Energy-stable discretization of the one-dimensional two-fluid model

J. F.H. Buist*, B. Sanderse, S. Dubinkina, C. W. Oosterlee, R. A.W.M. Henkes

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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 languageEnglish
Article number104756
Number of pages22
JournalInternational Journal of Multiphase Flow
Volume174
DOIs
Publication statusPublished - 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

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