MOF test case verifying temporal convergence

Configurations

Physical domain and geometry

The simulations take place in a box of fluid of coordinates (0,0) and (1,1). The second fluid initially occupies a rectangular domain in the box.

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.

Velocity

The velocity field is unidirectional. The direction is selected according to the variable direction. If direction=1, the velocity is expressed as \(u=(\alpha \cos(\beta t) + \gamma,0)\), where \( \alpha, \beta\) and \( \gamma \) are determined from the initial conditions.

Phase advection

The numerical method used for phase advection is MOF.

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.

UseAnalytic choice

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

UseFilaments choice

The UseFilaments variable is used to toggle the filaments in MOF method.

Direction and sign choices

The variables direction and sign allow to adjust the direction of the velocity and the position of the initial domain of the second fluid.

Comments

Using filaments and analytic reconstruction have no great impact on numerical results. We choose as default case enabling analytic reconstruction and disabling filaments.

Results

Numerical results

Figure 1 presents the volume fraction of the fluids at three different times for the default case.

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

Symmetric difference area

The area of symmetric difference is 9.63832518352091688E-007 m².

Temporal convergence

Five temporal discretizations were used to study the temporal convergence.