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Parameter · 07 Run Settings

Time scheme

simulation_control.transient.time_scheme Step 07 · Run Settings

The discretisation of the time derivative in a transient run: backward (second order, default) or Euler (first order, implicit).

Last updated

Theory

Both schemes are implicit: the new values appear in all terms, so in principle they are stable at any time step; the Courant limit serves accuracy and the nonlinear coupling (OpenFOAM user guide, 2026).

  • Euler uses the two most recent time levels, equation (1). It is first order; its truncation error damps fluctuations, like a numerical viscosity in time.
  • backward uses three time levels, equation (2), written here for a constant step; OpenFOAM uses the variable-step form when the time step adapts. It is second order and preserves the amplitude of the flow's oscillations far better at the same step.

A steady run uses steadyState (no time derivative).

Equations

(∂ϕ∂t)n+1≈ϕn+1−ϕnΔt\left(\frac{\partial\phi}{\partial t}\right)^{n+1} \approx \frac{\phi^{n+1} - \phi^{n}}{\Delta t}
(1)
(∂ϕ∂t)n+1≈3ϕn+1−4ϕn+ϕn−12Δt\left(\frac{\partial\phi}{\partial t}\right)^{n+1} \approx \frac{3\phi^{n+1} - 4\phi^{n} + \phi^{n-1}}{2\Delta t}
(2)
wheremeaningunit
ϕn\phi^{n}Value at time level nn-
Δt\Delta tTime steps

Default and rule

Default
backward
Rule

backward.

Source

This is the program's default; the schemes are OpenFOAM's Euler and backward (OpenFOAM user guide, 2026). The stable transient settings of the program's residual-sensitivity study were validated with backward.

Valid range backward | Euler

Choice

backward or Euler. Euler can help a difficult start, at the price of damped fluctuations and a less accurate time average.

References 1

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