
For timeaccurate calculations, explicit and implicit timestepping schemes are available. (The implicit approach is also referred to as "dual time stepping''.)
Explicit Time Stepping
In the explicit time stepping approach, the explicit scheme described above is employed, using the same time step in each cell of the domain, and with preconditioning disabled.
Dual Time Stepping
When performing unsteady simulations with the implicittime formulation (dualtime stepping), FLUENT uses a low Mach number preconditioner (for all flow regimes that span from zero speed to Mach one). To provide for efficient, timeaccurate solution of the preconditioned equations, FLUENT employs a dual timestepping, multistage scheme to produce accurate results both for pure convective processes (e.g., simulating unsteady turbulence) and for acoustic processes (e.g., simulating wave propagation) [ 85, 288]. Here we introduce a preconditioned pseudotimederivative term into Equation 26.41 as follows:
where denotes physicaltime and is a pseudotime used in the timemarching procedure. Note that as , the second term on the LHS of Equation 26.419 vanishes and Equation 26.41 is recovered.
The timedependent term in Equation 26.419 is discretized in an implicit fashion by means of either a first or secondorder accurate, backward difference in time. This is written in semidiscrete form as follows:
where { } gives firstorder time accuracy, and { } gives secondorder. is the inner iteration counter and represents any given physicaltime level.
The pseudotimederivative is driven to zero at each physical time level by a series of inner iterations using either the implicit or explicit timemarching algorithm. Throughout the (inner) iterations in pseudotime, and are held constant and is computed from . As , the solution at the next physical time level is given by .
Note that the physical time step is limited only by the level of desired temporal accuracy. The pseudotimestep is determined by the CFL condition of the (implicit or explicit) timemarching scheme.