Simulation of Incompressible Free Surface Flow Using the Volume Preserving Level Set Method (Communications in Computational Physics, 2020)
This study aims to develop a numerical scheme in collocated Cartesian gridsto 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 derivativeterms shown in the level set equation. Developed scheme has a higher accuracy with athree-point grid stencil to minimize phase error. To preserve the mass of each phase allthe time, the temporal derivative term in the level set equation is approximated by thesixth-order accurate symplectic Runge-Kutta (SRK6) scheme. All the simulated resultsfor the dam-break, Rayleigh-Taylor instability, bubble rising, two-bubble merging, andmilkcrown problems in two and three dimensions agree well with the available numericalor experimental results.