# How to compute the discretization length in OpenFOAM

To plot the convergence on unstructured meshes, the discretization length “h” is required.

OpenFOAM computes $$1.0/∥xPf−xNf∥2$$, inversed distance between two cell centers (N = neighbor, O = owner, O < N), for each face f in the mesh, and stores this in the deltaCoeffs field. This is computed by the surfaceInterpolation class, redirected from the fvMesh class:

Minimal example that computes minimal, average and the maximal discretization distance

#include "fvCFD.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

int main(int argc, char *argv[])
{
#include "setRootCase.H"
#include "createTime.H"
#include "createMesh.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

const auto& deltaCoeffs = mesh.deltaCoeffs();

Info << "h_min = " << 1. / max(deltaCoeffs()).value() << endl
<< "h_mean = " << 1. / average(deltaCoeffs()).value() << endl
<< "h_max = " << 1. / min(deltaCoeffs()).value() << endl;

Info<< nl;
runTime.printExecutionTime(Info);

Info<< "End\n" << endl;

return 0;
}


The application is found here.