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
Project Goal Provide an on-line simulator that allows students to study hydrodynamic waves using an interactive web-based interface
Types of Waves Linear Waves –Hydrodynamic (HD) –Magnetohydrodynamic (MHD) Shock Tubes
Simulator Output
Hydrodynamics Mass Conservation (Continuity Equation): Momentum Conservation: Energy Conservation: Convective Derivative:
Other Constraints Magnetic Induction Formula: Divergence-Free Formula: Ideal Gas Equation of State: Gravitational Potential (Poisson’s Equation):
Linear Waves “Perturb” the Conservation and Magnetic Induction Equations:
Linearized Hydrodynamic (HD) Equations
HD Natural Frequencies
HD Eigenvectors
Magnetohydrodynamic Waves Newly-defined variables for simplification: Alfven Speed: Also:
MHD Linearized Equations
MHD Natural Frequencies and Associated Eigenvectors
Fast/Slow Waves
Sample Run: Sound Wave Study of the Jean’s Length Stable Unstable
Stable wave (above Jean’s Length): Movie
Unstable wave (below Jean’s Length): Movie
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
It’s Been A Pleasure! The One-Dimensional Hydrodynamic Simulator Can Be Found At The Digital Demo Room: Conley “Lee” Ditsworth Rm 235 LLP or sorry, no office phone available…