The last year I did several calculations in tubes and stuff but I never succeeded to get a nice convergence with preconditioning. Does anyone know what could be the problem ?
In some cases, you need to change the coefficient beta and CFL number, expecially in ultra-slow flow conditions. In my idea, it's difficult to give a perfect method of selecting beta. However, it's normally true that beta should be larger when the flow speed becomes smaller. Meanwhile, it's better to decrease the CFL number.
In most cases, using the basic recommended practice outlined in the FINE manual will result in good convergence rate, and high prediction accuracy. However, for situations where problems are encountered, a number of recommendations have been outlined to maximize both convergence and accuracy of preconditioned incompressible flow calculations. The following text is overly brief, and it is therefore recommended that sections 4-3.8 and 9-4 of the FINE manual be consulted for adequate detail.
One important step in procuring convergence for preconditioned simulations is to select adequate values for the reference pressure and temperature. In preconditioned incompressible mode, changes in static pressure can be so slight that the reference pressure is incorporated into the update Pdyn = Ps – Pref. It is often necessary to set Pref reasonably close to initial and boundary condition pressure values to avoid adverse effects on accuracy.
Another important item is related to 2nd order artificial dissipation. Experience has shown that it is generally suitable to switch off the second order dissipation term in the present application. Provided that the flow is truly incompressible, there will be no loss of convergence stability, and generally no affect on accuracy.
A third item is the selected value for the preconditioning parameter beta, which is described in related public literature and the FINE manual. Preconditioning is applied to the compressible form of the Navier-Stokes equations, when simulating incompressible flows, to minimize stiffness of the matrix system eigenvalues. An adequate value for the beta coefficient will result in both acceptable convergence rate (due to it's link with artificial time step), and sufficiently low artificial diffusion - such that solution accuracy is not detracted from. In very general terms, increasing beta past an acceptable range will lead to significant artificial diffusion, and decreasing the coefficient past an acceptable range will lead to poor convergence stability.
The value of the beta coefficient should therefore be selected with some care. Page 4-45 of the FINE manual provides a graph (Figure 4.3.8-4) of generally appropriate values for Beta as a function of Reynolds Number. If the use of values given on the graph does not lead to convergence, we recommend the following strategy:
1) Start the simulation with beta= 3 (default value)
2) If convergence is not achieved with this value for beta, even when combined with a lowering of CFL number, beta should be increased to a point where the convergence rate is found to be satisfactory. A recommended succession of trial values is: beta= 3 ->30 -> 300. The value can be increased further, provided that the Reynolds number is very small.
3) Once a satisfactory level of convergence is achieved, restart the simulation with beta set to a lower value. This strategy will progressively limit the amount of numerical dissipation injected in the domain, while maintaining convergence in extreme situations. One such situation is sometimes manifested as temperature overshoots in buoyant flow heat transfer calculations. Please note that an immediate drop in residuals observed at each restart is due to the presence of beta in the normalization of residuals. In general, monitoring mass flow balance is a good way to confirm that accuracy is not being significantly affected.
A last item to consider is the impact of characteristic velocity Uref. As indicated in the FINE manual, Uref must be set to reasonably reflect the average flow field, because it is also linked with artificial dissipation. It is suggested that Uref be set to a value that is close to the mean inlet velocity.
I hope this information helps. Please let us know if you require further details.
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