45. 387-393 (2001)
• [Publications] K.Ohmori: "Convergence of the interface in the finite element approximation for two-fluid flows"Lecture Notes in Pure and Applied Mathematics,the Navier-Stokes Equations: Theory and Numerical Methods. 223. 279-293 (2001)
• [Publications] H.Fujita: "Non-stationary Stokes flows under leak boundary conditions of friction type"Journal of computing Mathematics. 19-1. 1-8 (2001)
• [Publications] S.Komurasaki, T.Kawamura, K.Kuwahara: "Simulation of Thermal Convection in a Stratified Fluid Flow"AIAA paper. 2002-0877. 1-10 (2002)
• [Publications] B.Yu, G.-C.Feng, S.-L.Zhang: "The aggregate constraint homotopy method for nonconvex nonlinear programming"Nonlinear Anal.. 45-7. 839-847 (2001)
• [Publications] 花田孝郎, 石村直之, 中村正彰: "相分離問題におけるEOM方程式の数値解析"第51回理論応用力学講演会講演論文集. 639-640 (2002)
• [Publications] 檜山聡, 篠田大輔, 藤間昌一: "高次モルタル型領域分割法とその並列計算"第51回理論応用力学講演会講演論文集. 501-502 (2002)
• [Publications] H.Fujita, N.Saito, T.Suzuki: "Operator Theory and Numerical Methods"Elsevier. 309 (2001)
• [Publications] 河村哲也, 菅牧子, 桑原邦郎, 小紫誠子: "環境流体シミュレーション"朝倉書店. 199 (2001)