Computer-Based Simulation of Multiphase Flow

A new version of numerical solver for simulating two-phase incompressible viscous flows is developed in the present study. The governing equations consists of the Navier-Stokes equations with Boussinesq approximation and surface tension terms acting at the interface coupled with the phase field equation representing the moving interface. The system of equations is cast into a conservative form suitable for the implementation with artificial compressibility method. The resulting hyperbolic system is discretized in space with high order weighted essentially non-oscillatory (WENO) finite difference scheme. The well known dual-time stepping technique is applied for obtaining time accuracy at each physical time step, and the approximate factorization based alternating direction implicit (AF-ADI) algorithm is used to solve the resulting system of equations. Endowing the system with suitable initial and boundary conditions, the performance of the method is analyzed by computing several benchmark two-fluid flow problems with moving interface.