Level set analysis of two-fluid interfacial flows

Abstract

In this study incompressible immiscible two-phase ows have been analyzed in two dimensions using Level Set method. Firstly, a brief explanation about other numerical methods existing in the field of modelling interfacial two-phase flows is presented. Then, Level Set methodology and its coupling with Navier-Stokes equations are introduced in detail. Discretization method used in this study is Finite Difference method and derivations of Level Set function and convective terms are done using fth order Weighted Essentially Non-Oscillatory (WENO) scheme. In order to solve the pressure field implicitly, a projection method is applied. Afterwards, the reliability of method is tested by making comparison with Smoothed Particle Hydrodynamic (SPH) method for di erent test cases such as Rayleigh-Taylor instability, rising bubble, droplet fall, bursting bubble at free surface and droplet fall onto free surface. Effects of non-dimensional parameters like Reynolds (Re) and Eotvos (Eo) numbers on the evolution of interface in two-phase flows are investigated. Lastly, dam breaking problem is considered in order to analyze the performance of Level Set method in simulating free surface flows.