Module: tide.cfl

Numerical stability helper for explicit FDTD time stepping.

Functions

• cfl_condition

cfl_condition

Signature:

cfl_condition(grid_spacing, dt, max_vel, c_max=1.0, eps=1e-15)

Returns:

• inner_dt: stable internal time step
• step_ratio: integer number of internal steps per user step

Usage notes:

• grid_spacing accepts a scalar or list of spacings.
• If step_ratio >= 2, a warning is emitted to indicate sub-stepping.
• max_vel must be positive.

Interpretation

The returned inner_dt divides the requested dt by the integer step_ratio. TIDE can therefore map source and receiver data between the user sampling grid and a stable internal grid without changing the number of returned user samples.

inner_dt, ratio = tide.cfl_condition(
    grid_spacing=(0.02, 0.03),
    dt=4.0e-11,
    max_vel=299_792_458.0,
)
assert ratio >= 1
assert inner_dt == dt / ratio

grid_spacing may be scalar or per-axis. max_vel must bound the fastest material used with the operator. Underestimating it invalidates the stability calculation.

c_max is the method-specific Courant factor. Application code should normally leave it at the solver default rather than using it as a performance control.