TimeIntegration

Order of time integration

Choose the order of time integration for the temporal discretization. Default behavior is implicit time integration. However, it is possible to switch to an explicit or semi-implicit (a.k.a. implicit-explicit) scheme for velocity and temperature separately.

Note: This only applies to LIQUID.

Available orders of time integration:

V:IMPLICIT
Implicit time integration in general.
V:EXPLICIT
Use explicit Euler time integration for the velocity.
V:EXPIMP(0.5)
Mixed integration scheme for velocities. Any parameter value between 0 and 1 is allowed, where 0 is explicit Euler and 1 is implicit Euler. 0.5 is the Crank-Nicholson scheme.
V:BDF2
use BDF2 scheme for velocity, see remark below.
V:NONE
Turn off solving for velocity and pressure.
T:EXPLICIT
Use fully explicit time integration for temperature.
T:EXPIMP(0.5)
Mixed integration scheme for temperature. Any parameter value between 0 and 1 is allowed, where 0 is fully ecplicit and 1 is fully implicit. 0.5 is the Crank-Nicholson scheme.
T:BDF2
use BDF2 scheme, see remark below.
T:NONE
Turn off solving of temperature equations.
TURBULENCE::explicit
Use explicit time integration for turbulence, see KepsilonAlgorithm.
TURBULENCE::BDF2
Use BDF2 time integration for turbulence, see KepsilonAlgorithm , see remark below.
TURBULENCE:
no definition of the time integration scheme always triggers implicit-Euler time integration.
PDYN:NONE
Turn off the solution of DynamicPressureAlgorithm . Instead, the new dynamic pressure is kept as
ALL:NONE
Completely turn off the time integration of LIQUID . All values are kept as they are, including the results of TurbulenceModel and CODI . Points still are moving according to their appropriate velocity. If point movement is to be stopped as well, work with EULER instead of LAGRANGE. The LIQUID pointcloud then is as passive in the same way as a STANDBY pointcloud. \begin{align} p_{dyn}^{n+1}= \mathcal{C} \cdot p^n_{dyn} + c\end{align} where \( c\) is the correction pressure as produced by the CorrectionPressureAlgorithm and \( \mathcal{C}\) is the value of damping_p_corr , provided by the user, see also.

Remark: for BDF2-scheme, see for example https://en.wikipedia.org/wiki/Backward_differentiation_formula in general. For BDF2 with variable time step size, refer for example to Nishikawa, Hiroaki. (2021). Derivation of BDF2/BDF3 for Variable Step Size. DOI:10.13140/RG.2.2.28649.42083.