The global time step formulation for the pseudo time method is only compatible with steady-state cases that use the pressure-based coupled solver or the density-based implicit solver. It uses a single pseudo time step size for the whole simulation domain. You have the option of specifying the pseudo time step size or you can have Ansys Fluent calculate it automatically; the automatically calculated value can be further modified if you specify a time scale factor other than 1. Ansys Fluent allows you to use a different time step size for the fluid domain and the following solid domains:
Solid zones
Porous zones
Solidification and melting model
The automatic time step is calculated as follows:
Fluid Time Scale
The automatic fluid time scale for fluid zones (
) is calculated using the minimum of the different time scales: 
(23–102)
where
, 
, 
, 
, 
, and 
represent the convection, dynamic, buoyancy, gravitational, rotational, and
compressible time scales.Depending on the physics of the problem and applicability of the previously mentioned time scales, they may be used for computing the global pseudo time step size. Each time scale can be obtained by dividing a representative velocity scale by a representative length scale
.The convective time scale
is calculated as:
(23–103)
where the velocity
is the maximum of the arithmetic average of the velocity at the domain
boundary faces, and 
is the arithmetic average of the velocity over the cells in the domain. For
the VOF and mixture models, the average velocity is calculated using the velocity in
interfacial cells only.The dynamic time scale
is calculated as:
(23–104)
where the velocity scale
is based on the pressure difference at open boundaries, such as pressure
inlet, pressure outlet or velocity inlet, and is defined by the following:
(23–105)
where
is the maximum pressure value at the open boundary, 
is the minimum pressure value at the open boundary, and 
is the average density over the domain.When using the Boussinesq buoyancy model, the buoyancy time scale
is calculated as:
(23–106)
where
is the magnitude of the gravitational vector (that is, 
), 
is the thermal expansion coefficient, and 
and 
are the maximum and minimum temperatures, respectively.For the full (non-Boussinesq) buoyancy model, the gravitational time scale
is calculated as:
(23–107)
where
and 
are the maximum and minimum mixture densities, respectively, and
is the average of the phase densities.For cases with rotational velocities, the rotational time scale
is calculated as
(23–108)
where
is the maximum of the magnitude of the angular velocity vector (that is,
).If the simulation Mach number
is greater than 0.3, then the compressible time scale 
is obtained from the following formula: 
(23–109)
The simulation Mach number
is computed as
(23–110)
where
is the average speed of sound over all cells. Two length scale calculation methods are available: aggressive and conservative. If the aggressive length scale method is applied, then the length scale in all of the equations shown previously are defined as
(23–111)
On the other hand, if the conservative length scale method is applied, then the length scale is defined as
(23–112)
where the volumetric length scale is defined as
(23–113)
and the domain length scale is defined as
(23–114)
where
is the volume of the domain and (
) are the domain extents in the x, y, and z direction, respectively.Solid Time Scale
The automatic solid time scale for solid zones, porous zones, and the solidification and melting model is assumed to be infinite (1e20 s); however, this value can be reduced by reducing the time scale factor for the solid zones.
For details on applying the automatic time step for the global time step method, refer to Global Time Step Method Settings in the User’s Guide.