MOF test case with periodic boundary conditions

This test case simulates a three fluid domain with periodic boundary conditions.

Configurations

Physical domain and geometry

The simulations take place in a box of fluid of coordinates (0,0) and (1,1). The second fluid is placed in four equally spaced circles of radius 0,15. The third fluid is placed in five circles of radius 0,15.

Fluids' properties

The three fluids have the same properties wich are:

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.

Boundary conditions

The boundary conditions considered are periodic along both horizontal and vertical axis.

Velocity

The velocity field is uniform unidirectional.

Phase advection

The MOF technique is used for the phase advection.

Runtime parameters

Spatial discretization

A regular randomly perturbed mesh with \(\dfrac{L}{\Delta x}=100\) for each direction is considered.

Time discretization

The time step is fixed and equals to \(5.10^{-3}s\). The final time is set to \(\sqrt2s\).

UseAnalytic choice

The UseAnalytic variable is used to choose between the analytic reconstruction and minimization. The tolerance angle and derivative are respectively \(10^{-5}\) and 0.

UseFilaments choice

The UseFilaments variable is used to enable or disable Filaments while using the MOF method.

Sign choice

The variable Sign is included to change the velocity field direction.

Comments

Taking into account all the cases, one always observes the periodic boundary conditions with almost the same quality. The numerical results with minimization are the same as the results obtained with analytic reconstruction. It is the same case for the use of filaments.

Numerical results

Figure 1 presents the volume fraction of the main fluids at different times of the default case simulation. At the final time which corresponds to one period, one finds exactly the initial form.

Figure 1: Volume fraction of the main fluids for the default case at different times

Area of symmetric difference

The average value of the symmetric difference area is: 4.309676390332247 \(10^{-5}m^2\)