TY - JOUR
T1 - Isogeometric Analysis of the Navier–Stokes–Cahn–Hilliard equations with application to incompressible two-phase flows
AU - Hosseini, Babak S.
AU - Turek, Stefan
AU - Möller, Matthias
AU - Palmes, Christian
PY - 2017/11
Y1 - 2017/11
N2 - 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.
AB - 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.
KW - B-splines/NURBS
KW - Cahn–Hilliard phase field model
KW - Isogeometric analysis
KW - Isogeometric finite elements
KW - Navier–Stokes–Cahn–Hilliard equations
KW - Rayleigh–Taylor instability
KW - Rising bubble
KW - Two-phase flow
UR - http://www.scopus.com/inward/record.url?scp=85026254087&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2017.07.029
DO - 10.1016/j.jcp.2017.07.029
M3 - Article
AN - SCOPUS:85026254087
SN - 0021-9991
VL - 348
SP - 171
EP - 194
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -