A CURVILINEAR LEVEL SET FORMULATION FOR HIGHLY DEFORMABLE FREE SURFACE PROBLEMS WITH APPLICATION TO SOLIDIFICATION

A curvilinear level set formulation has been developed for highly deformable free surface problems. In this new scheme, the grid lines follow the irregular domain generated by the multizone adaptive grid-generation (MAGG) scheme [1] and free surfaces are captured by level set functions among the curvilinear grids. Navier-Stokes equations are discretized and solved based on a multiphase curvilinear finite-volume method [2], and the level set function is solved based on a finite-difference method using the second-order essentially nonoscillatory (ENO) scheme [3]. The scheme is capable of accurately and efficiently representing the deformation, oscillation, merger, and separation of free surfaces. The effectiveness and robustness of the algorithm are demonstrated by using it for problems involving merger of bubbles, mold filling, and the spreading and solidification of molten droplets on a cold substrate where both free surface and solidification interfaces move and the mass of the liquid phase is continuous...

[1]  A. A. Amsden,et al.  A numerical fluid dynamics calculation method for all flow speeds , 1971 .

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

[3]  J. H. Kim.  An analytical mixing model for buoyant jet injected into pipe flow , 1983 .

[4]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[5]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

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

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

[8]  M. K. Moallemi,et al.  Thermal Analysis of the Hot Dip-Coating Process , 1993 .

[9]  Wei Shyy,et al.  Computational Modeling for Fluid Flow and Interfacial Transport (Dover Books on Engineering) , 1993 .

[10]  Analytical and Numerical Modeling of the Dip-Coating Process , 1993 .

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

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

[13]  Roger H. Rangel,et al.  Modeling of molten droplet impingement on a non-flat surface , 1995 .

[14]  Hui Zhang,et al.  MAGG: a multizone adaptive grid-generation technique for simulation of moving and free boundary problems , 1995 .

[15]  Peter E. Raad,et al.  Velocity Boundary Conditions for the Simulation of Free Surface Fluid Flow , 1995 .

[16]  W. Rider,et al.  Stretching and tearing interface tracking methods , 1995 .

[17]  Thomas Y. Hou,et al.  Numerical Solutions to Free Boundary Problems , 1995, Acta Numerica.

[18]  Vishwanath Prasad,et al.  Numerical algorithm using multizone adaptive grid generation for multiphase transport processes with moving and free boundaries , 1996 .

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

[20]  Dimos Poulikakos,et al.  Heat transfer and fluid dynamics in the process of spray deposition , 1996 .

[21]  D. B. Kothe,et al.  High resolution finite volume parallel simulations of mould filling and binary alloy solidification on unstructured 3-D meshes , 1997 .

[22]  Three dimensional simulation of side jet thermal and flows mixing in nuclear cooling systems , 1997 .