The function kelvin_force_coeff

It is used to define the coefficient \(g(T)\) of the Kelvin force for ferrofluid problems. This coefficient only depends of the temperature. We refer to the section SFEMaNS's possibilities for more information on the formulation of the Navier-Stokes equations in SFEMaNS for ferrofluid problem.

This function defines a scalar coefficient for a given temperature defined in the physical space.

Inputs and outputs

The inputs of this function is a real denoted temp. It represents the value of the temperature at a given point of the 3D Navier-Stokes domain (radial, azimuthal and vertical cylindrical coordinates are fixed).

The output of this function is a real vv.

Remark:

1. The input temperature is given in the physical space for a coordinate \((r,\theta,z)\). It means you can use product, division, etc.
2. The output vv is also defined in the physical space and not in the Fourier space. Meaning it is defined for the coordinates \((r,\theta,z)\) where the given temperature is defined.

Exemple

Here is an exemple where the following coeffcient for the Kelvin force is considered: \(g(T)=1+ |T| + 3 T^2\).

The corresponding code lines are written as follows.

vv = 1.d0 + ABS(temp) + 3.d0*temp**2
RETURN

We refer to the sections Examples with manufactured solutions (see test 33) and Examples on physical problems for more examples.