Accurate solution algorithms for incompressible multiphase flows

A number of advances in modeling multiphase incompressible flow are described. These advances include high-order Godunov projection methods, piecewise linear interface reconstruction and tracking and the continuum surface force model. Examples are given.

[1]  Francis H. Harlow,et al.  The Splash of a Liquid Drop , 1967 .

[2]  P. Colella.  A Direct Eulerian MUSCL Scheme for Gas Dynamics , 1985 .

[3]  J. U. Brackbill,et al.  The ringing instability in particle-in-cell calculations of low-speed flow , 1988 .

[4]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[5]  Eric Yu Tau.  A second-order projection method for the incompressible Navier-Stokes equations in arbitrary domains , 1994 .

[6]  B. J. Daly.  Numerical Study of Two Fluid Rayleigh‐Taylor Instability , 1967 .

[7]  Roger H. Rangel,et al.  NUMERICAL INVESTIGATION OF MICROPORE FORMATION DURING SUBSTRATE IMPACT OF MOLTEN DROPLETS IN PLASMA SPRAY PROCESSES , 1994 .

[8]  S. Zaleski,et al.  Modelling Merging and Fragmentation in Multiphase Flows with SURFER , 1994 .

[9]  H. Haj-Hariri,et al.  The effects of convection on the motion of deformable drops , 1994 .

[10]  P. Colella.  Multidimensional upwind methods for hyperbolic conservation laws , 1990 .

[11]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[12]  A. A. Amsden,et al.  A simplified MAC technique for incompressible fluid flow calculations , 1970 .

[13]  P. Wesseling.  An Introduction to Multigrid Methods , 1992 .

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

[15]  P. Colella,et al.  A second-order projection method for the incompressible navier-stokes equations , 1989 .

[16]  J. Hochstein,et al.  Marangoni Convection With a Curved and Deforming Free Surface in a Cavity , 1994 .

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

[18]  P. Woodward,et al.  SLIC (Simple Line Interface Calculation) , 1976 .

[19]  K. S. Holian,et al.  MESA: A 3-D computer code for armor/anti-armor applications , 1989 .

[20]  Kent G. Budge,et al.  Rhale: A 3-D Mmale Code For Unstructured Grids , 1993 .

[21]  John B. Bell,et al.  A projection method for combustion in the zero Mach number limit , 1993 .

[22]  A. A. Amsden,et al.  The SMAC method: A numerical technique for calculating incompressible fluid flow , 1970 .

[23]  Elbridge Gerry Puckett,et al.  A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics , 1991 .

[24]  William L. Briggs,et al.  A multigrid tutorial , 1987 .

[25]  A. Borhan,et al.  Effect of local property smearing on global variables: Implication for numerical simulations of multiphase flows , 1994 .

[26]  J. Bell,et al.  A Second-Order Projection Method for Variable- Density Flows* , 1992 .

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

[28]  C. Liu,et al.  An efficient multigrid scheme for elliptic equations with discontinuous coefficients , 1992 .

[29]  Mei-Lin Lai,et al.  A Projection Method for Reacting Flow in the Zero Mach Number Limit , 1994 .

[30]  Francis H. Harlow,et al.  PIC and its progeny , 1987 .

[31]  F. Harlow,et al.  Distortion of a Splashing Liquid Drop , 1967, Science.

[32]  Abraham M. Lenhoff,et al.  Dynamic breakup of liquid–liquid jets , 1994 .

[33]  John B. Bell,et al.  A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection , 1996, SIAM J. Sci. Comput..

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

[35]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[36]  F. Harlow,et al.  Liquid Waves by Computer , 1965, Science.

[37]  Francis H. Harlow,et al.  Numerical Study of Large‐Amplitude Free‐Surface Motions , 1966 .

[38]  D. B. Kothe,et al.  A comparison of interface tracking methods , 1995 .

[39]  William E. Pracht,et al.  Numerical Study of Density‐Current Surges , 1968 .

[40]  J. Marsden,et al.  A mathematical introduction to fluid mechanics , 1979 .

[41]  Gretar Tryggvason,et al.  Computations of multi-fluid flows , 1992 .

[42]  Osamu Tatebe,et al.  The multigrid preconditioned conjugate gradient method , 1993 .

[43]  Long Chen.  INTRODUCTION TO MULTIGRID METHODS , 2005 .

[44]  Joel C. W. Rogers,et al.  A numerical algorithm for hydrodynamic free boundary problems , 1993 .

[45]  D. B. Kothe,et al.  RIPPLE: A Computer Program for Incompressible Flows with Free Surfaces , 1991 .

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

[47]  J. Brackbill,et al.  Flip: A low-dissipation, particle-in-cell method for fluid flow , 1988 .

[48]  D. B. Kothe,et al.  RIPPLE: A NEW MODEL FOR INCOMPRESSIBLE FLOWS WITH FREE SURFACES , 1991 .

[49]  Francis H. Harlow,et al.  Hydrodynamic Problems Involving Large Fluid Distortions , 1957, JACM.