Math 716, Mathematical Fluid Dynamics II




НазваниеMath 716, Mathematical Fluid Dynamics II
Дата конвертации29.01.2013
Размер8.67 Kb.
ТипДокументы
Math 716, Mathematical Fluid Dynamics II


Michael Siegel

515B Cullimore Hall


596-5835

misieg@oak.njit.edu

Office Hours: M, W, F 1-2 or by appointment



Course Description: Further development of the ideas of fluid dynamics, with an emphasis on mathematical developments and issues. A selection of topics will be developed in some detail, for example: Stokes flow and low-Reynolds-number hydrodynamics; flow at high Reynolds number and boundary layers; shock waves and hyperbolic systems; dynamics of interfacial flows; hydrodynamic stability; rotating fluids.


Textbooks: 1. Viscous Flow, H. Ockendon and J. R. Ockendon, Cambridge University Press. ISBN: 0521458811

2. Waves and Compressible Flow, H. Ockendon and J. R. Ockendon, Springer. ISBN: 038740399X


Other useful References:

1. A Mathematical Introduction to Fluid Mechanics, A. J. Chorin and J. E. Marsden, Third Edition, Springer Verlag.

2. Elementary Fluid Dynamics, D. J. Acheson, Oxford University Press.

3. Fluid Mechanics, L. D. Landau and E. M. Lifschitz, Pergamon Press.


Grading: 5 to 6 HW assignments 30%, Midterm 30%, Final 40%


A tentative course outline for Math 716 is provided below:


Week 1: Introduction to viscous flow, Stokes equations


Week 2: Stokes paradox, complex variable solution of biharmonic equation


Weeks 3-4: Interfacial problems, stress boundary conditions, Hele-Shaw flow


Week 5: Thin films, lubrication theory


Week 6: Boundary Layers: Prandtl’s equations, boundary layers on a flat plate


Week 7: Midterm examination. Boundary Layer’s (continued): Rotating flows controlled by boundary layers, boundary layer separation


Week 8: Gas flow in one dimension, hyperbolic equations


Week 9: Theory of hyperbolic equations: Characteristics and Shocks, Weak solutions


Week 10: Theory of hyperbolic equations (continued): The Riemann Problem


Week 11: Combustion waves


Week 12: Stability Theory: Linear theory, thermal instability


Week 13: Centrifugal instability, instability of parallel shear flow


Week 14: Theorems on stability of viscous flow


Week 15: Final examination

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