11.1 – Iterative cycle stopping criteria

11.1 – Iterative cycle stopping criteria

There are two stopping criteria in the iterative cycle. The first is the convergence, in which the errors are compared to previously defined tolerances. The second criterion is based on the maximum number of iterations, i. e., we define a maximum number of iterations and if this number is reached the iteration stops, even if the first criterion is not satisfied.
As mentioned in the previous section, there are four convergence criteria for the iterative cycle. And they are:

- A non-dimensional difference between the two fields of properties in distinct and consecutive times for variables u, v, P and T. This difference is also known as error in time, and it is evaluated by the following expression:

(11.1.1)

In which:

ERRO^f = error of property f in time;

= property f in time t;

= property f in previous time t anterior;

= the greatest value of property f in time t;

= the smallest value of property f in time t;

- Mass balance residue on the faces of the physical domain. This residue is also called error in mass, and it is given by:

(11.1.2)

In which:

ERRO^m = mass error;

= mass flux that cross the East face of physical domain;

= mass flux that cross the West face of physical domain;

= mass flux that cross the North face of physical domain;

= mass flux that cross the South face of physical domain;

And the mass fluxes are given by:

(11.1.3)

(11.1.4)

(11.1.5)

(11.1.6)

In which:

= sum of the contravariant velocities on the East face of the physical domain;

=sum of the contravariant velocities on the West face of the physical domain;

= sum of the contravariant velocities on the North face of the physical domain;

= sum of the contravariant velocities on the South face of the physical domain;


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