SIMPLE, ACCURATE TREATMENT OF CURVED BOUNDARIES WITH DIRICHLET AND NEUMANN CONDITIONS

REFERENCES

• Jung , J. Y. 2000 . Numerical Simulation of Alloy Solidification , Ann Arbor, MI : University of Michigan . Ph.D. thesis
   Google Scholar
• Jung , J. Y. and Chen , M. M. 2003 . A Second-Order Front-Tracking Method for Phase Change Computations . in preparation
   Google Scholar
• Lee , H. and Chen , M. M. An Efficient Method for Flow Computations for Bodies with Curved Boundaries . Proc. IMECE 2002, ASME Int. Mechanical Engineering Congress & Exposition . November 17–22 , New Orleans, LA.
   Google Scholar
• Lee , H. and Chen , M. M. Higher Order Computations of the Convection-Diffusion Equation with Curved Boundaries . Proc. IMECE 2003, ASME Int. Mechanical Engineering Congress & Exposition . November 16–22 , Washington, DC.
   Google Scholar
• Davies , A. M. and Stephens , C. V. 1983 . Comparison of the Finite Difference and Galerkin Methods as Applied to the Solution of the Hyrodynamic Equations . Appl. Math. Model. , 7 : 226 – 240 .
   Web of Science ®Google Scholar
• Ferziger , J. H. and Perić , M. 1996 . Computational Methods for Fluid Mechanics , Berlin : Springer-Verlag .
   Google Scholar
• Fletcher , C. A. J. 1991 . Computational Techniques for Fluid Mechanics, Vol. II, Specific Techniques for Different Flow Categories , Berlin : Springer-Verlag .
   Google Scholar
• Thompson , F. C. , Thames , J. F. and Mastin , C. W. 1974 . Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate System for Field Containing Any Number of Arbitrary Two-Dimensional Bodies . J. Comput. Phys. , 15 : 299 – 319 .
   Web of Science ®Google Scholar
• Patera , A. T. and Spectral , A . 1984 . Element Method for Fluid Dynamics: Laminar Flow in a Channel Expansion . J. Comput. Phys. , 54 : 468 – 488 .
   Web of Science ®Google Scholar
• Karniadakis , G. E. and Henderson , R. D. 1998 . “ Spectral Element Methods for Incompressible Flows ” . In The handbook of Fluid Mechanics , 29.1 – 29.41 . Boca Raton, FL : CRC Press .
   Google Scholar
• Pan , D. and Cheng , J. C. 1993 . A 2nd-order upwind Finite-Volume Method for the Euler Solution on Unstructured Triangular Meshes . Int. J. Numer. Meth. Fluids , 16 ( 12 ) : 1079 – 1098 .
   Web of Science ®Google Scholar
• Peskin , C. S. 1977 . Numerical Analysis of Flow in the Heart . J. Comput. Phys. , 25 : 220
   Web of Science ®Google Scholar
• Fadlun , E. A. , Verzicco , R. , Orlandi , P. and Mohd-Yusof , J. 2000 . Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulation . J. Comput. Phys. , 161 : 35 – 60 .
   Web of Science ®Google Scholar
• Unverdi , S. O. , Tryggvason , G. and Front-Tracking , A . 1992 . Method for Viscous, Incompressible, Multi-fluid Flows . J. Comput. Phys. , 100 : 25 – 37 .
   Web of Science ®Google Scholar
• Juric , D. , Tryggvason , G. and Front-Tracking , A . 1996 . Method for Dendritic Solidification . J. Comput. Phys. , 123 : 127 – 148 .
   Web of Science ®Google Scholar
• Clarke , D. K. , Salas , M. D. and Hassan , H. A. 1986 . Euler Calculation for Multielement Airfoils Using Cartesian Grids . AIAA. J. , 24 ( 3 ) : 353 – 358 .
   Google Scholar
• Quirk , J. J. 1994 . An Alternative to Unstructured Grids for Computing Fast Dynamic Flows around Arbitrarily Complex Two-Dimensional Bodies . Comput. Fluids , 23 ( 1 ) : 125 – 142 .
   Web of Science ®Google Scholar
• Pember , R. B. , Bell , J. B. , Colella , P. , Crutchfield , W. Y. and Welcome , M. L. 1995 . An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions . J. Comput. Phys. , 120 : 278 – 304 .
   Web of Science ®Google Scholar
• Yang , G. , Causon , D. M. , Ingram , D. M. , Saunders , R. and Batten , P. 1997 . A Cartesian Cut Cell Method for Compressible Flows Part A: Static Body Problems . Aeronaut. J. , 101 : 47 – 56 .
   Web of Science ®Google Scholar
• Yang , G. , Causon , D. M. , Ingram , D. M. , Saunders , R. and Batten , P. 1997 . A Cartesian Cut Cell Method for Compressible Flows Part B: Moving Body Problems . Aeronaut. J. , 101 : 57 – 65 .
   Web of Science ®Google Scholar
• Tucker , P. G. , Pan , Z. and Cartesian , A . 2000 . Cut Cell Method for Incompressible Viscous Flow . Appl. Math. Model. , 24 : 591 – 606 .
   Web of Science ®Google Scholar
• Ye , T. , Mittal , R. , Udaykumar , H. S. and Shyy , W. 1999 . An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries . J. Comput. Phys. , 156 : 209 – 240 .
   Web of Science ®Google Scholar
• Osher , S. and Sethian , J. A. 1988 . Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations . J. Comput. Phys. , 79
   Web of Science ®Google Scholar
• Incropera , F. P. and DeWitt , D. P. 1996 . Introduction to Heat Transfer , 3d ed. , New York : Wiley .
   Google Scholar
• Lee , H. 2003 . A Simple and Accurate Method for Incompressible Flow Computations , Ann Arbor, MI : University of Michigan . Ph.D. thesis
   Google Scholar