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

It is used to define the source term \(\textbf{f}\) of the NavierStokes equations. We refer to the section Approximation of the NavierStokes equations for more information on the formulation of the NavierStokes equations in SFEMaNS.
This function defines the source term for one given Fourier mode, one given component (radial cosine, radial sine, azimuthal cosine, azimuthal sine, vertical cosine or vertical sine) on all the nodes 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:
TYPE
is the component of the source term that we compute (radial cosine, radial sine, etc.). It is an integer between one and six. rr
is a real valued tabular that contains two columns with dimensions (2,vv_mesh%np). The tabular rr(1,:) contains the radial cylindrical coordinate of all the nodes of the finite element mesh vv_mesh. Respectively, rr(2,:) contains the vertical coordinates of these nodes. mode
is the Fourier mode considered. It is an integer. i
is the label that the processor associates to the Fourier mode considered. It is an integer. time
is the time at which the source term is computed. It is a real number. opt_density
is the density. This input is optional. opt_tempn
is the temperature. This input is optional. The output of this function is a real valued tabular vv of dimension SIZE(rr,2).
Remarks:
Here is an exemple where the source term is equal to \(\rho \textbf{e}_z\) with \(\rho\) being the density and \(\textbf{e}_z\) being the unit vector in the vertical direction.
Remarks:
error_petsc
. We refer to the sections Examples with manufactured solutions and Examples on physical problems for more examples.