Two-phase flow simulations using Diffuse interface model

In this work, a numerical scheme based on artificial compressibility formulation of a diffuse-interface model is developed for simulating two-dimensional two-phase incompressible flows. The coupled nonlinear systems composing of the incompressible Navier-Stoke equations(NSeqs) and volume preserving Allen-Cahn type phase equation are recast into conservative forms with source terms, which are suited to implementing high-order schemes. The Boussinesq approximation is used for buoyancy effects in flows with small density densities. The fifth-order weighted essentially non-oscillatory scheme is used for discretizing the convective terms while for obtaining time accuracy at each physical time step dual-time stepping (DTS) approach is used. Beam-Warming approximate factorization scheme is utilized so as to obtain block tridiagonal system of equations in each spatial direction which can be solved efficiently with the alternating direction implicit (ADI) algorithm. The performance of the numerical method is demonstrated by its application to benchmark viscous two-phase flow problems. Numerical experiments shows that the method allows larger time-steps and smaller interface value η than previous projection methods in literature when computing problems with moving interfaces and topological changes.