ADAPTIVE UNSTRUCTURED GRID FOR THREE-DIMENSIONAL INTERFACE REPRESENTATION

References

• W. S. Shyy , H. S. Udaykumar , M. M. Rao , and R. W. Smith , Computational Fluid Dynamics with Moving Boundaries , Taylor & Francis , Washington , DC , 1996 ,
   Google Scholar
• J. M. Floryan and H. Rasmussen , Numerical Methods for Viscous Flows with Moving Boundaries . Appl, Mech. Rev. , vol 42 , pp. 323 – 341 . 1989 .
   Google Scholar
• S. Osher and J. Sethian , Fronts Propagating with Curvature Dependent Speed Algorithms Based on Hamilton-Jacobi Formulations , J. Comput. Phys. , vol. 79 , pp. 12 – 49 , 1988 .
   Web of Science ®Google Scholar
• J. A. Sethian , Numerical Algorithms for Propagating Interfaces Hamilton-Jacobi Equations and Conservation Laws , J. Diff, Geom. , vol. 31 , pp. 131 – 161 , 1990 .
   Google Scholar
• J. Zhu and J. Sethian , Projection Methods Coupled to Level Set Interface Techniques , J. Comput. Phys. , vol. 102 , pp. 128 – 138 , 1992 .
   Web of Science ®Google Scholar
• C. W. Hirt and B. D. Nichols , Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries , J. Comput. Phys. , vol. 39 , pp. 201 – 225 , 1981 .
   Web of Science ®Google Scholar
• N. Ashgriz and J. Y. Poo , FLAIR Flux Line-Segment Model for Advection and Interface Reconstruction , J. Comput. Phys. , vol. 93 , pp. 449 – 468 , 1991 .
   Web of Science ®Google Scholar
• F. H. Harlow and J. E. Welch , Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface , Phys. Fluids , vol. 8 , no. 12 , pp. 2182 – 2189 , 1965 .
   Web of Science ®Google Scholar
• S. O. Unverdi and G. Tryggvason , A Front Tracking Method for Viscous, Incompressible, Multi-Fluid Flows , J. Comput. Phys. , vol. 100 , pp. 25 – 37 , 1992 .
   Web of Science ®Google Scholar
• H. S. Udaykumar , W. S. Shyy , and M. M. Rao , ELAFINT A Mixed Eulerian-Lagrangian Method for Fluid Flows with Complex and Moving Boundaries , Int. J. Numer. Meth. Fluids , vol. 22 , no. 8 , pp. 691 – 712 , 1996 .
   Google Scholar
• P. H. Todd and R. J. Y. McLeod , Numerical Estimation of the Curvature of Surfaces , CAD , vol. 18 , no. 1 , pp. 33 – 37 , 1986 .
   Google Scholar
• A. Bowyer , Computing Dirichlet Tesselations , Comput. J. , vol. 24 , no. 2 , pp. 162 – 166 , 1981 .
   Web of Science ®Google Scholar
• D. F. Watson , Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , Comput. J. , vol. 24 , no. 2 , pp. 167 – 172 , 1981 .
   Web of Science ®Google Scholar
• L. P. Chew , Guaranteed-Quality Mesh Generation for Curved Surfaces , ACM Proc. 9th Annual Symp. Computational Geometry , New York , pp. 274 – 280 , 1993 .
   Google Scholar
• J. Ruppert , New and Simple Algorithm for Quality 2-Dimensional Mesh Generation , ACM Proc. 4th Annual ACM SLAM Symp. Discrete Algorithms , New York , pp. 83 – 92 , 1992 .
   Google Scholar
• R. Lohner and P. Parikh , Three-Dimensional Grid Generation by the Advancing Front Method , AIAA-95-1686-CP , 1995 .
   Google Scholar
• N. P. Weatherill , Delaunay Triangulation in Computational Fluid Dynamics , Comput. Math. Appl. , vol. 24 , no. 5/6 , pp. 129 – 150 , 1992 .
   Google Scholar
• L. Guibas and J. Stolfi , Primitives for the Manipulation of General Sub-Divisions and the Computation of Voronoi Diagrams , SIAM J. Stat. Comput. , vol. 9 , no. 1 , pp. 61 – 79 , 1985 .
   Google Scholar
• S. Rebay , Efficient Unstructured Mesh Generation by Means of Delaunay Triangulation and Bowyer-Watson Algorithm , J. Comput. Phys. , vol. 106 , pp. 125 – 138 , 1993 .
   Web of Science ®Google Scholar
• D. Holmes and D. Snyder , The Generation of Unstructured Triangular Meshes Using Delaunay Triangulation , Proc. 2nd Int. Conf. on Numerical Grid Generation in Computational Fluid Mechanics , Miami , FL , 1988 .
   Google Scholar
• K. Nakahashi and D. Sharov , Direct Surface Triangulation Using Advancing Front Method , AIAA-95-1686-CP , 1995 .
   Google Scholar
• M. J. Aftosmis , J. E. Melton , and M. J. Berger , Adaptation and Surface Modeling for Cartesian Mesh Methods , AIAA-95-1725-CP , 1995 .
   Google Scholar
• D. J. Struik , Lectures on Classical Differential Geometry , Addison-Wesley , Cambridge , MA , 1950 .
   Google Scholar
• T. J. Wellmore , An Introduction to Differential Geometry , Oxford University Press , Oxford , 1959 .
   Google Scholar
• Address correspondence to Professor Wei Shyy, Department of Aerospace Engineering, Mechanics, and Engineering Science, University of Florida, 231 Aerospace Building, Gainesville, FL 32611-6250, USA. E-mail: [email protected]
   Google Scholar