Initial time step

Theory

The transient incompressible solver starts with $\Delta t_0$ and reduces it at once when the Courant number of the initial field would exceed the maximum, equation (1). From then on the step grows by at most 20 % per step towards the Courant limit (Maximum Courant number) (OpenFOAM user guide, 2026).

A too large $\Delta t_0$ is therefore corrected immediately. A very small one costs a few dozen steps of growth: at a factor of 1.2 per step, about 13 steps per decade.

Equations

\Delta t^{1} = \min\!\left(\frac{Co_{max}}{Co^{0}_{max}}\,\Delta t_0,\ \Delta t_0,\ \Delta t_{max}\right)

(1)

where	meaning	unit
$\Delta t_0$	Initial time step (this setting)	s
$Co^{0}_{max}$	Largest Courant number of the initial field with $\Delta t_0$	-
$Co_{max}$	Maximum Courant number	-
$\Delta t_{max}$	Maximum time step	s

Default and rule

Default: 1e-4 s
Rule: $10^{-4}$ s.
Source: This is the program's default. The start-up limitation of equation (1) is OpenFOAM's initial time-step adjustment as used by the transient incompressible solver.

Valid range > 0

Values

Above 0. Any reasonable value works; it should not exceed the maximum time step.

References 1

OpenCFD Ltd. (2026). OpenFOAM user guide. openfoam.com. Web page