These transform to

where . The specific parameter used were

and

The latter number corresponds to a maximum car density of

We used the constant switch curve introduced by Sopasakis [1]:

with feet. For initial data we chose 3 sets of data:

for and , and 3. The observation that

and

implies we may interpret the data as initial data for a ring-road with 400 cars which is of length 1.5151... miles. We chose constant initial velocities

or

These data guarantee points on both sides of the switch curve. Simulations were run with relaxation times

A word is inorder about the simulations which follow. The first two frames in each figure are self-explanatory. In the third frame of each figure we plot the curve . This curve is shown in black. The blue curves are the equilibrium curves and and the red curve is the image of . The red dot - o - is the image of . The discontinuities in the profiles propagate at the speed

e = 1 | e = 2 | e = 4 | e = 8 | |

k = 1 | view | view | view | view |

k = 2 | view | view | view | view |

k = 3 | view | view | view | view |

e = 1 | e = 2 | e = 4 | e = 8 | |

k = 1 | view | view | view | view |

k = 2 | view | view | view | view |

k = 3 | view | view | view | view |

Lagrangian Representation source code

Eulerian Representation source code

Pei-Jen Lin 2001-08-22