SFEMaNS
version 4.1 (work in progress)
Reference documentation for SFEMaNS

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 NavierStokes 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.
The inputs of this function are the following:
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. 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).
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.
We refer to the sections Examples with manufactured solutions (see test 24) and Examples on physical problems for more examples.