TY - JOUR
T1 - Preconditioning of a Coupled Cahn-Hilliard Navier-Stokes System
AU - Jessica Bosch, Christian Kahle & Martin Stoll
JO - Communications in Computational Physics
VL - 2
SP - 603
EP - 628
PY - 2018
DA - 2018/02
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2017-0037
UR - https://global-sci.org/intro/article_detail/cicp/10540.html
KW - Navier-Stokes, Cahn-Hilliard, two-phase flow, preconditioning, Schur complement approximation, saddle-point problems.
AB - <p style="text-align: justify;">Recently, Garcke et al. [H. Garcke, M. Hinze, C. Kahle, Appl. Numer.
Math. 99 (2016), 151–171)] developed a consistent discretization scheme for a thermodynamically
consistent diffuse interface model for incompressible two-phase flows
with different densities [H. Abels, H. Garcke, G. Grün, Math. Models Methods Appl.
Sci. 22(3) (2012)]. At the heart of this method lies the solution of large and sparse linear
systems that arise in a semismooth Newton method.&nbsp;</p><p style="text-align: justify;">In this work we propose the use of preconditioned Krylov subspace solvers using
effective Schur complement approximations. Numerical results illustrate the efficiency
of our approach. In particular, our preconditioner is shown to be robust with respect
to parameter changes.<br/></p>