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.
- Cahn–Hilliard phase field model
- Isogeometric analysis
- Isogeometric finite elements
- Navier–Stokes–Cahn–Hilliard equations
- Rayleigh–Taylor instability
- Rising bubble
- Two-phase flow