Print Email Facebook Twitter Energy-stable discretization of the one-dimensional two-fluid model Title Energy-stable discretization of the one-dimensional two-fluid model Author Buist, J.F.H. (TU Delft Fluid Mechanics; Centrum Wiskunde & Informatica (CWI)) Sanderse, B. (Centrum Wiskunde & Informatica (CWI)) Dubinkina, S. (Vrije Universiteit Amsterdam) Oosterlee, C. W. (Universiteit Utrecht) Henkes, R.A.W.M. (TU Delft Fluid Mechanics) Date 2024 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. Subject DissipationEnergy conservationEnergy-stable schemeStabilitySurface tensionTwo-phase pipe flow To reference this document use: http://resolver.tudelft.nl/uuid:3d56ecc0-51f7-44c2-82fb-93562942298b DOI https://doi.org/10.1016/j.ijmultiphaseflow.2024.104756 ISSN 0301-9322 Source International Journal of Multiphase Flow, 174 Part of collection Institutional Repository Document type journal article Rights © 2024 J.F.H. Buist, B. Sanderse, S. Dubinkina, C. W. Oosterlee, R.A.W.M. Henkes Files PDF 1-s2.0-S0301932224000375-main.pdf 1.58 MB Close viewer /islandora/object/uuid:3d56ecc0-51f7-44c2-82fb-93562942298b/datastream/OBJ/view