Data Scaling

The wide variety of scales in astrophysical variables is a chronic problem for numerical simulation codes. When variables of widely disparate scales are combined in a machine calculation, the results are vulnerable to ​truncation error, especially if the order-of-magnitude difference between two values is below ​machine precision. Handled improperly, these scaling differences can cause massive problems in a simulation.

AstroBEAR handles the problem by dividing a scaling constant out of certain variables. The equations of ideal MHD are scale-free, so the scaling of variables does not change the results of the simulation. This does not hold true if physical source terms such as cooling or gravity are present; during source term steps, physical scaling must be reintroduced.

Scaling in AstroBEAR

Data File Parameters

The most basic physical scaling options are set by the user in the physics.data file:

nScale	number density scale (cm-3)
rScale	density scale (g cm-3)
pScale	pressure scale (dynes cm-2)
TempScale	temperature scale (K)
lScale	length scale (cm)

AstroBEAR derives other scaling constants such as magnetic pressure and velocity from these basic parameters:

VelScale	velocity scale (cm s-1)
BScale	magnetic field scale (esu)
TimeScale	time scale (s)
ScaleGrav*	gravity scale (cm3)
ScaleCool**	cooling scale (erg-1 cm3)

*requires elliptic source terms.
**requires cooling source terms.

Calculating the appropriate scales to use is not always a trivial task, especially if the important scale for your problem is a derived one. For instance,