Isogeometric Analysis of the Navier-Stokes-Cahn-Hilliard equations with application to incompressible two-phase flows

In this work, we provide a unified and comparative description of the most prominent phase field based two-phase flow models and present our numerical results of the application of Galerkin-based Isogeometric Analysis (IGA) to incompressible Navier-Stokes-Cahn-Hilliard (NSCH) equations in velocity-pressure-phase field-chemical potential formulation. For the approximation of the velocity and pressure fields, LBB compatible non-uniform rational B-spline spaces are used which can be regarded as smooth generalizations of Taylor-Hood pairs of finite element spaces. The one-step θ-scheme is used for the discretization in time. The static and rising bubble, in addition to the nonlinear Rayleigh-Taylor instability flow problems, are considered in two dimensions as model problems in order to investigate the numerical properties of the scheme.