The Digital Demo RoomOne-Dimensional Hydrodynamics

Simulator

Conley “Lee” Ditsworthunder the care and feeding of

Dr. Charles F. Gammieand 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

SimulatorOutput

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

StableUnstable

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:

http://rainman.physics.uiuc.edu/ddr/oned/index.html

Conley “Lee” DitsworthRm 235 LLP

lee@shout.net or ditswort@uiuc.edusorry, no office phone available…