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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  12. Jibben, Z.; Carlson, N. N.; Francois, M. M.: A paraboloid fitting technique for calculating curvature from piecewise-linear interface reconstructions on 3D unstructured meshes (2019)
  13. Ling, Y.; Fuster, D.; Tryggvason, G.; Zaleski, S.: A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability (2019)
  14. Wenzel, E. A.; Garrick, S. C.: A point-mass particle method for the simulation of immiscible multiphase flows on an Eulerian grid (2019)
  15. Zhang, Yu; Chandra, Anirban; Yang, Fan; Shams, Ehsan; Sahni, Onkar; Shephard, Mark; Oberai, Assad A.: A locally discontinuous ALE finite element formulation for compressible phase change problems (2019)
  16. Aboukhedr, M.; Georgoulas, A.; Marengo, M.; Gavaises, M.; Vogiatzaki, K.: Simulation of micro-flow dynamics at low capillary numbers using adaptive interface compression (2018)
  17. Abu-Al-Saud, Moataz O.; Popinet, Stéphane; Tchelepi, Hamdi A.: A conservative and well-balanced surface tension model (2018)
  18. Anumolu, Lakshman; Trujillo, Mario F.: Gradient augmented level set method for phase change simulations (2018)
  19. Cifani, P.; Kuerten, J. G. M.; Geurts, B. J.: Highly scalable DNS solver for turbulent bubble-laden channel flow (2018)
  20. Gibou, Frederic; Fedkiw, Ronald; Osher, Stanley: A review of level-set methods and some recent applications (2018)

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