Residuals

The residuals are evaluated by substituting the iterations’ solution into the theretical equation, taking out the non-zero result; it is also normalised to make it independent of the scale of the problem being analysed. Consequently, before solving an equation for a particular field, the initial residual is evaluated based on the current values of the field. After each solver iteration the residual is re-evaluated. To terminate the case, the initial residual of the field equations should fall below user-specified threshold values.

Check convergence on turbulent flows

A simple trick to check the converge of the calculations properly, consits in checking the \( ν_{t} \) convergence value since it is dependent from \( k \) and \( ε \) which both must converge to get a good \( ν_{t} \), hence it is one of the best indicator of convergence.

Convergence visualization

Residuals can be monitored via terminal live or in a log file afterwards. Nonetheless solutions are present to generate charts:

GNUPlot

GNUPlot (gnuplot) is program for plotting mathematical expressions and data, to install it use the following:

sudo apt install gnuplot

Activate the object function in /system/controlDict:

    ...
    functions
    {
        #includeFunc  residuals
        ...
    }

Then the simualtion can be started as:

foamInfo residuals
foamGet residuals
foamRun > log &
foamMonitor -l ./postprocessing/0/residuals

Manual GNUPlot file

A manual file for plotting the simualtion data follow:

set logscale y
set title "Residuals"
set ylabel 'Residual'
set xlabel 'Iteration'
plot "< cat log | grep 'Solving for Ux' | cut -d' ' -f9 | tr -d ','" title 'Ux' with lines,\
"< cat log | grep 'Solving for Uy' | cut -d' ' -f9 | tr -d ','" title 'Uy' with lines,\
"< cat log | grep 'Solving for Uz' | cut -d' ' -f9 | tr -d ','" title 'Uz' with lines,\
"< cat log | grep 'Solving for omega' | cut -d' ' -f9 | tr -d ','" title 'omega' with lines,\
"< cat log | grep 'Solving for k' | cut -d' ' -f9 | tr -d ','" title 'k' with lines,\
"< cat log | grep 'Solving for p' | cut -d' ' -f9 | tr -d ','" title 'p' with lines
pause 1
reread