A Stable and Efficient Method for Treating Surface Tension in Incompressible Two-Phase Flow

A new approach based on volume preserving motion by mean curvature for treating surface tension in two-phase flows is introduced. Many numerical tests and a theoretical justification are included which provide evidence regarding the efficacy of the new approach. For many flows, which exhibit stiff surface tension effects, the new approach gives a factor of at least three and sometimes five or more speed-up for a given accuracy. The new method is easy to implement in the context of (1) level set methods, or coupled level set and volume-of-fluid methods, (2) complicated interfaces separating gas from liquid, and (3) three-dimensional axisymmetric, or fully three-dimensional adaptive mesh refinement.

[1]  T. Hou,et al.  Removing the stiffness from interfacial flows with surface tension , 1994 .

[2]  M. Sussman.  A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles , 2003 .

[3]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[4]  J. Hochstein,et al.  An implicit surface tension model , 1996 .

[5]  P. J. Slikkerveer,et al.  An implicit surface tension algorithm for Picard solvers of surface-tension-dominated free and moving boundary problems , 1996 .

[6]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[7]  P. Colella,et al.  Non-convex profile evolution in two dimensions using volume of fluids , 1997 .

[8]  S. Hysing,et al.  A new implicit surface tension implementation for interfacial flows , 2006 .

[9]  J. G. Hnat,et al.  Spherical cap bubbles and skirt formation , 1976 .

[10]  Paul Vigneaux,et al.  On stability condition for bifluid flows with surface tension: Application to microfluidics , 2008, J. Comput. Phys..

[11]  Mark Sussman,et al.  Improvements for calculating two-phase bubble and drop motion using an adaptive sharp interface method. , 2007 .

[12]  H. J.,et al.  Hydrodynamics , 1924, Nature.

[13]  Mark Sussman,et al.  A sharp interface method for incompressible two-phase flows , 2007, J. Comput. Phys..

[14]  Mark Sussman,et al.  A parallelized, adaptive algorithm for multiphase flows in general geometries , 2005 .

[15]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[16]  Ronald Fedkiw,et al.  A Boundary Condition Capturing Method for Multiphase Incompressible Flow , 2000, J. Sci. Comput..

[17]  Jonathan M. Cohen,et al.  Practical simulation of surface tension flows , 2004, SIGGRAPH '04.

[18]  J. Mostaghimi,et al.  A semi‐implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows , 2009 .

[19]  Mark Sussman,et al.  An Improved Sharp Interface Method for Viscoelastic and Viscous Two-Phase Flows , 2008, J. Sci. Comput..