Numerical integration of fluid dynamics problems by discrete dynamical systems

Chaos, Solitons & Fractals - Tập 11 - Trang 193-206 - 2000
F.N. Koumboulis1, M.G. Skarpetis2, B.G. Mertzios3
1University of Thessaly, Department of Mechanical and Industrial Engineering, Pedion Areos, 383 34 Volos, Greece
2National Technical University of Athens, Department of Electrical and Computer Engineering, Division of Electroscience, Greece
3Democritus University of Thrace, Department of Electrical and Computer Engineering, 67100 Xanthi, Greece

Tài liệu tham khảo

R.D. Richtmyer, K.W. Morton, Difference method for initial-value problems, Interscience, New York, 1967 LeBail, 1972, Use of fast Fourier Transform for solving partial differential equations, J. Comput. Phys., 9, 440, 10.1016/0021-9991(72)90005-8 Gustafson, 1979, Cavity flow dynamics at higher Reynolds number and higher aspect ratios, J. Comput. Phys., 70, 271, 10.1016/0021-9991(87)90182-3 S.F. McCormick, Multilevel adaptive methods for partial differential equations, in: SIAM Studies in Applied Mathematics, 1989 S.F. McCormick, Multilevel projection methods for partial differential equations, in: SIAM Studies in Applied Mathematics, 1992 R.E. Bank, PLTMG: a software package for solving elliptic partial differential equations, in: SIAM Studies in Applied Mathematics, 1994 Sell, 1996, Global attractors for the three dimensional Navier–Stokes equations, J. Dynamics and Differential Equations, 8, 1, 10.1007/BF02218613 Prestin, 1997, A parallel Navier–Stokes solver: the Meikp implementation, J. Supercomputing, 9, 347, 10.1007/BF01206272 Fettweis, 1992, Multidimensional wave digital filters for discrete-time modeling of Maxwell’s equations, Int. J. Num. Modeling, 5, 1 Fettweis, 1992, Discrete modeling of losseless fluid dynamic systems, AEÜ, 46, 209 Fettweis, 1991, Numerical integration of partial differential equations using principles of multidimensional wave digital filters, Journal of VLSI Signal Proc., 3, 7, 10.1007/BF00927832 Fettweis, 1986, Wave digital filters: theory and practice, Proc. IEEE, 74, 270, 10.1109/PROC.1986.13458 A. Fettweis, Discrete passive modeling of viscous fluids, Proceedings of the IEEE International Symposium on Circuits and Systems, San Diego, CA, WSA, May 1992, pp. 1640–1643 F.M. White, Viscous Fluid Flow, McGraw-Hill, New York, 1974 Fettweis, 1991, Transformation approach to numerically integrating of PDEs by mean of WDF principles, Multidimensional Systems and Signal Proc., 2, 127, 10.1007/BF01938221 K. Meerköter, Incremental passivity of wave digital filters, Proceedings of the European Signal Processing Conference, Lausanne, Switzerland, 1980, pp. 27–31 Fettweis, 1990, On assessing robustness of recursive digital filters, European Transactions on Telecommunications, 1, 103, 10.1002/ett.4460010205 F.N. Koumboulis, M.G. Skarpetis, B.G. Mertzios, On the derivation of the nonlinear discrete equations numerically intergrating the euler PDEs, Discrete Dynamics in Nature and Society (DDNS), 2 (1998) 41–51