EFFICIENT IMPLEMENTATION OF A COUPLED LEVEL-SET AND VOLUME-OF-FLUID METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE TWO-PHASE FLOWS

A level-set method is combined with the volume-of-fluid method for computing incompressible two-phase flows in three dimensions, where the interface configurations are much more diverse and complicated. For efficient implementation of the coupled method, we propose geometric formulations necessary for interface reconstruction, advection of the volume fraction, and reinitialization of the level-set function. The calculation procedures are based on an explicit relation between the interface configuration and the volume fraction. This allows us to reduce the number of iterations required for reconstructing the interface. The coupled method is applied for computations of bubbles rising in a liquid and droplets adhering to a vertical wall.

[1]  Gihun Son.  A NUMERICAL METHOD FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH OPEN OR PERIODIC BOUNDARIES , 2001 .

[2]  Nahmkeon Hur,et al.  A COUPLED LEVEL SET AND VOLUME-OF-FLUID METHOD FOR THE BUOYANCY-DRIVEN MOTION OF FLUID PARTICLES , 2002 .

[3]  E. Puckett,et al.  A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows , 1997 .

[4]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[5]  A. Marmur.  Contact-angle hysteresis on heterogeneous smooth surfaces: theoretical comparison of the captive bubble and drop methods , 1998 .

[6]  L YoungsD,et al.  Time-dependent multi-material flow with large fluid distortion. , 1982 .

[7]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[8]  Takashi Yabe,et al.  A universal solver for hyperbolic equations by cubic-polynomial interpolation. II, Two- and three-dimensional solvers , 1991 .

[9]  L. G. Leal,et al.  Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid , 1984, Journal of Fluid Mechanics.

[10]  J. Brock,et al.  Volume tracking of interfaces having surface tension in two and three dimensions , 1996 .

[11]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[12]  S. Osher,et al.  An improved level set method for incompressible two-phase flows , 1998 .

[13]  J. Higdon,et al.  On the gravitational displacement of three-dimensional fluid droplets from inclined solid surfaces , 1999, Journal of Fluid Mechanics.

[14]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[15]  G. Son.  A Numerical Method for Bubble Motion with Phase Change , 2001 .

[16]  Takashi Yabe,et al.  A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver , 1991 .

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

[18]  L. G. Leal,et al.  Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique , 1984, Journal of Fluid Mechanics.

[19]  S. Zaleski,et al.  Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows , 1999 .

[20]  M. Rudman.  INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 24, 671–691 (1997) VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS , 2022 .

[21]  H. Takewaki,et al.  The cubic-interpolated Pseudo particle (cip) method: application to nonlinear and multi-dimensional hyperbolic equations , 1987 .

[22]  Philip M. Gresho,et al.  On the theory of semi‐implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory , 1990 .