**Rotated 1D Problem**

As shown in the picture, a 1D problem defined along the direction which has an non-zero angle with respect with respect to x-direction. Computation is conducted in x-y coordinate (in region OABC ).The physical variables in x-y coordinate are obtained from those in the new coordinate, and vice versa. This is often employed to test numerical methods for keeping constraint of for 2D problems. |

**Smooth Alfven Wave problem**

Initial condition:r=5/3u=1 for standing wave problem_{x}u=0 for moving wave problem_{x}Computational Domain: Rotated Angle: 60 ^{°}Computational time: t=5 |

Standing wave problem |
Moving wave problem |
||

Profile of component B_{h}
is plot along line *y* = 0 (blue line in the plot of computational domain)

**MHD Shock tub problem**

Rotated angle:
f=45°
Computational domain: Computational time: t=0.1 Mesh: 399x799 grid points Initial condition: with and . |

In above figures, dots stand for 2D results and
lines for 1D results.

Movie: evolution of
component *B _{x
}* along x
direction (yellow line).