@Article{CiCP-11-1347,
author = {Tony W. H. Sheu and C. H. Yu},
title = {Numerical Simulation of Free Surface by an Area-Preserving Level Set Method},
journal = {Communications in Computational Physics},
year = {2012},
volume = {11},
number = {4},
pages = {1347--1371},
abstract = {<p style="text-align: justify;">We apply in this study an area preserving level set method to simulate
gas/water interface flow. For the sake of accuracy, the spatial derivative terms in the
equations of motion for an incompressible fluid flow are approximated by the fifth-order accurate upwinding combined compact difference (UCCD) scheme. This scheme
development employs two coupled equations to calculate the first- and second-order
derivative terms in the momentum equations. For accurately predicting the level set
value, the interface tracking scheme is also developed to minimize phase error of the
first-order derivative term shown in the pure advection equation. For the purpose of
retaining the long-term accurate Hamiltonian in the advection equation for the level
set function, the time derivative term is discretized by the sixth-order accurate symplectic Runge-Kutta scheme. Also, to keep as a distance function for ensuring the front
having a finite thickness for all time, the re-initialization equation is used. For the verification of the optimized UCCD scheme for the pure advection equation, two benchmark problems have been chosen to investigate in this study. The level set method
with excellent area conservation property proposed for capturing the interface in incompressible fluid flows is also verified by solving the dam-break, Rayleigh-Taylor
instability, two-bubble rising in water, and droplet falling problems.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.120510.150511s},
url = {http://global-sci.org/intro/article_detail/cicp/7416.html}
}