Solving the Burgers’ Equation with a “double-step” initial condition.

As the last illustration for the Burgers’ equation, case study-1 presented in Wouwer et al has been considered. The initial & boundary values are defined by the equation (which is also an exact solution of the Burgers’ equation):

 where

The initial values at time t=0, and the boundary conditions for t>0 can be calculated from the above equations. The Method of Lines can then be used to solve the discretized ODE form of the Burgers’ equations. A 120-element model was used to solve the “double-step” input. I have referred to it as the double-step, as it will be evident from the solution. At t=0, the drop from boundary condition of 1 (at x=0) to 0.10 (at x=1) comprises of two step changes (as opposed to the single step change in the previous post).