Energy-consistent formulations of the one-dimensional two-fluid model

The one-dimensional incompressible two-fluid model is a dynamic model for two-phase flow in pipes, which resolves only cross-sectionally averaged quantities. It can be used to predict the flow in long pipelines at low computational cost. However, the simplification of three-dimensional reality to a one-dimensional model requires making assumptions, which can result in nonphysical behavior. Similarly, the process of discretizing the equations can yield a computational model with different properties than the continuous model. This thesis focuses on retaining energy conservation properties in both continuous and discrete versions of the one-dimensional model, yielding improved physical fidelity and nonlinear stability.

It is shown that an energy conservation equation can be derived from the continuous model equations, proving that the mechanical energy is a secondary conserved quantity of the model. A finite volume scheme on a staggered grid is carefully designed such that a semi-discrete energy conservation equation follows naturally from the semi-discrete model equations, matching the behavior of the continuous equations. The computational model is extended with higher order stabilizing terms that are designed to be either energy-conserving or strictly dissipative, according to the physics of the specific added effect. The demand for energy conservation is also used to make the solutions to a new pressure-free version of the two-fluid model consistent with those of the original model, while retaining the pressure-free model's advantage in computational efficiency. The end result is a robust computational model that yields smoothly converging solutions under difficult conditions, such as the appearance of shocks and the existence of a large velocity difference between the two fluids.