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