PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. Volume-of-fluid (VOF) methods are popular for the direct numerical simulation of time-dependent viscous incompressible flow of multiple liquids. As in any numerical method, however, it has its weaknesses, namely, for flows in which the capillary force is the dominant physical mechanism. The lack of convergence with spatial refinement, or convergence to a solution that is slightly different from the exact solution, has been documented in the literature. A well-known limiting case for this is the existence of spurious currents for the simulation of a spherical drop with zero initial velocity. These currents are present in all previous versions of VOF algorithms. In this paper, we develop an accurate representation of the body force due to surface tension, which effectively eliminates spurious currents. We call this algorithm PROST: parabolic reconstruction of surface tension. There are several components to this procedure, including the new body force algorithm, improvements in the projection method for the Navier-Stokes solver, and a higher order interface advection scheme. The curvature to the interface is calculated from an optimal fit for a quadratic approximation to the interface over groups of cells.

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  1. Estivalezes, J.-L.; Aniszewski, W.; Auguste, F.; Ling, Y.; Osmar, L.; Caltagirone, J.-P.; Chirco, L.; Pedrono, A.; Popinet, S.; Berlemont, A.; Magnaudet, J.; Ménard, T.; Vincent, S.; Zaleski, S.: A phase inversion benchmark for multiscale multiphase flows (2022)
  2. Larios-Cárdenas, Luis Ángel; Gibou, Frédéric: A hybrid inference system for improved curvature estimation in the level-set method using machine learning (2022)
  3. Mostafaiyan, Mehdi; Wießner, Sven; Heinrich, Gert: Moving least-squares aided finite element method (MLS-FEM): a powerful means to consider simultaneously velocity and pressure discontinuities of multi-phase flow fields (2022)
  4. Zhang, Bo; Boyd, Bradley; Ling, Yue: Direct numerical simulation of compressible interfacial multiphase flows using a mass-momentum-energy consistent volume-of-fluid method (2022)
  5. Han, Tian-Yang; Zhang, Jie; Tan, Hua; Ni, Ming-Jiu: A consistent and parallelized height function based scheme for applying contact angle to 3D volume-of-fluid simulations (2021)
  6. Jiang, D.; Ling, Y.: Impact of inlet gas turbulence on the formation, development and breakup of interfacial waves in a two-phase mixing layer (2021)
  7. Kumar, Ronit; Cheng, Lidong; Xiong, Yunong; Xie, Bin; Abgrall, Rémi; Xiao, Feng: THINC scaling method that bridges VOF and level set schemes (2021)
  8. Larios-Cárdenas, Luis Ángel; Gibou, Frederic: A deep learning approach for the computation of curvature in the level-set method (2021)
  9. Mohan, Ananthan; Tomar, Gaurav: Interface reconstruction and advection schemes for volume of fluid method in axisymmetric coordinates (2021)
  10. Vachaparambil, Kurian J.; Einarsrud, Kristian Etienne: Numerical simulation of continuum scale electrochemical hydrogen bubble evolution (2021)
  11. Agnese, Marco; Nürnberg, Robert: Fitted front tracking methods for two-phase ncompressible Navier-Stokes flow: Eulerian and ALE finite element discretizations (2020)
  12. Cheng, Zekang; Li, Jie; Loh, Ching Y.; Luo, Li-Shi: An exactly force-balanced boundary-conforming arbitrary-Lagrangian-Eulerian method for interfacial dynamics (2020)
  13. Corot, T.; Hoch, P.; Labourasse, E.: Surface tension for compressible fluids in ALE framework (2020)
  14. Das, Pratik; Udaykumar, H. S.: A sharp-interface method for the simulation of shock-induced vaporization of droplets (2020)
  15. Fagbemi, Samuel; Tahmasebi, Pejman; Piri, Mohammad: Elastocapillarity modeling of multiphase flow-induced solid deformation using volume of fluid method (2020)
  16. Gu, Zhenghua; Yao, Yuan; Yu, Ching-Hao; An, Ruidong: Development of a volume of fluid method for computing interfacial incompressible fluid flows (2020)
  17. Howard, Amanda A.; Tartakovsky, Alexandre M.: Non-local model for surface tension in fluid-fluid simulations (2020)
  18. Ilangakoon, Niran A.; Malan, Arnaud G.; Jones, Bevan W. S.: A higher-order accurate surface tension modelling volume-of-fluid scheme for 2D curvilinear meshes (2020)
  19. Marić, Tomislav; Kothe, Douglas B.; Bothe, Dieter: Unstructured un-split geometrical volume-of-fluid methods - a review (2020)
  20. Ngo, Long Cu; Choi, Hyoung Gwon: A multi-level adaptive mesh refinement for an integrated finite element/level set formulation to simulate multiphase flows with surface tension (2020)

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