COMPUTATION OF INTERNAL FLOW WITH FREE SURFACES USING ARTIFICIAL COMPRESSIBILITY

In this article an upwind flux-differencing scheme using artificial compressibility is generalized to allow time-accurate computation of incompressible flows on a dynamic grid system. By treating the free surface as a moving grid line that connects in a Lagrangian fashion, the scheme can be applied to solve a variety of free surface flows of moderate surface deformation. The surface tension effects can also be included using a source term and via boundary condition.

[1]  M. Vinokur,et al.  An analysis of finite-difference and finite-volume formulations of conservation laws , 1986 .

[2]  J. Sheu,et al.  NUMERICAL COMPUTATION OF THERMOCAPILLARY CONVECTION IN A RECTANGULAR CAVITY , 1990 .

[3]  S. H. Davis,et al.  Steady thermocapillary flows in two-dimensional slots , 1982, Journal of Fluid Mechanics.

[4]  A. R. Paterson A first course in fluid dynamics , 1983 .

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

[6]  C. Cuvelier,et al.  Thermocapillary free boundaries in crystal growth , 1986, Journal of Fluid Mechanics.

[7]  D. Pan,et al.  Upwind finite-volume method for natural and forced convection , 1994 .

[8]  T. Pulliam,et al.  A diagonal form of an implicit approximate-factorization algorithm , 1981 .

[9]  Antony Jameson,et al.  Fast multigrid method for solving incompressible hydrodynamic problems with free surfaces , 1993 .

[10]  Balasubramaniam Ramaswamy,et al.  Numerical simulation of unsteady viscous free surface flow , 1990 .

[11]  M. Kawahara,et al.  LAGRANGIAN FINITE ELEMENT ANALYSIS APPLIED TO VISCOUS FREE SURFACE FLUID FLOW , 1987 .

[12]  M. F. Tomé,et al.  GENSMAC: a computational marker and cell method for free surface flows in general domains , 1994 .

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

[14]  M. Ikehata,et al.  Computation of free surface waves around an arbitrary body by a Navier‐Stokes solver using the psuedocompressibility technique , 1994 .

[15]  Jerzy M. Floryan,et al.  Numerical Methods for Viscous Flows With Moving Boundaries , 1989 .

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