Where, \(n+1\) is the new or current time step, \(n\) is the previous time step, \(\alpha_{q,f}^{n}\) is face value of the volume fraction of\(q\) computed from before, \(V\) is volume of cell, \(U_{f}\) is normal velocity of volume flux through the face.

Turbulence modelling

A standard kinetic energy (k) and dissipation rate (ɛ) (k-ɛ) model is used to control the flow behaviour by solving the unknowns of Navier-Stokes (RANS) equations through Reynolds-averaging. The transportation of kinetic energy across the domain is equated as: