11 – Iterative cycle

The iterative cycle is constituted of several loops, and the greatest of them is the time loop, called itGlobal, which involves temperature (itT) and pressure-velocity coupling (itPV) equations looping.

The itPV looping is responsible for the momentum and mass conservation equation resolution. Already, the itT looping is responsible for the energy conservation equation resolution.

Still in the forced convection steady state cases, the calculation of energy conservation equation in itT is not coupled to momentum and mass conservation equations of itPV.

We do this in order to improve the speed of the program execution. We should keep in mind that because the pressure-velocity coupling the chosen Dt has some influence over the convergence or divergence of the iterative linear system solution.

Below, we have a detailed explanation about the iterative cycle used in CFD Sinflow Library 1.0.

1. Initialization of all variables (u, v, P, T, etc.).

Begin of time looping (itGlobal).
{

Begin of velocity correction with temperature looping (itT).
{

Begin of pressure-velocity coupling looping (itPV).
{

2. Calculate of estimated velocities.

3. Calculate of P’ (pressure field correction).

4. Pressure field correction.

5. Velocities correction.

6. Calculate of errors and comparison with admitted tolerances, in itPV looping. The velocity and pressure fields are compared
with the previous iteration.

}
End of pressure-velocity coupling looping (itPV).

7. Calculate of temperature fields for the velocities gotten in itPV looping.

8. Calculate of errors and comparison with admitted tolerances, in itT looping. The calculated temperature field is compared
with the previous iteration.

}
End of velocity correction with temperature looping (itT).

9. The time error is verified for the each variable (u, v, P and T) comparing the gotten fields with the previous iteration in the
end of itT looping. Also the global mass balance of domain is verified. The mentioned errors calculation is discribed in the Section (11.1).

}
End of time looping (itGlobal).