The following length scales are calculated by Ansys CFX:

(1–267)

where is the domain volume (over all domains), , and are the , and extents of the domain (over all domains) and is the area of an ‘open’ boundary (that is, inlets, outlets or openings).

Further length scales are then calculated depending on the Length Scale Option parameter, which can be Conservative, Aggressive or Specified Length Scale:

(1–268)

The velocity scales used to calculate a timestep are:

(1–269)

where is the arithmetic average of the velocity on a boundary, is the arithmetic average of the nodal velocities, and are the maximum and minimum pressure values on an ‘open’ boundary and is the arithmetic average nodal density.

For compressible flows, a Mach number for the simulation is calculated as:

(1–270)

where is the arithmetic averaged speed of sound over all nodes.

For buoyant flows using the full buoyancy model:

(1–271)

and for the Boussinesq model:

(1–272)

where is the thermal expansivity and and are the maximum and minimum domain temperatures (over all domains).

The final fluid time scale used is calculated as:

(1–273)

where:

(1–274)

with the dynamic viscosity μ, the total mass m and the total mass flow into the system .

For very small geometries, where the Reynolds number may be very small, including the diffusion scale in the automatic timescale calculation can lead to very small timesteps, which can unnecessarily slow down convergence. For such cases it may be better to use a physical timescale based on advection scales instead.

(1–275)

If , then

(1–276)