1. The Digital Demo Room One-Dimensional Hydrodynamics Simulator Conley “Lee” Ditsworth under the care and feeding of Dr. Charles F. Gammie and close supervision of graduate student Eric Engelhard

2. Project Goal Provide an on-line simulator that allows students to study hydrodynamic waves using an interactive web-based interface

3. Types of Waves Linear Waves –Hydrodynamic (HD) –Magnetohydrodynamic (MHD) Shock Tubes

4. Simulator Output

5. Hydrodynamics Mass Conservation (Continuity Equation): Momentum Conservation: Energy Conservation: Convective Derivative:

6. Other Constraints Magnetic Induction Formula: Divergence-Free Formula: Ideal Gas Equation of State: Gravitational Potential (Poisson’s Equation):

7. Linear Waves “Perturb” the Conservation and Magnetic Induction Equations:

8. Linearized Hydrodynamic (HD) Equations

9. HD Natural Frequencies

10. HD Eigenvectors

11. Magnetohydrodynamic Waves Newly-defined variables for simplification: Alfven Speed: Also:

12. MHD Linearized Equations

13. MHD Natural Frequencies and Associated Eigenvectors

14. Fast/Slow Waves

15. Sample Run: Sound Wave Study of the Jean’s Length Stable Unstable

16. Stable wave (above Jean’s Length): Movie

17. Unstable wave (below Jean’s Length): Movie

18. Sample Shock Tube Shock Tube Just For Fun: Here’s a sample shock tube; simulation is set up with equal left and right states, but with opposite fluid velocities

19. It’s Been A Pleasure! The One-Dimensional Hydrodynamic Simulator Can Be Found At The Digital Demo Room: http://rainman.physics.uiuc.edu/ddr/oned/index.html Conley “Lee” Ditsworth Rm 235 LLP lee@shout.netlee@shout.net or ditswort@uiuc.eduditswort@uiuc.edu sorry, no office phone available…