@Article{CiCP-10-1333,
author = {},
title = {An Implementation of MAC Grid-Based IIM-Stokes Solver for Incompressible Two-Phase Flows},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {5},
pages = {1333--1362},
abstract = {<p style="text-align: justify;">In this paper, a novel implementation of immersed interface method combined
with Stokes solver on a MAC staggered grid for solving the steady two-fluid
Stokes equations with interfaces. The velocity components along the interface are introduced
as two augmented variables and the resulting augmented equation is then
solved by the GMRES method. The augmented variables and/or the forces are related
to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,
and are interpolated using cubic splines and are then applied to the fluid through
the jump conditions. The Stokes equations are discretized on a staggered Cartesian
grid via a second order finite difference method and solved by the conjugate gradient
Uzawa-type method. The numerical results show that the overall scheme is second order
accuracy. The major advantages of the present IIM-Stokes solver are the efficiency
and flexibility in terms of types of fluid flow and different boundary conditions. The
proposed method avoids solution of the pressure Poisson equation, and comparisons
are made to show the advantages of time savings by the present method. The generalized
two-phase Stokes solver with correction terms has also been applied to incompressible
two-phase Navier-Stokes flow.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.161009.220211a},
url = {http://global-sci.org/intro/article_detail/cicp/7487.html}
}