# Traveling Wave Profiles for a Follow-the-Leader Model for Traffic Flow with Rough Road Condition

## Numerical simulation codes and results

## Wen Shen

The simulations were carried out in Scilab. One can download the open
source software from www.scilab.org.

The code for the profiles Q(x), for various cases:
- Case 1A: Scilab code , which
generates the following plot:

- Case 1B: Scilab code , which
generates the following plot:

- Case 2A: Scilab code , which
generates the following plot:

- Case 2B: Scilab code , which
generates the following plot:

The stationary viscous profiles for various cases are generated with
this code .
It generated the following plots:

- For Case 1A:

- For Case 1B:

- For Case 1C:

- For Case 2A:

- For Case 2B:

- For Case 2C:

For the solutions of the Follow-the-Leader model, I use
this code . Here are the plots it generates:
- For Case 1A:

- For Case 1B:

- For Case 1C:

- For Case 1D:

- For Case 2A:

- For Case 2B:

- For Case 2C:

- For Case 2D:

One can easily modify the plotting command, to view an animation of
the solution.

For the simulation of FtL model with Riemann data, I use
this code.
It generates the following plots:

One can easily test with any Riemann data with this code.

For the simulation of the viscous conservation law with Reiamnn data,
I use
this code.
It generates the following plot:

Again, one can easily test with any Riemann data with this code.

Wen Shen
Last modified: Tue Oct 31 13:02:41 EDT 2017