The function imposed_velocity_by_penalty

It is used to define the velocity in the solid obstacle denoted \(\bu_\text{obs}\). We note this velocity does not depends of the cylindrical coordinate \(\theta\). We refer to the section Extension to non axisymmetric geometry for more information on the formulation of the Navier-Stokes equations in SFEMaNS.

This function defines a velocity for the Fourier mode zero, for all components (radial cosine, radial sine, azimuthal cosine, azimuthal sine, vertical cosine or vertical sine) on a number of nodes, denoted nb_node, of the finite element mesh. We denote by vv_mesh the finite element mesh used to approximate the velocity field.

Inputs and outputs

The inputs of this function are the following:

1. rr is a real valued tabular that contains two columns with dimensions (2,nb_node). The tabular rr(1,:) contains the radial cylindrical coordinate of each nodes considered. Respectively, rr(2,:) contains the vertical coordinates of these nodes. We note that the integer nb_node is generally equal to the total number of node vv_mesh%np.
2. t is the time at which this term is computed. It is a real number.

The output of this function is a real valued tabular vv with two columns of dimension (SIZE(rr,2),6).

Exemple

Here is an exemple where we impose a solid rotation. It means that we set \(\bu=r\textbf{e}_\theta\) on the boundary of the domain where \(\textbf{e}_\theta\) is the unit vector in the azimuthal direction.

The corresponding code lines are written as follows.

vv(:,1)   = rr(1,:)
vv(:,2:6) = 0.d0
RETURN

We refer to the sections Examples with manufactured solutions (see test 24) and Examples on physical problems for more examples.