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. 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)
  2. Zheng, Ping; Zhao, Liang: Correcting interface turbulence viscosity using CFD modeling for predicting stratified gas-liquid flow shear stress in horizontal pipes (2020)
  3. Gómez, Pablo; Zanzi, Claudio; López, Joaquín; Hernández, Julio: Simulation of high density ratio interfacial flows on cell vertex/edge-based staggered octree grids with second-order discretization at irregular nodes (2019)
  4. Guo, Ruchi; Lin, Tao: A higher degree immersed finite element method based on a Cauchy extension for elliptic interface problems (2019)
  5. 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)
  6. 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)
  7. Aboukhedr, M.; Georgoulas, A.; Marengo, M.; Gavaises, M.; Vogiatzaki, K.: Simulation of micro-flow dynamics at low capillary numbers using adaptive interface compression (2018)
  8. Abu-Al-Saud, Moataz O.; Popinet, Stéphane; Tchelepi, Hamdi A.: A conservative and well-balanced surface tension model (2018)
  9. Anumolu, Lakshman; Trujillo, Mario F.: Gradient augmented level set method for phase change simulations (2018)
  10. Cifani, P.; Kuerten, J. G. M.; Geurts, B. J.: Highly scalable DNS solver for turbulent bubble-laden channel flow (2018)
  11. Gibou, Frederic; Fedkiw, Ronald; Osher, Stanley: A review of level-set methods and some recent applications (2018)
  12. Patel, H. V.; Kuipers, J. A. M.; Peters, E. A. J. F.: Computing interface curvature from volume fractions: a hybrid approach (2018)
  13. 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)
  14. Wang, Zhibin; Li, Shuzhe; Chen, Rong; Zhu, Xun; Liao, Qiang; Ye, Dingding; Zhang, Biao: Numerical study on dynamic behaviors of the coalescence between the advancing liquid meniscus and multi-droplets in a microchannel using CLSVOF method (2018)
  15. Denner, Fabian; Evrard, Fabien; Serfaty, Ricardo; van Wachem, Berend G. M.: Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension (2017)
  16. Evrard, Fabien; Denner, Fabian; van Wachem, Berend: Estimation of curvature from volume fractions using parabolic reconstruction on two-dimensional unstructured meshes (2017)
  17. Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.: A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension (2017)
  18. Hernandez, Franz H.; Rangel, Roger H.: Breakup of drops in simple shear flows with high-confinement geometry (2017)
  19. Marić, Tomislav: Lagrangian/Eulerian numerical methods for fluid interface advection on unstructured meshes (2017)
  20. Patel, Jitendra Kumar; Natarajan, Ganesh: A novel consistent and well-balanced algorithm for simulations of multiphase flows on unstructured grids (2017)

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