[khoder Alshaar]

Hi,
I know that the normal vector can be defined in OpenFOAM as follows:

// Face area normal vectors
const surfaceVectorField& Sf = mesh.Sf();

// Face areas
const surfaceScalarField& magSf = mesh.magSf();

// Face normals
const surfaceVectorField& N = Sf/magSf;

My question is, how do we define the tangent vectors to the surface?

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[Tobermory]

Okay - this is a maths question, rather than an OpenFOAM question, but here goes.

You want to find a vector that is normal to unit vector N - let's call it t. There are of course an inifite number of these, but let's assume that you are not too bothered which one you get. Then:
1. define a vector t1 = (1,0,0)
2. calculate the dot product of t1.N and check whether this equals 1?
3. if it does, then N is pointing in the same direction as t1, and so you can set t=(0,1,0)
3. if it does not, then calculate t2 = t1 x N (cross product) and then divide this through by its norm to get the unit vector t.

[olesen]

Originally Posted by Tobermory

Okay - this is a maths question, rather than an OpenFOAM question, but here goes.

You want to find a vector that is normal to unit vector N - let's call it t. There are of course an inifite number of these, but let's assume that you are not too bothered which one you get. Then:
1. define a vector t1 = (1,0,0)
2. calculate the dot product of t1.N and check whether this equals 1?
3. if it does, then N is pointing in the same direction as t1, and so you can set t=(0,1,0)
3. if it does not, then calculate t2 = t1 x N (cross product) and then divide this through by its norm to get the unit vector t.

Indeed, this is similar to what is being done in
https://develop.openfoam.com/Develop...ref_type=heads
https://develop.openfoam.com/Develop...ref_type=heads

// Guess second axis
axes::rotation(axis, Zero, E3_E1)

In those cases, it uses a best guess of some principal axis (x,y,z direction) and goes from there.
findOrthogonal() and then the removeCollinear()