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. Anumolu, Lakshman; Trujillo, Mario F.: Gradient augmented level set method for phase change simulations (2018)
  2. Gibou, Frederic; Fedkiw, Ronald; Osher, Stanley: A review of level-set methods and some recent applications (2018)
  3. Shams, Mosayeb; Raeini, Ali Q.; Blunt, Martin J.; Bijeljic, Branko: A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method (2018)
  4. Evrard, Fabien; Denner, Fabian; van Wachem, Berend: Estimation of curvature from volume fractions using parabolic reconstruction on two-dimensional unstructured meshes (2017)
  5. Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.: A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension (2017)
  6. Patel, Jitendra Kumar; Natarajan, Ganesh: A novel consistent and well-balanced algorithm for simulations of multiphase flows on unstructured grids (2017)
  7. Xie, Bin; Xiao, Feng: Toward efficient and accurate interface capturing on arbitrary hybrid unstructured grids: the THINC method with quadratic surface representation and Gaussian quadrature (2017)
  8. Zhang, Qinghai: HFES: a height function method with explicit input and signed output for high-order estimations of curvature and unit vectors of planar curves (2017)
  9. Yokoi, Kensuke; Onishi, Ryo; Deng, Xiao-Long; Sussman, Mark: Density-scaled balanced continuum surface force model with a level set based curvature interpolation technique (2016)
  10. Abadie, T.; Aubin, J.; Legendre, D.: On the combined effects of surface tension force calculation and interface advection on spurious currents within volume of fluid and level set frameworks (2015)
  11. Barrett, John W.; Garcke, Harald; Nürnberg, Robert: A stable parametric finite element discretization of two-phase Navier-Stokes flow (2015)
  12. Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri: Cellwise conservative unsplit advection for the volume of fluid method (2015)
  13. Jemison, Matthew; Sussman, Mark; Shashkov, Mikhail: Filament capturing with the multimaterial moment-of-fluid method (2015)
  14. Mahady, Kyle; Afkhami, Shahriar; Kondic, Lou: A volume of fluid method for simulating fluid/fluid interfaces in contact with solid boundaries (2015)
  15. Owkes, Mark; Desjardins, Olivier: A mesh-decoupled height function method for computing interface curvature (2015)
  16. Denner, Fabian; van Wachem, Berend G.M.: Compressive VOF method with skewness correction to capture sharp interfaces on arbitrary meshes (2014)
  17. Ding, Hang; Yuan, Cheng-jun: On the diffuse interface method using a dual-resolution Cartesian grid (2014)
  18. 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)
  19. Yokoi, Kensuke: A density-scaled continuum surface force model within a balanced force formulation (2014)
  20. Barrett, John W.; Garcke, Harald; Nürnberg, Robert: Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow (2013)

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