Efficient Numerical Methods for Waves in One-Dimensional Two-Phase Pipe Flows

This thesis is aimed at improving simulation efficiency for stratified-wavy gasliquid flows. Towards this goad, the simpler nature of incompressible two-phase flows is utilized for predicting hydraulic wave dynamics, both through theoretical analysis and numerical simulation. Numerical methods proposed for the incompressible two-fluid model include a hybridization of a finite volume method with analytical roll-wave profile solutions, a Method of Characteristics and finite volume hybridizations thereof, and a linearized Riemann solver (Roe scheme.) Theoretical analyses based on the same model further the understanding of Kelvin- Helmholtz stability in stratified pipe flows and provide a comprehensive account of how the flow stability predictions of numerical simulators depend on model discretization. Kelvin-Helmholtz/von Neumann analysis is shown to be a valuable support tool for choosing numerical scheme and simulation parameters. Finally, a dual grid scheme is proposed which enables us to extend the computational benefits of incompressible flow models to compressible systems. The dual grid scheme effectively decouples the length scales and numerical CFL restrictions of hydraulic (incompressible) waves from that of acoustic (compressibility) waves. Efficiency is observed to be improved by several orders of magnitude for a wide range of simulation cases