MOF test case with rigid rotation

The aim of this test case is to simulate the behavior of two fluids in a box with a zalesak's slotted disk.

The verification criteria is:

• The main volume fraction;
• The symmetric difference area.

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 a zalesak's slotted disk positioned at (0.5,0.75).

Fluids' properties

Both of 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

In this test case, the properties of the fluids are not very important since only the phase-advection equation is solved.

Velocity field

We consider the case of the rigid rotation. The velocity is set to : \(u(x,y)=(2 \pi (\dfrac{1}{2}-y) ,2 \pi (x- \dfrac{1}{2}))\)

Phase advection

The numerical method used for phase advection is MOF.

Runtime parameters

Spatial discretization

We involve the variable CellsPerDirection to change the regular mesh in order to study the convergence. By default, this variable takes the value 16. We consider \(\dfrac{L}{\Delta x}=CellsPerDirection\) for each direction of the grid.

Time discretization

The time step is fixed for the numerical resolution but depends on the variable CellsPerDirection. Time step is defined as: \(\Delta t=CFL \dfrac{\Delta x}{V_{max}}\) where \(V_{max}= \dfrac{\pi}{\sqrt2}\). The final time is set to 1s.

UseAnalyticReconstruction choice

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

UseFilaments choice

The UseFilaments variable is added for using Filaments at MOF method.

Comments

After running many cases, one observes that neither using filaments nor analytic reconstruction make a difference.

Note

We choose to enable both filaments and analytic reconstruction since we obtain a lower value for the symmetric difference area with filaments.

Results

Numerical results

Figure 1 shows the volume fraction of the fluids at different times when CellsPerDirection=128.

Figure 1: Volume fraction of the fluids at different times with CellsPerDirection=128

Note

• The corners are rounded by advection.

Spatial convergence

Five spatial discretizations are used to study the convergence of the mesh.