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…