This is a code block from nutWallFunction library in OpenFOAM where in, effective kinematic viscosity ($\nut_w$) at the wall is calculated using resolved field(in case of LES)/ mean field(in case of RANS) and $y^+_p$ (wall normal distance of the first cell center). this allows to set a new viscosity value as boundary condition at the wall using log law. Considering the first cell center is in the logarithmic layer of the universal velocity profile.
Now, in this code block of member function defined as nutUWallFunctionFvPatchScalarField::calcYPlus()
There has been iterations done for the yPlus value to reach convergence with maximum of 10 iterations. Why are these iterations needed? and why is the maximum number of iterations 10. I have given a reference of the code below;
tmp nutUWallFunctionFvPatchScalarField::calcYPlus
(
const scalarField& magUp
) const
{
const label patchi = patch().index();
const turbulenceModel& turbModel = db().lookupObject
(
IOobject::groupName
(
turbulenceModel::propertiesName,
internalField().group()
)
);
const scalarField& y = turbModel.y()[patchi];
const tmp tnuw = turbModel.nu(patchi);
const scalarField& nuw = tnuw();
tmp tyPlus(new scalarField(patch().size(), 0.0));
scalarField& yPlus = tyPlus.ref();
forAll(yPlus, facei)
{
scalar kappaRe = kappa_*magUp[facei]*y[facei]/nuw[facei];
scalar yp = yPlusLam_;
scalar ryPlusLam = 1.0/yp;
int iter = 0;
scalar yPlusLast = 0.0;
do
{
yPlusLast = yp;
yp = (kappaRe + yp)/(1.0 + log(E_*yp));
} while (mag(ryPlusLam*(yp - yPlusLast)) > 0.01 && ++iter < 10 );
yPlus[facei] = max(0.0, yp);
}
return tyPlus;
}
My doubt is concerning the do-while loop at the end for yPlus iteration.
In our C++ program, we repeatedly refine our solution through an iterative process until we achieve a convergence target of 10^-8. Each iteration updates our result based on some computation or algorithm, and we track the error estimate until it falls below the specified target value. This approach ensures that our program converges towards the desired accuracy level, meeting the numerical requirements of our task.
CFD software's are based on numerical methods or techniques to predict the fluid behavior for various types of problems e.g. LES and RANS turbulence modelling etc. Unlike exact solutions , the numerical methods involve approximations of the governing fluid equations /parameters which cannot be evaluated at once and need iterative computational solvers that utilize grids to solve the governing equations.
During this process several types of errors are introduced while approximating variable property e.g. round off errors ( computer /machine floating point precision) , truncation errors introduced by the type of numerical scheme used.
However , according to the nature of fluid and it's interaction with surrounding environment , ( in your e.g. yplus wall function which is measure of the fluid friction resistance near wall ) the solutions obtained through numerical schemes present a significant source of error which can interpret the fluid behavior in entirely different manner.
Therefore, the solution is often tested by repeating the process using better approximations and schemes with an objective to obtain the accurate value of the parameter.
During iteration process , these errors can amplify or reduce ( which is indicative of the stability of solution ) depending on boundary conditions used to obtain solution. So, often an error tolerance is introduced as condition in numerical algorithm to make the solution more meaningful and realistic during iteration steps.. In your case wall shear stress is being approximated using wall units in logarithmic boundary layer.
Once that condition is satisfied, the process stops and proceeds further by evaluating the next dependent variable and so on until consistent and complete solution is obtained for a problem.
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