TY - JOUR
T1 - Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and Their Connection to Divergence-Free Coupled Schemes
AU - Rebholz , Leo G.
AU - M. Wise , Steven
AU - Xiao , Mengying
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 649
EP - 676
PY - 2018
DA - 2018/04
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12536.html
KW - Cahn-Hilliard-Navier-Stokes system, penalty-projection method and strong divergence-free elements.
AB - <p style="text-align: justify;">We study and compare fully discrete numerical approximations for the Cahn-Hilliard-Navier-Stokes
(CHNS) system of equations that enforce the divergence constraint in different ways,
one method via penalization in a projection-type splitting scheme, and the other via strongly
divergence-free elements in a fully coupled scheme. We prove a connection between these two
approaches, and test the methods against standard ones with several numerical experiments. The
tests reveal that CHNS system solutions can be efficiently and accurately computed with penalty-projection
methods.</p>