| Abstract: | This study aims to develop a numerical scheme in collocated Cartesian grids
to solve the level set equation together with the incompressible two-phase flow equations.
A seventh-order accurate upwinding combined compact difference (UCCD7)
scheme has been developed for the approximation of the first-order spatial derivative
terms shown in the level set equation. Developed scheme has a higher accuracy with a
three-point grid stencil to minimize phase error. To preserve the mass of each phase all
the time, the temporal derivative term in the level set equation is approximated by the
sixth-order accurate symplectic Runge-Kutta (SRK6) scheme. All the simulated results
for the dam-break, Rayleigh-Taylor instability, bubble rising, two-bubble merging, and
milkcrown problems in two and three dimensions agree well with the available numerical
or experimental results. |
