Lectures, Recommended Reading and Problem Sets:
I. An Introduction to Fluid Mechanics, Lagrangian derivative,
Conservation laws, the Stress Tensor, Hydrostatic equilibrium,
Microphysical basis for continuum fluid equations
 Lecture Notes 1: pdf
 Problem set 1: pdf,
due Friday 1/24 in class,
Solutions
 Problem set 1b: pdf,
due Friday 2/7 in class,
Solutions
Reading: Clarke and Carswell chapters 15 or
Shu's chapter 2,4, or Pringle and King chapter 1 or
Blandford and Thorne Chapter 12
Watch the film on the Eulerian/Lagrangian Description at
NCFMF
II. Spherical flows, Bondi flow, Bernoulli's equation,
Characteristics, Riemann invariants, Shock jump conditions, Blastwaves,
Selfsimilar flows
 Lecture Notes 2: pdf
 Problem set 2a: pdf,
due Friday 2/21 in class,
Solutions
 Problem set 2b: pdf
due Friday 3/7 in class,
Solutions

Reading:
on Bondi flow:
Clarke and Carswell's Chapter 9,
Pringle and King Chapter 3,
Shu's Chapter 6,
Blandford and Thorne Chapter 16
on Characteristics:
Shu's chapter 12,
and Scott Sarra's article
The Method of Characteristics with applications to Conservation Laws
Check out Scott Sarra's applet
(let me know if you know how to defeat the security settings, right
now I can't run it ...)
applet
on Shocks:
Clarke and Carswell's Chapter 7,
Shu's chapter 15
on Selfsimilar flows and blast waves:
Shu's chapter 17,
Clarke and Carswell's Chapter 8,
Watch the film on Channel Flow of a Compression Fluid at
NCFMF
III. Viscous Flows, Accretion and Excretion Disks,
NavierStokes equations, Viscous Dissipation,
Alphadisk structure,
Kelvin's circulation theorem,
Vorticity, Helmholtz equation,
Geostrophic flows
 Lecture Notes 3: pdf
 Problem set 3a: pdf
due Fri 3/28 in class,
Solutions
 Problem set 3b: pdf
due Fri 4/11 in class,
Solutions
Reading:
on Viscous flow and accretion disks:
Clarke and Carswell's Chapters 11 and 12,
Shu's chapter 7
Watch films on the Fluid Dynamics of Drag and on Vorticity at
NCFMF
IV. Numerical methods for hydrodynamics. Finite Difference schemes,
Truncation error, Numerical Stability, the CFL condition, Numerically generated dispersion and dissipation, the Riemann problem
 Lecture Notes 4: pdf
Reading:
"Numerical Methods in Astrophysics" (Bodenheimer et al) Chapter 2
The first few chapters of
"Riemann solvers and numerical methods for fluid dynamics: a practical introduction" (Toro)
V. Waves and Instabilities. Sound waves, Instability at an Interface (RayleighTaylor and Kelvin Helmholtz instabilities), Jeans Instability,
Convective Instability, Waves in a PlaneParallel Atmosphere
 Lecture Notes 5: pdf
Reading: Pringle and King chapter 79, Clarke and Carswell Chapter 10, Shu's chapter 8
Watch the film on Fluid Instabilities at
NCFMF
Numerical Project.
Choose an astrophysical problem involving
hydrodynamic flow in 1 dimension. Numerically integrate the flow
to explore the evolution of the flow.
April 18: be able to integrate something in python.
April 25: Choose an astrophysical setting for your project.
April 30: (Last class) talk for 5 minutes about your project in class!
May 9: Final write up due.
Project Requirements:
1) Cite astrophysical literature relevant to your project.
2) Describe your numerical implementation/scheme
3) Describe a test of your numerical scheme
4) Explore evolution of your flow. Show some plots!
Discuss in terms of some astrophysical literature.
Some python examples
Numerical integration of the diffusion equation with a low order finite difference
Subroutines diffusion.py
Calling these subroutines c_diffusion.py
Integration of the advective diffusion equation with
Lax Wendroff scheme
Subroutines advec_diff.py
Calling these subroutines c_advec_difff.py
Integrating a 1d version of Euler equations
with a Lax Friedrichs scheme
Subroutines euler.py
Calling these subroutines c_euler.py
Integrating a 1d wave equation
Subroutines wave.py
Calling these subroutines c_wave.py