Computation of free surfaces is complex because of the continuous change in the location of the boundary layer.
The steps for a fully conservative FV method of this type are: The main problem with the algorithm in this procedure is that there is only one equation for one cell but large number of grid nodes moving.
To avoid instability and wave reflection, the method is modified as follows: From the previous steps, we can calculate the volume of fluid to be flowed in or out of the CV to have mass conservation.
To obtain the coordinates of CV vertices at free surface, we have more unknowns and less equations due to single volumetric flow rate for each cell.
In computation of two-fluid flows, in some cases the interface might be too complex to track while keeping the frequency of re-meshing at an acceptable level.
Not being able to reduce the frequency of re-meshing in 3D might introduce overwhelming mesh generation and projection costs, making the computations with the interface-tracking technique no longer feasible.
To determine the shape of the free surface, the fraction of each cell near the interface is computed that is partially filled.
In this method, fraction of the cell occupied by the liquid phase can be calculated by solving the transport equation.
For the computation of such two-phase flows which do not come under any of the above discussed categories, elements are borrowed from both surface-capturing and surface-tracking methods.
In this method, fluid properties are smeared over a fixed number of grid points normal to the interface.
Interface is also tracked as in interface-tracking method to prevent it from smearing by moving the marker particles using the velocity field generated by the flow solver.
marker particles are added and removed to maintain the accuracy by keeping the approximate spacing between them equal.