MOF test case with filaments and periodic boundary conditions

Configurations

Physical domain and geometry

We simulate three fluids in a box with filaments of coordinates (0,0) and (1,1).

Fluids' properties

All the fluids considered have the same properties :

where \(\rho\) is the density, \(\mu\) the dynamic viscosity coefficient, \(\sigma\) the conductivity, C the specific heat capacity, \(\alpha\) the thermal expansion coefficient and \(T_{0}\) the reference temperature.

Note

The results are not affected by fluid properties since the only equation solved is phase advection.

Velocity

The velocity field is uniform unidirectional. It is set as: \( u=(\pm \dfrac{1}{2},\pm \dfrac{1}{2})\)

Boundary conditions

We consider periodic boundary conditions along both horizontal and vertical axis.

Phase advection

The numerical method considered for Phase advection is MOF with filaments.

Runtime parameters

Spatial discretization

A regular mesh with \(\dfrac{L}{\Delta x}=32\) for each direction is considered.

Time discretization

The time step is fixed and equals to \(0.01 \ s\). The final time is set to \(2 \ s\) and corresponds to one period.

use_analytic choice

The use_analytic variable is used to toggle the analytic reconstruction. The tolerance angle and derivative are respectively \(10^{-15}\) and \(0\).

Velocity choices

Two variables are included: sign and direction. sign allows to change the velocity direction. direction variable concerns the positioning of the filaments.

Comments

• The quality of the numerical results is not influenced by the analytical reconstruction.
• The quality of results obtained by switching the variables sign and direction is the same but there is a difference in the symmetric difference area especially for the variable direction.

Results

Numerical results

Figure 1 shows the volume fraction of the main fluids at three different times with analytic reconstruction.

Figure 1: Volume fraction of the fluids at different times with analytic reconstruction

Symmetric difference area