Implement the third set of NRBC treatment for 1D Euler solver

[yungyuc]

For the 1D Euler solver, implement the third set of NRBC treatment documented in NASA/TM-2003-212495-REV1, i.e., NRBC type 3. $\lambda$ is chosen to be 0.

Here copying the type-3 NRBC treatment (the third set of NRBC in section 4.3 in page 15 of the TM) at the right and left boundaries, respectively:

$$u_{A_l} = u_{B_{l-1}} \quad \mathrm{and} \quad (u_x^+)_{A_l} = (1-2\lambda)(u_x^+)_{B_{l-1}}, \, l = 2, 4, 6, \ldots$$ $$u_{A'_l} = u_{B'_{l-1}} \quad \mathrm{and} \quad (u_x^+)_{A'_l} = (1-2\lambda)(u_x^+)_{B'_{l-1}}, \, l = 2, 4, 6, \ldots$$

Choosing $\lambda=0$, the treatment becomes:

$$u_{A_l} = u_{B_{l-1}} \quad \mathrm{and} \quad (u_x^+)_{A_l} = (u_x^+)_{B_{l-1}}, \, l = 2, 4, 6, \ldots$$ $$u_{A'_l} = u_{B'_{l-1}} \quad \mathrm{and} \quad (u_x^+)_{A'_l} = (u_x^+)_{B'_{l-1}}, \, l = 2, 4, 6, \ldots$$

After implementing the type-3 NRBC treatment, waves go outside the boundary:

Comparing with the result with the tentatively implemented (and wrong) BC treatment:

[yungyuc]

The changes make NRBC the only BC treatment in the 1D Euler solver. In the future we should implement more.

[yungyuc]

Only extend outside the computing domain by a BCE.

[yungyuc]

Treat the NRBC only at the first half time marching.