MWF 1:25 - 2:15 PM (Schedule #869257)
Instructor: Andrew Belmonte
Contact info: 322 McAllister Building, telephone: 865-2491, email: belmonte.AT.math.psu.edu
Office hours: Tues 2:30-3:30, Wed 2:30-3:30, or by appointment.
Class location: 322 Sackett Bldg
Prerequisites: Basic familiarity with the laws of physics; advanced undergraduate knowledge of ordinary and partial differential equations; rudiments of thermodynamics. For more information, please contact the instructor.
Course Texts (required):
Supplementary Texts (optional):
This one semester graduate course provides an overview and introduction to fluid dynamics -- a subject rich in both mathematical and experimental results and challenges.
We will start from the foundations of the subject, introducing the governing partial differential equations for a flowing continuum and solving them in various limits:
inviscid or irrotational (Euler's equation), viscous, the Navier-Stokes equation, acoustics, viscous flows, and non-Newtonian fluids. Following Prandtl and the development of asymptotic theory, we will discuss boundary layers and turbulence (including Kolmogorov's approach).
Finally, we will examine the most important external forces applied to fluids from both a mathematical and experimental perspective. A common theme throughout the course will be the connections between the structure of the equations and experimental observations.
The basic syllabus for this course will be as follows:
I. Mathematical Approach to a Moving Continuum
II. Euler's Equation
III. Aspects of the Navier-Stokes Equation
IV. Overviews of Complex Fluids, Microfluidics, and Turbulence
V. Other forces applied to fluids: electrical, thermal, rotational