NUMERICAL SIMULATION OF TWO-PHASE FLOW USING THE LEVEL SET APPROACH

In this dissertation, we present numerical schemes in simulating immiscible two-phase flow problems. The goal of this work is to find unified solutions for numerical modeling of any kind of immiscible two-phase flow with moving interface. Fluid flows are modeled using Navier Stokes equations with discontinuous coefficients. We introduce the Volume Fraction method to evaluate discontinuous integrals arise from the variational formulation in the Finite Element method. The use of Volume Fraction method avoids the approximation of the Dirac Delta function, and therefore no regularization procedures are needed. Several operator splitting variants are studied in detail in linearized and non-linearized fashion, when we want to evaluate the discontinuous coefficients. Interface is captured using the Level Set approach, where a transport equation is solved numerically with fourth order scheme without any stabilization terms. The surface tension effect is implemented in a semi-implicit way, thus larger time steps can be used compared with the explicit method. A recent, well-developed re-initialization technique is included as a way to preserve the signed distance property of the Level Set function. All mentioned numerical methods are used to build two-dimensional solvers. Solvers have been tested both with single-phase flow and two-phase flow benchmark problems. In particular, the bubble dynamics are presented to validate stated numerical schemes.