[thiagopl]

Hi all,

I'm trying to solve the problem of a square cavity heated and coole at the vertical walls using the buoyantBoussinesqsimpleFoam. The problem converges well and the results are qualitatively ok.
I have two problems:
- When I calculate the average Nusselt at the cold wall and compare against the benchmark solution by DeVahl (1983) the results are quite poor.
- I solved the problem for Ra = 10³, Pr = 0.71 for a cavity of length 1m (100x100 grid) modifying the gravitty vector accordingly, then when I solve the same problem setting g=-9.81 and modifying the cavity length to get Ra=10³, I obtain a different Nusselt number!!

I solved this problem using a FORTRAN package (90x90 grid) and the results are pretty good (Nu=1.118). The Nusselt number for the FORTRAN results are calculated in the same way as the OpenFoam case (same file!), so the problem is not there.

Now, I don't know what am I doing wrong. Older threads in this forum did not help me. My case is attached and I would appreciate if somebody could help me.

https://drive.google.com/file/d/0BypOSbibeu1nZlZyQVotQjBDM0k/view?usp=sharing
Note: if the link doesn't work, copy paste the address.

[nimasam]

1- did you try grid independence test? maybe you need much more refined cells near wall
2- did you use second order schemes?

[thiagopl]

Hi nimasam,

Thank you for your attetion.

1. Yes, I did. The variation in Nu is of 0,4% from a 100x100 to a 140x140 uniform grid. Nu=1,982 (!!) for 140x140 (this authors reported Nu=1,109 for 100x100 using the same solver and schemes).

2. Yes. I used bound Gauss QUICK for divSchemes in div(phi,U) and div(phi,T), the rest remains the same as the problem is laminar (the turbulence is off in RASproperties). Also, I used a forward second order scheme to calculate Nu at the cold wall and trapezoidal rule to integrate. I defined Teta = (T-Th)/(Th-Tc), X=x/L, then Nu = Int_0_1(dTeta/dX). Th=301, Tc=300, L=1.

The BC are:
- p and p_rgh are the same of the horRoom tutorial.
- T fixedValue (hot and cold wall) and zeroGradient (adiabatic walls)
- U fixedValue (0,0,0), no slip.

[thiagopl]

I think I found the reason why the Nu differs even when I run the cases with the same Ra and Pr (although it makes no sense). If I run the case 1 (Ra=10³ w/ L=1, g=4.6e-5) and case 2 (Ra=10³ w/ L=0.016, g=9.81), both give the same Nu (as it should) if I start the simulation from uniform initial fields.
The problem appears, for example, when I run case 1 using mapFields from a coarser grid. The problem coverges, but it results in a Nu that differs from the case 2 solved without mapFields.

Summarizing: A case with the same Ra and Pr gives different converged solutions depending on its initial fields (!!). Of course it makes no sense, but why it could be happen?

[nimasam]

How about your fvSolution, you may want to reduce your convergence criteria

[thiagopl]

Hi nimasam,

In fact the SIMPLE residualControl was low, so I changed as shown below.

solvers
{
    p_rgh
    {
        solver          PCG;
        preconditioner  DIC;
        tolerance       1e-08;
        relTol          0.01;
    }
    "(U|T|k|epsilon|R)"
    {
        solver          PBiCG;
        preconditioner  DILU;
        tolerance       1e-05;
        relTol          0.01;
    }
}
SIMPLE
{
    nNonOrthogonalCorrectors 0;
    pRefCell        0;
    pRefValue       0;

    residualControl
    {
        p_rgh           1e-5;
        U               1e-5;
        T               1e-5;
        // possibly check turbulence fields
        "(k|epsilon|omega)" 1e-3;
    }
}

Now I have a Nu that is closer to the benchmark (7% error, still not good), but my residuals behavior a bit strange (figure attached)

I also notice that the No Iterations for Ux and Uy is never more than 2 (it reachs 0 as the problems converge). The residuals for Ux, Uy and T fall rapidly, but it seems strange, don't you think?

It should be a simple problem...

[nimasam]

convergence does not mean correct answer , i suggest:
1-reduce relTol to zero
2-use linearUpwind

[thiagopl]

Sure, actually, convergence doesn't mean it's the end of your problems.
It seems that the problem is in fvSolutions. I'll make some changes, see the results and post when something good happens.

I have one question about the tolerance and the residualControl, is there one that prevails over the other or they are verified in different points during the solution process?

Thank you!

[nimasam]

Residual control just checks initial residuals, and if the value of initial residual for all variables become below the criteria, it will stop.