A Solution of the Burgers’ Equation

As intimidating as it looks, the Burgers’ equation does have closed form solutions for a handful of cases. Blom et al present a few such examples of initial value problems that do offer closed form solutions.

Presented here is a solution of the Burgers’ equation, for a Reynolds number of 100. The initial values at t=0 follow the solution:

 

A 60-element MOL approach was implemented with the Rosenbrock-Shampine method. Plotted below is the 3-D solution.

The real challenge, however, is to obtain solutions for Re's >= 1000!