Numerical Simulation of Three Dimensional Free Surface Flows with Bubbles

A numerical model is presented for the simulation of free surface flows. The unknowns are the volume fraction of liquid, the velocity and pressure in the liquid and the pressure in the bubbles of gas which can appear in the liquid flow.

[1]  Hong Wang,et al.  An ELLAM Scheme for Advection-Diffusion Equations in Two Dimensions , 1999, SIAM J. Sci. Comput..

[2]  J. C. Martin An experimental study of the collapse of liquid column on a rigid horizontal plane , 1952 .

[3]  A. Chorin Flame advection and propagation algorithms , 1980 .

[4]  D. M. Gao,et al.  A finite element simulation of metal flow in moulds , 1990 .

[5]  C. K. Thornhill,et al.  Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , 1952, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[6]  J. Rappaz,et al.  Numerical simulation of three‐dimensional free surface flows , 2003 .

[7]  M. Renardy,et al.  PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method , 2002 .

[8]  Eugenio Oñate,et al.  Mould filling simulation using finite elements , 1994 .

[9]  Peter Hansbo,et al.  The characteristic streamline diffusion method for the time-dependent incompressible Navier-Stokes equations , 1992 .

[10]  Randall J. LeVeque,et al.  Two-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods , 1996 .

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

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

[13]  M. Jaeger,et al.  NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS WITH MOVING INTERFACES , 1997 .

[14]  Marc Medale,et al.  Local mesh adaptation technique for front tracking problems , 1998 .

[15]  Vincent Maronnier Simulation numérique d'écoulements de fluides incompressibles avec surface libre , 2000 .

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

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

[18]  L. Quartapelle The incompressible Navier—Stokes equations , 1993 .

[19]  P. Colella,et al.  An Adaptive Level Set Approach for Incompressible Two-Phase Flows , 1997 .

[20]  L. Franca,et al.  Stabilized finite element methods. II: The incompressible Navier-Stokes equations , 1992 .

[21]  M. Chaudhry,et al.  Numerical Simulation of Free-Surface Flows , 1998 .

[22]  G. P. Boerstoel,et al.  The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces , 2000 .

[23]  T. Hughes,et al.  Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations , 1993 .

[24]  Thierry Coupez,et al.  Lagrangian finite‐element analysis of time‐dependent viscous free‐surface flow using an automatic remeshing technique: Application to metal casting flow , 1993 .

[25]  O. Pironneau,et al.  Characteristic-Galerkin and Galerkin/least-squares space-time formulations for the advection-diffusion equation with time-dependent domains , 1992 .

[26]  J. Rappaz,et al.  Stability of time‐splitting schemes for the Stokes problem with stabilized finite elements , 2001 .

[27]  L. Franca,et al.  Stabilized Finite Element Methods , 1993 .

[28]  J. Rappaz,et al.  Regular Article: Numerical Simulation of Free Surface Flows , 1999 .

[29]  Peter Hansbo Lagrangian incompressible flow computations in three dimensions by use of space‐time finite elements , 1995 .

[30]  S. Mittal,et al.  Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements , 1992 .

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

[32]  Farzad Mashayek,et al.  A hybrid finite‐element–volume‐of‐fluid method for simulating free surface flows and interfaces , 1995 .

[33]  Erik G. Thompson,et al.  Use of pseudo‐concentrations to follow creeping viscous flows during transient analysis , 1986 .

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

[35]  O. Pironneau Finite Element Methods for Fluids , 1990 .