Weighted Essentially Non-Oscillatory (WENO) Scheme for Euler

A one-dimensional implementation of 5th-order WENO scheme as introduced by

[1] Shu, Chi-Wang. "Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws." Advanced numerical approximation of nonlinear hyperbolic equations. Springer, Berlin, Heidelberg, 1998. 325-432.

and

[2] Jiang, Guang-Shan, and Cheng-chin Wu. "A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics." Journal of Computational Physics 150.2 (1999): 561-594. The present code is intended to be a guide to the implementation of the method.

It exemplifies the implementation of the component-wise reconstruction for finite-difference (FD) and finite-volume (FV) methods. In this update, I also include the characteristic-wise reconstruction in FV methodology.
As always, the philosophy behind this code is to be readable rather than efficient. Here, I dedicate this example to all the CFD students starting their path in numerical methods. Manuel A. Diaz (June 2018)