SFEMaNS  version 4.1 (work in progress) Reference documentation for SFEMaNS
The function Vexact

It is used to define the velocity field $$\bu_\text{given}$$ when the Navier-Stokes equations are not approximated. Moreover, in the data file the following line has to be set to false:

===Restart on velocity (true/false)

If it set to true, the velocity is read from a suite file of the Navier-Stokes equations and not this function.

This function defines a time independent velocity field for one given Fourier mode on all of the nodes of the finite element mesh.

### Inputs and outputs

The inputs of this function are the following:

1. m is the Fourier mode $$m$$ considered. It is an integer.
2. H_mesh is the finite element mesh used to approximate the magnetic field.

The output of this function is a real valued tabular vv of dimension (H_mesh%np,6).

### Exemple

Here is an exemple where we set $$\bu_\text{given}=r\textbf{e}_\theta$$ where $$\textbf{e}_\theta$$ is the unit vector in the azimuthal direction.

The corresponding code lines are written as follows.

IF (TYPE==3.AND.m==0) THEN
vv = rr(1,:)
ELSE
vv = 0.d0
END IF
RETURN

Remark: The divergence of the velocity field has to be zero.

We refer to the sections Examples with manufactured solutions and Examples on physical problems for more examples.