The function sigma_bar_in_fourier_space

It is used to define a stabilization term \(\overline{\sigma}(r,z)\) for multiphase problems where the electrical conductivity varies between the fluids considered. We refer to the section Extension to multiphase flow problem for more information on the formulation of the Navier-Stokes equations in SFEMaNS.

This function defines a scalar function depending only of the radial and vertical coordinates. It is defined on the nodes of the finite element mesh.

Inputs and outputs

The input of this function the mesh H_mesh where the magnetic field is approximated.

The output of this function is a real valued tabular vv of dimension SIZE(H_meshrr,2). It is equal to the number of nodes, H_mesh%np, of the finite element mesh used to approximate the magnetic field.

Remark:

1. The electrical conducitivites of the fluids are set in the data as follows.

   ===Conductivity of fluid 0, fluid 1, ...
   1.d0 2.d0

2. These electrical conductivities are stored in the variable inputs%sigma_fluid. It is a real valued tabular of dimension the number of fluids considered.

Exemple

Here is an exemple where we set the stabilization term \(\overline{\sigma}\) to half of the minimum of the fluids electrical conductivities.

The corresponding code lines are written as follows.

vv=0.5d0*MINVAL(inputs%sigma_fluid)
RETURN

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