[Benben]

Hello,

I am using a modified rhoBuoyantReactingFoam solver from openFoam 6.0.
I am solving a transient case.

For each time step, my initial residuals are falling as expected until convergence is reached:

PIMPLE: Iteration 98
DILUPBiCGStab:  Solving for Ux, Initial residual = 9.8539e-06, Final residual = 1.07935e-07, No Iterations 1
DILUPBiCGStab:  Solving for Uy, Initial residual = 2.44866e-05, Final residual = 2.35497e-07, No Iterations 1
DILUPBiCGStab:  Solving for Uz, Initial residual = 3.85062e-05, Final residual = 3.43768e-07, No Iterations 1
DICPCG:  Solving for p, Initial residual = 0.000102216, Final residual = 9.9092e-07, No Iterations 15
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 3.31665e-09, global = -9.50722e-10, cumulative = 8.78471e-05
PIMPLE: Iteration 99
DILUPBiCGStab:  Solving for Ux, Initial residual = 9.59792e-06, Final residual = 1.05153e-07, No Iterations 1
DILUPBiCGStab:  Solving for Uy, Initial residual = 2.3872e-05, Final residual = 2.29636e-07, No Iterations 1
DILUPBiCGStab:  Solving for Uz, Initial residual = 3.74963e-05, Final residual = 3.34476e-07, No Iterations 1
DICPCG:  Solving for p, Initial residual = 9.88698e-05, Final residual = 9.94734e-07, No Iterations 166
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 3.4152e-09, global = -4.49583e-10, cumulative = 8.78466e-05

And at the last itteration, the residuals goes up once again.

PIMPLE: Converged
        Doing final iteration
PIMPLE: Iteration 100
DILUPBiCGStab:  Solving for Ux, Initial residual = 0.000108962, Final residual = 9.29881e-07, No Iterations 13
DILUPBiCGStab:  Solving for Uy, Initial residual = 0.000238293, Final residual = 6.89688e-07, No Iterations 15
DILUPBiCGStab:  Solving for Uz, Initial residual = 0.000525947, Final residual = 7.80032e-07, No Iterations 19
DICPCG:  Solving for p, Initial residual = 0.196718, Final residual = 9.90858e-07, No Iterations 304
diagonal:  Solving for rho, Initial residual = 0, Final residual = 0, No Iterations 0
time step continuity errors : sum local = 5.80521e-09, global = 4.83121e-12, cumulative = 8.78466e-05
PIMPLE: Converged in 100 iterations
ExecutionTime = 28.24 s  ClockTime = 29 s

Should i worry about the precision of my simulation results ?
Should i use a final relaxation factor different from 1 ?

[jherb]

No, this is normal. For the last iteration of a time step, no under-relaxation is down, so the solver for the U field is "disturbing" the solution of p.


By applying under-relaxation in the other iterations the new result of the U-solver is only partly used, so the solution of the p solver is more or less still good and therefore the initial residual is low.

[Benben]

Thank you for your help jherb.

Why is the lat itteration's under-relaxation factor different by default ? Is there something to gain to have a different value of under relaxation at the last itteration ?

[jherb]

I think, you do not want under-relaxation in the last iteration, to make sure, that your boundary conditions are really fulfilled. If your simulation has perfectly converged then there would be no problem, because under-relaxation would have no effect. But if it had not converged perfectly then your fields might not match the boundary conditions.



So e.g. for a pipe, you specify a velocity of 1 m/s at the inlet, but due to under-relaxation, the internal value (and the value at the outlet) might be different. By setting the under-relaxation to 1.0, meaning no under-relaxation, you really calculate an internal field corresponding to your boundary conditions.

[Benben]

Thank you Jherb, this was really helpfull.

I made a test with a 10 meters long "pipe" (without walls, a 1D problem) filled with gas at U=1m/s and at T=300K. I set the temperature at the inlet to T=400K.

When i run the simulation for 10 seconds with dt = 1E-3 s:

• if i set an under-relaxation at the last iteration to 1, the heat travels completly to the extremity of the pipe. Just like the analytical solution.
• if i set un under relaxation at the last iteration of 0.5, the heat travels to ~ 90% of the pipe's length. There is an error compared to analytical solution.

This mean that I had not realy understood how relaxation is applied mathematically.
Is it the ddt term of the equations that is multiplied by the under-relaxation factor ?

[Robin.Kamenicky]

Hi Benoit,

By under-relaxation of the last iteration you can loose some information. If you want to under-relax your final iteration you need to perform a lot of outer iterations.

There are two kinds of relaxation. Field relaxation and matrix relaxation.
Field relaxation can be found in GeometricField.C:949

 operator==(prevIter() + alpha*(*this - prevIter()));

\phi^_{n+1} = \phi^{n-1} + \alpha(\phi^n-\phi^_{n-1})

This clearly shows how you can loose the information.

The matrix relaxation makes matrices more diagonal dominant. You can find in fvMatrix class

Kind regards,
Robin