Resistive Clump Simulation Results (low res)

After fixing bugs (previously it does not diffuse the field lines correctly due to a sign mistake) and adding the magnetic energy flux, the resistive solver work better now. About the energy flux:

Previously we diffuse the magnetic field according to the equation:



But we do not explicitly treat the change of energy due to this movement of magnetic field lines. Therefore the total energy of one cell stays the same before and after resistive diffusion. This is not right since the total energy per cell will change (thermal energy stays the same). In the new code, we calculate the energy flux resulted from the resistive diffusion explicitly at the cell faces:



From this flux we update the total energy at each cell using the divergence law. With this calculation, the cell where field is diffusing away from does not magically get instantly heated up like before. There can be an inaccuracy resulting from the finite grid size during this calculation. This inaccuracy can be observed by looking at the thermal energy contained in one cell and test whether it's kept the same. At low resolution (16 zones per clump radii), this error gets to 0.3%. The solver is completely divergence free: during resistive diffusion, the magnetic field divergence is kept zero.

The next figure is the "Bx" (magnetic field parallel to the shock normal) case at around 3 clump crushing time scales. The Rm labeled in the figure is the magnetic Reynolds number. The plot at the bottom is the case where the fluid is perfectly conductive (Rm is infinite).

http://www.pas.rochester.edu/~shuleli/Resistive_Clump/denpara_lr__0100.png

Here is a movie for it:
​http://www.pas.rochester.edu/~shuleli/Resistive_Clump/denpara_lr.gif

The following figure is the "By" (magnetic field perpendicular to the shock normal) case at around 3 clump crushing time scales.

http://www.pas.rochester.edu/~shuleli/Resistive_Clump/denperp_lr_0100.png

Here is a movie for it:
​http://www.pas.rochester.edu/~shuleli/Resistive_Clump/denperp_lr.gif

We can see that although at Rm=100 still show quite a difference in the two field configurations, the difference is beginning to diminish. We will be doing production runs with high resolution (64 zones per clump radii) on the bluegene cluster in the next few weeks.

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