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. Barrett, John W.; Garcke, Harald; Nürnberg, Robert: A stable parametric finite element discretization of two-phase Navier-Stokes flow (2015)
  2. Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri: Cellwise conservative unsplit advection for the volume of fluid method (2015)
  3. Jemison, Matthew; Sussman, Mark; Shashkov, Mikhail: Filament capturing with the multimaterial moment-of-fluid method (2015)
  4. Mahady, Kyle; Afkhami, Shahriar; Kondic, Lou: A volume of fluid method for simulating fluid/fluid interfaces in contact with solid boundaries (2015)
  5. Owkes, Mark; Desjardins, Olivier: A mesh-decoupled height function method for computing interface curvature (2015)
  6. Denner, Fabian; van Wachem, Berend G.M.: Compressive VOF method with skewness correction to capture sharp interfaces on arbitrary meshes (2014)
  7. Ding, Hang; Yuan, Cheng-jun: On the diffuse interface method using a dual-resolution Cartesian grid (2014)
  8. Pino-Muñoz, Daniel; Bruchon, J.; Drapier, S.; Valdivieso, F.: Sintering at particle scale: an Eulerian computing framework to deal with strong topological and material discontinuities (2014)
  9. Yokoi, Kensuke: A density-scaled continuum surface force model within a balanced force formulation (2014)
  10. Barrett, John W.; Garcke, Harald; Nürnberg, Robert: Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow (2013)
  11. Gibou, Frédéric; Min, Chohong; Fedkiw, Ron: High resolution sharp computational methods for elliptic and parabolic problems in complex geometries (2013)
  12. Kumar, Himanshu; Alam, Sharf; Ahmad, Suhail: Surface tension with normal curvature in curved space-time (2013)
  13. Le Chenadec, Vincent; Pitsch, Heinz: A monotonicity preserving conservative sharp interface flow solver for high density ratio two-phase flows (2013)
  14. Le Chenadec, Vincent; Pitsch, Heinz: A 3D unsplit forward/backward volume-of-fluid approach and coupling to the level set method (2013)
  15. Li, Jie: An arbitrary Lagrangian Eulerian method for three-phase flows with triple junction points (2013)
  16. Puckett, Elbridge Gerry: Second-order accuracy of volume-of-fluid interface reconstruction algorithms. II: An improved constraint on the cell size (2013)
  17. Scarbolo, Luca; Molin, Dafne; Perlekar, Prasad; Sbragaglia, Mauro; Soldati, Alfredo; Toschi, Federico: Unified framework for a side-by-side comparison of different multicomponent algorithms: lattice Boltzmann vs. phase field model (2013)
  18. Ii, Satoshi; Sugiyama, Kazuyasu; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro; Xiao, Feng: An interface capturing method with a continuous function: The THINC method with multi-dimensional reconstruction (2012)
  19. Lee, Hyun Geun; Kim, Junseok: Regularized Dirac delta functions for phase field models (2012)
  20. Bhamidipati, Kanthi Latha; Didari, Sima; Bedell, Prince; Harris, Tequila A.L.: Wetting phenomena during processing of high-viscosity shear-thinning fluid (2011)

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