A numerical method for three-dimensional gas-liquid flow computations

A numerical method for multiphase flow computations based on a finite-difference formulation with a fixed grid is described. The method combines ideas from front tracking and the Ghost Fluid Method, with a numerical technique for velocity extrapolation near the interface. It is shown that the method is able to solve three-dimensional free-surface flow problems with an incompressible liquid and a compressible gas maintaining the interface sharp. Numerical results are compared with numerical solutions of the Rayleigh Plesset equation for the free oscillation of a gas bubble, and independent front-tracking results for buoyant bubbles. Finally, the effects of an imposed sinusoidal liquid flow on a gas bubble are investigated.

[1]  Gretar Tryggvason,et al.  Computations of multiphase flows by a finite difference/front tracking method. I. Multi-fluid flows , 1998 .

[2]  Howard H. Hu.  Direct simulation of flows of solid-liquid mixtures , 1996 .

[3]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[4]  Ronald Fedkiw,et al.  Regular Article: The Ghost Fluid Method for Deflagration and Detonation Discontinuities , 1999 .

[5]  Peter Smereka,et al.  Axisymmetric free boundary problems , 1997, Journal of Fluid Mechanics.

[6]  D. Juric,et al.  A front-tracking method for the computations of multiphase flow , 2001 .

[7]  A. Prosperetti,et al.  Bubble Dynamics and Cavitation , 1977 .

[8]  Marek Behr,et al.  Enhanced-Discretization Interface-Capturing Technique (EDICT) for computation of unsteady flows with interfaces , 1998 .

[9]  Ivan B. Bazhlekov,et al.  Interaction of a deformable bubble with a rigid wall at moderate Reynolds numbers , 1990, Journal of Fluid Mechanics.

[10]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[11]  Daniel D. Joseph,et al.  Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows , 1994, Journal of Fluid Mechanics.

[12]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[13]  A. Chorin.  Numerical Solution of the Navier-Stokes Equations* , 1989 .

[14]  Andrea Prosperetti,et al.  Navier-Stokes Numerical Algorithms for Free-Surface Flow Computations: An Overview , 2002 .

[15]  James Glimm,et al.  Subgrid resolution of fluid discontinuities, II , 1980 .

[16]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[17]  Dimos Poulikakos,et al.  Wetting effects on the spreading of a liquid droplet colliding with a flat surface: Experiment and modeling , 1995 .

[18]  James J. Feng,et al.  Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation , 1994, Journal of Fluid Mechanics.

[19]  A. Szeri,et al.  Shape stability of unsteadily translating bubbles , 2002 .

[20]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[21]  Melvyn W. Jeter.  Mathematical Programming: An Introduction to Optimization , 1986 .

[22]  R. Fedkiw,et al.  A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains , 2000 .

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

[24]  R. Fedkiw,et al.  A numerical method for two-phase flow consisting of separate compressible and incompressible regions , 2000 .

[25]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[26]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[27]  Stéphane Popinet,et al.  Bubble collapse near a solid boundary: a numerical study of the influence of viscosity , 2002, Journal of Fluid Mechanics.

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

[29]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[30]  J. Glimm,et al.  A critical analysis of Rayleigh-Taylor growth rates , 2001 .

[31]  Charles S. Peskin,et al.  Improved Volume Conservation in the Computation of Flows with Immersed Elastic Boundaries , 1993 .

[32]  T. Brooke Benjamin,et al.  Self-propulsion of asymmetrically vibrating bubbles , 1990, Journal of Fluid Mechanics.

[33]  Andrea Prosperetti,et al.  The Dynamics of Vapor Bubbles in Acoustic Pressure Fields , 1999 .

[34]  L. G. Leal,et al.  Translational instability of a bubble undergoing shape oscillations , 1995 .