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Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability of flow predictions are however strongly dependent upon the numerics within these simulator tools, the scheme type and resolution in particular. A Kelvin-Helmholtz stability analysis for the differential two-fluid model is in the present work presented and extended to discrete representations of said model. This analysis provides algebraic expressions which give instantaneous, quantitative information into i) when a studied scheme will predict linear wave growth, ii) the rate of growth and the expected growing wavelength, and iii) the wave speeds. These stability expressions adhere to a wider family of finite volume methods, directly applicable to any specific formulation within this group. Both the spatial and temporal discretization are found to play decisive roles in a method's predictive capability. Fundamental aspects of how numerical errors from the temporal integration affects the predicted stability are explored. Numerical errors are observed to manifest in increased, as well as reduced, wave growth. Low-frequency growth from numerical errors is not always easily distinguished from physical wave growth. The linear analysis is demonstrated to be useful in understanding the predictions made by simulator tools, and in choosing the appropriate numerical method and simulation parameters for optimizing the simulation efficiency and reliability.

Roll-wave trains constitutes a well-known two-phase flow regime in pipes. There exists a one-parameter family of steady roll-wave train solutions, provided the flow conditions are within the roll-wave range. This means that wave train solutions can be constructed from out of a wide range of wavelengths. That band of wavelengths which will be observed in nature is however fairly narrow. The wavelength distribution is believed to be related to wave train stability and the flow disturbances. Steady roll-wave train solutions are in this article subjected to a linear stability analysis. Comparisons are made with predictions from direct numerical Roe scheme simulations. Good agreement is observed; after an initial stage of wave coalescence, simulated wavelengths are distributed among the shorter of those wavelengths which are predicted linearly stable. Also the observed disturbance frequency and rate of decay agrees with the analysis predictions. Finally, the stability of pressure driven gas-liquid trains is compared to that of gravity driven free surface trains.

This article examines the use of characteristic methods in stratified two-phase pipe flow simulations for obtaining non-dissipative flow predictions. A Roe scheme and several methods based on the principle of characteristics are presented for the two-fluid model. The main focus is finding numerically efficient ways of capturing wave dynamics and flow regime transitions through direct simulation. Characteristic methods offer the possibility of simulating hyperbolic systems without numerical dissipation. These methods do however lack certain fundamental conservation properties. Challenges related to information scattering and clustering in space and time, particularly around shocks, are also an issue in some method variants. Hybridisations with the finite volume method are proposed which overcome these shortcomings. All methods are compared, evaluating predictions on the onset of linear wave growth and simulations of non-linear, discontinuous roll-waves. The following observations are made: 1. Characteristic methods are excellent at predicting the onset of linear hydrodynamic instability, even with a small number of computational nodes. 2. Dissipative errors in finite volume methods and characteristic hybrids will be closely linked to the Courant number. The Roe scheme and the characteristic hybrids give very little dissipation error as the Courant number approaches unity. This then becomes a question of numerical stability. 3. Adapting dynamic grid cells, moving along with the characteristics information drift, greatly improves simulation efficiency by allowing for longer time steps. Dynamic grid cells are also useful for alleviating the need for interpolation in characteristic methods. These methods easily out-perform the more basic upwind and Lax-Friedrich schemes.

The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and hydraulic waves existing at vastly different spatial and temporal scales. If simulated on the same numerical grid, the need for accuracy in hydraulic waves will necessitate an exaggerated resolution of acoustic waves. Likewise, time steps restricted by the speed of sound are small compared to the time scales active in hydraulic waves. This constitutes a waste of computational potential. The method proposed herein decouples the hydraulic and acoustic scales, greatly improving computational efficiency. The proposed dual grid method solves a four-equation compressible two-fluid model on a principal grid which robustly accounts for the pressure evolution and conserves mass and momentum. An incompressible two-equation model is at the same time solved on a finer grid, resolving the details of the hydraulic evolution. Information from both model formulations is coupled through the terms of the governing transport equations, providing consistency between the grids. Accurate and finely resolved schemes can then be employed for the incompressible two-fluid model without suffering from the time and stability restrictions otherwise enforced by acoustic waves. At the same time, the Hybrid Central-Upwind flux splitting scheme of Evje and Fl{\aa}tten (2005a) allows for an explicit and numerically robust treatment of the acoustic waves without losing hydraulic accuracy. The dual grid method is tested against four dissimilar problems. In all problems, the proposed scheme provided significant increases in computational efficiency and accuracy as compared with a single grid arrangement.