Characteristic methods and Roe's method for the incompressible two-fluid model for stratified pipe flow. (March 2017) - Akselsen, A.H.
Highlights: Efficient Roe and characteristic methods are applied to the two-fluid model. New conservative hybrids of characteristic and finite volume methods are proposed. Characteristic schemes predict the onset of hydrodynamic instability most accurately. A strong sensitivity to the Courant number is observed with finite volume methods. Time steps can be significantly increased if a dynamic numerical grid is adopted. Abstract: 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. Capturing flow regime transitions both effciently and precisely necessitates schemes which remain stable in a numerical sense, yet predicts wave growth once the flow conditions turn unstable. 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 CFL number. The Roe scheme and the characteristic hybrids give very little dissipation error as the CFL 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. On the whole, the performance of the characteristic hybridisations are similar to that of the Roe scheme at large CFL numbers. Characteristic hybridisations perform somewhat better in predicting linear instability while the Roe scheme is better suited for the shock fronts found in the roll-wave flow regime. These method easily out-perform the more basic upwind and Lax–Friedrich schemes.