If you are performing a steady-state calculation, the governing equations for the pressure-based solver do not contain time-dependent terms. For steady-state flows, Discretization describes control-volume-based discretization of the steady-state transport equation (see Equation 23–1).
The under-relaxation of variables is used in all cases for some material properties, in the NITA solver for solution variables, and in the pressure-based coupled algorithm where this explicit under-relaxation is used for momentum and pressure.
Because of the nonlinearity of the equation set being solved
by Ansys Fluent, it is necessary to control the change of 
. This is typically
achieved by under-relaxation of variables (also referred to as explicit
relaxation), which reduces the change of 
produced during each iteration.
In a simple form, the new value of the variable 
within a cell depends upon
the old value, 
, the computed change in 
, 
, and the
under-relaxation factor, 
, as follows:
 | (23–65) |
The under-relaxation of equations, also known as implicit relaxation,
is used in the pressure-based solver to stabilize the convergence
behavior of the outer nonlinear iterations by introducing selective
amounts of 
in the system of discretized equations.
This is equivalent to the location-specific time step.
 | (23–66) |
The CFL number is a solution parameter in the pressure-based
coupled algorithm and can be written in terms of 
:
 | (23–67) |