Phase Field-Based Incompressible Two-Component Liquid Flow Simulation

In this work, we consider a Cahn–Hilliard phase field-based computational model for immiscible and incompressible two-component liquid flows with interfacial phenomena. This diffuse-interface complex-fluid model is given by the incompressible Navier–Stokes–Cahn–Hilliard (NSCH) equations. The coupling of the flow and phase field equations is given by an extra phase induced surface tension force term in the flow equations and a fluid induced transport term in the Cahn–Hilliard (CH) equations. Galerkin-based isogeometric finite element analysis is applied for space discretization of the coupled system 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. For the validation of the two-phase flow model, we present numerical results for the challenging Rayleigh-Taylor instability flow problem in two dimensions and compare them to reference results.