Lax Wendroff 1D Burgers

Lax Wendroff scheme derived from Taylor-Galerkin procedure

Simple implementation of the Taylor-Galerkin discretization for the 1D Burgers equation, which reduces to the Lax-Wendroff scheme when the element size is constant. Description of derivation included. For a practical usage, run a coarse mesh/time-step size combination and, based on the max(abs(u)), re-estimate dt using a finer mesh and CFL = 0.8. Although a higher value is technically more accurate, in practise the spurious oscillations (typical of LW scheme for hyperbolic conservation) impose and additional, hard-to-predict penalty on stability. Implementation of a "real" viscous term helps controlling the oscillations, but imposes another restriction on mesh/time-step size ratio (B = u_max*((dt^2)/(dx^2)) ). Remark that, even with oscillating solution near discontinuities, it is still better at capturing shocks than 1st order upwinding methods.