CFL_limit_electromagnetic_yee

plasmapy.simulation.resolution_constraints.CFL_limit_electromagnetic_yee( dx: Annotated[Quantity, Unit('m')], ) → Annotated[Quantity, Unit('s')][source]

Calculates the limiting time-step for a finite difference time-domain electromagnetic Yee solver which uses a Cartesian grid.

This limit is defined by the Courant-Friederichs-Lewy (CFL) Condition:

\[\Delta t = \frac{1}{c\sqrt{{\sum_{i=1}^{n} \Delta x_i^{-2}}}}\]

where \(\Delta x_i\) corresponds to the grid resolution along the \(i\)-th dimension and \(n\) is the number of dimensions. For example, in 3D this corresponds to:

\[\Delta t = \frac{1}{c\sqrt{\frac{1}{\Delta x^2} +\frac{1}{\Delta y^2} +\frac{1}{\Delta z^2}}}\]

Parameters:: dx (Quantity) – Array with grid resolution along the different dimensions.
Returns:: dt – Computed CFL limiting time-step.
Return type:: Quantity

Notes

For details, see [Courant et al., 1928, Courant et al., 1967]

Examples

>>> import astropy.units as u
>>> import numpy as np
>>> CFL_limit_electromagnetic_yee(10 * u.nm)
<Quantity 3.33564...e-17 s>
>>> CFL_limit_electromagnetic_yee(np.array([5, 10, 15]) * u.nm)
<Quantity 1.42956...e-17 s>