mpo662 - 1 Numerical Methods in Fluid Dynamics MPO 662...

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1 Numerical Methods in Fluid Dynamics MPO 662 Instructor Mohamed Iskandarani MSC 320 x 4045 [email protected] Grades 60% Homework (involve programming) 20% Mid term 20% Term project Syllabus 1. Introduction 2. Classifications of PDE’s and their properties 3. Basics of the finite difference method 4. Finite difference solutions of ODE 5. Finite difference solutions of time-dependent linear PDEs (a) advection equation (b) heat equation (c) Stability and dispersion properties of time differencing schemes 6. Numerical solution of finite difference approximation of elliptic equations 7. Special advection schemes 8. Energetically consistant finite difference schemes 9. The Finite Element Method 10. Additional topics (time permitting)
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2 Background 1. Name 2. Degree Sought (what field) 3. Advisor (if any) 4. Background 5. Scientific Interest 6. Background in numerical modeling 7. Programming experience/language
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3 Reserve List Dale B. Haidvogel and Aike Beckmann, Numerical Ocean Circulation Modeling Imperial College Press, 1999. (CGFD) Dale R. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dy- namics , Springer, New York, 1998. (CGFD) George J. Haltiner Roger T. Williams, Numerical Prediction and Dynamic Meteo- rology , Wiley, 1980. (CGFD) John C. Tannehill, Dale A. Anderson, and Richard H. Pletcher, Computational Fluid Mechanics and Heat Transfer , Taylor and Francis, 1997. (FDM) G. E. Forsythe and W. R. Wasow Finite-Difference Methods for Partial Differential Equations , John Wiley and Sons, Inc., New York, 1960. (FDM) R. D. Richtmyer and K. W. Morton, Difference Methods for Initial–Value Problems , Interscience Publishers (J. Wiley & Sons), New York, 1967. Useful References Gordon D. Smith, Numerical Solution of Partial Differential Equations : Finite Difference Methods , Oxford University Press, New York, 1985. (FDM) K.W. Morton and D.F. Mayers, Numerical Solution of Partial Differential Equa- tions : An Introduction , Cambridge University Press, New York, 1994. (FDM) P.J. Roache, Computational Fluid Dynamics , Hermosa Publisher, 1972, ISBN 0- 913478-05-9. (FDM) C.A.J. Fletcher, Computational Techniques for Fluid Dynamics , 2 volumes, 2nd ed., Springer-Verlag, New York, 1991-1992. (Num. Sol. of PDE’s) Roger Peyret and Thomas D. Taylor, Computational Methods for Fluid Flow , Springer-Verlag, New York, 1990. (Num. Sol. of PDE’s) Roger Peyret, Handbook of Computational Fluid Mechanics , Academic Press, San Diego, 1996. (QA911 .H347 1996) Joel H. Ferziger and M. Peric Computational Methods For Fluid Dynamics , Springer- Verlag, New York, 1996. R. S. Varga, Matrix Iterative Analysis , Prentice–Hall, New York, 1962. Bengt Fornberg, A Practical Guide to Pseudospectral Methods , Cambridge Univer- sity Press, Cambridge, 1998. (Spectral methods) C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics , Springer-Verlag, New York, 1991. (Spectral Methods)
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4 John P. Boyd, Chebyshev and Fourier Spectral Methods Dover Publications, 2000.
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