TY - JOUR
T1 - A diffuse-interface model for axisymmetric immiscible two-phase flow
AU - Kim, Junseok
N1 - Funding Information:
The author thanks his advisor, John Lowengrub, for intellectual and financial support. This work was supported by the Department of Energy (Office of Basic Sciences), The National Science Foundation and the Minnesota Supercomputer Institute.
PY - 2005/1/14
Y1 - 2005/1/14
N2 - A diffuse-interface model is considered for solving axisymmetric immiscible two-phase flow with surface tension. The Navier-Stokes (NS) equations are modified by the addition of a continuum forcing. The interface between the two fluids is considered as the half level set of a mass concentration c, which is governed by the Cahn-Hilliard (CH) equation - a fourth order, degenerate, nonlinear parabolic diffusion equation. In this work, we develop a nonlinear multigrid method to solve the CH equation with degenerate mobility and couple this to a projection method for the incompressible NS equations. The diffuse-interface method can deal with topological transitions such as breakup and coalescence smoothly without ad hoc 'cut and connect' or other artificial procedures. We present results for Rayleigh's capillary instability up to forming satellite drops. The results agree well with the linear stability theory.
AB - A diffuse-interface model is considered for solving axisymmetric immiscible two-phase flow with surface tension. The Navier-Stokes (NS) equations are modified by the addition of a continuum forcing. The interface between the two fluids is considered as the half level set of a mass concentration c, which is governed by the Cahn-Hilliard (CH) equation - a fourth order, degenerate, nonlinear parabolic diffusion equation. In this work, we develop a nonlinear multigrid method to solve the CH equation with degenerate mobility and couple this to a projection method for the incompressible NS equations. The diffuse-interface method can deal with topological transitions such as breakup and coalescence smoothly without ad hoc 'cut and connect' or other artificial procedures. We present results for Rayleigh's capillary instability up to forming satellite drops. The results agree well with the linear stability theory.
KW - Cahn-Hilliard equation
KW - Coalescence
KW - Nonlinear multigrid method
KW - Pinch-off
KW - Rayleigh instability
KW - Satellite drops
UR - http://www.scopus.com/inward/record.url?scp=9644260709&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2003.11.020
DO - 10.1016/j.amc.2003.11.020
M3 - Article
AN - SCOPUS:9644260709
SN - 0096-3003
VL - 160
SP - 589
EP - 606
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 2
ER -