MA692B, Fall 2004
Approximations of Navier-Stokes Equations: numerical analysis
and implementation
Instructor: Jie Shen
TTh 1:30-2:45PM at REC 123
Office: MATH 806
Office Hours: TTh 3:00-4:00pm
or by appointment |
Phone: 4-1923
Message: 4-1901
E-mail: shen@math.purdue.edu |
Topics:
- Basic existence and uniqueness theory for the Stokes and Navier-Stokes
equations;
- Approximations of time dependent Navier-Stokes equations: coupled methods,
penalty methods, artificial compressibility methods, projection
methods;
- Implementation with spectral-Galerkin methods;
- Numerical approximations for some other related nonlinear PDEs.
Prerequisite:
MA611 and CS514. The courses CS614 and CS615 would be
helpful but not necessary.
Grading Policy:
There will be no exam. Grades will be based on course participation,
homework assignments and programming projects.
Reference books:
- 1.
- Roger Temam, Navier-Stokes equations.
Theory and numerical analysis. Reprint of the 1984 edition.
AMS Chelsea Publishing, Providence, RI, 2001. xiv+408 pp. ISBN 0-8218-2737-5.
- 2.
- Roger Temam, Navier-Stokes equations and nonlinear functional analysis. CBMS-NSF regional conference series in applied mathematics, 66, 1995.
- 3.
- V. Girault and P.A. Raviart, Finite element methods for
Navier-Stokes equations: theory and algorithms, Springer-Verlag, 1986.
Some useful papers
A Navier-Stokes solver by spectral-projection method
A finite diffrence Poisson solver