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=5/3
      ux=1 for standing wave problem
      ux=0 for moving wave problem

Computational Domain: 

     

Rotated Angle: 60
Computational time: t=5

Standing wave problem

 Moving wave problem

 

 

 

 

 

 

 

 

             Profile of component Bh 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 Bx  along x direction (yellow line).