@Article{CiCP-8-51,
author = {Hector D. Ceniceros, Alexandre M. Roma, Aristeu Silveira-Neto and Millena M. Villar},
title = {A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation},
journal = {Communications in Computational Physics},
year = {2010},
volume = {8},
number = {1},
pages = {51--94},
abstract = {<p style="text-align: justify;">We present a variable time step, fully adaptive in space, hybrid method for
the accurate simulation of incompressible two-phase flows in the presence of surface
tension in two dimensions. The method is based on the hybrid level set/front-tracking
approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391-400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the
immersed-boundary setting while the signed distance (level set) function, which is
evaluated fast and to machine precision, is used as a fluid indicator. The surface tension
force is obtained by employing the mixed Eulerian/Lagrangian representation
introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203,
493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated.
The use of our accurate fluid indicator together with effective Lagrangian
marker control enhance this parasitic current reduction by several orders of magnitude.
To resolve accurately and efficiently sharp gradients and salient flow features we
employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert
with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface
and a variable time step, linearly implicit time integration scheme. We present
numerical examples designed to test the capabilities and performance of the proposed
approach as well as three applications: the long-time evolution of a fluid interface undergoing
Rayleigh-Taylor instability, an example of bubble ascending dynamics, and
a drop impacting on a free interface whose dynamics we compare with both existing
numerical and experimental data.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.050509.141009a},
url = {http://global-sci.org/intro/article_detail/cicp/7563.html}
}