Abstract
Two-phase flows are characterized by the co-existence of two immiscible phases, i.e., gas and liquid, separated by an interface. They exist in various natural and industrial processes, such as ocean waves, bubble column reactors, spray cooling, fuel injection for internal combustion engines, inkjet printing, etc. A better understanding of those processes requires insights into the physics of two-phase flows. Along with experiments, computational simulations are are reliable tool for investigating such flows because of their ability to resolve the small length scales and short time scales properly using powerful computers. However, computational challenges still arise from the variation of length scales in a two-phase flow system. Resolving such a system with uniform mesh resolution throughout the computational domain requires huge computational resources and time. This thesis develops a flow solver that adopts a variable mesh resolution strategy, known as adaptive mesh refinement (AMR), for flows that constitute a variety of length scales. With AMR, the mesh resolution is deployed efficiently in a way that captures the small length scales using fine mesh resolution, while the large length scales are resolved with coarse mesh resolution. This brings the computational cost down for complex two-phase flows significantly. The solver incorporates the Message Passing Interface (MPI) parallelism and uses the finite volume approach for solving the full Navier Stokes equations with the two-step projection method. It employs a geometric volume of-fluid (gVOF) method with piecewise linear interface calculation (PLIC) to capture the gas-liquid interface. The AMR implementation is supported by the AMReX framework and ensures consistency in mass and momentum transport, which is especially critical in simulating flows with large density ratios to avoid non-physical momentum transfer and consequently, numerical deformation of the gas-liquid interface. The efficacy of the solver as well as the performance of its individual components has been assessed across a wide range of canonical test cases. Firstly, the efficiency of the pressure solver was demonstrated in two static test cases. Then, the volume advection was validated in three benchmark test cases: drop translation, Zalesak’s disk rotation, and drop deformation in a vortex field. Finally, the performance of the fully coupled solver was assessed in challenging test cases that included extremely large density drop translation, dam break, rising bubble, and drop splashing on a thin film. The results demonstrate that the solver is well capable of simulating two-phase flows with accuracy and efficiency using AMR.