Abstract
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid model, our new framework includes diffusion, friction, and surface tension. We show that surface tension can be added in an energy-conserving manner, and that diffusion and friction have a strictly dissipative effect on the energy. We then propose spatial discretizations for these terms such that a semi-discrete model is obtained that has the same conservation properties as the continuous model. Additionally, we propose a new energy-stable advective flux scheme that is energy-conserving in smooth regions of the flow and strictly dissipative where sharp gradients appear. This is obtained by combining, using flux limiters, a previously developed energy-conserving advective flux with a novel first-order upwind scheme that is shown to be strictly dissipative. The complete framework, with diffusion, surface tension, and a bounded energy, is linearly stable to short wavelength perturbations, and exhibits nonlinear damping near shocks. The model yields smoothly converging numerical solutions, even under conditions for which the basic two-fluid model is ill-posed. With our explicit expressions for the dissipation rates, we are able to attribute the nonlinear damping to the different dissipation mechanisms, and compare their effects.
Original language | English |
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Article number | 104756 |
Number of pages | 22 |
Journal | International Journal of Multiphase Flow |
Volume | 174 |
DOIs | |
Publication status | Published - 2024 |
Funding
This work was supported by the research program Shell-NWO/FOM Computational Sciences for Energy Research (CSER), project number 15CSER017, which is partly financed by the Dutch Research Council (NWO).Keywords
- Dissipation
- Energy conservation
- Energy-stable scheme
- Stability
- Surface tension
- Two-phase pipe flow