A composite adaptive grid generation and migration technique for materials processing problems

SIAM Journal on Scientific Computing

Volumn 24, Issue 4, 2003, Pages 1175-1202

  Sahoo, R K ^a   Prasad, V ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b FLORIDA INTERNATIONAL UNIVERSITY   (United States)

Author keywords

Adaptive grid generation; Materials processing; Numerical methods; Variational methods

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; COMPUTER HARDWARE; COMPUTER SOFTWARE; CURVE FITTING; INTERFACES (COMPUTER); MATERIALS HANDLING; NUMERICAL METHODS; VARIATIONAL TECHNIQUES;

ADAPTIVE GRID GENERATION;

ADAPTIVE SYSTEMS;

EID: 0042379613     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501392235     Document Type: Article

References (55)

1. H. AKIMA, A new method of interpolation and smooth curve fitting based on local procedures, J. ACM, 17 (1970), pp. 589-602.
2. H. AKIMA, A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points, ACM Trans. Math. Software, 4 (1978), pp. 148-159.
3. H. AKIMA, A method of univariate interpolation that has the accuracy of a third degree polynomial, ACM Trans. Math. Software, 17 (1991), pp. 341-366.
4. H. AKIMA, Algorithm 760: Rectangular-grid-data surface fitting that has the accuracy of a bicubic polynomial, ACM Trans. Math. Software, 22 (1996), pp. 357-361.
5. H. AKIMA, Algorithm 761: Scattered-data surface fitting that has the accuracy of a cubic polynomial, ACM Trans. Math. Software, 22 (1996), pp. 362-371.
6. O. BAYSAL, K. FOULADI, AND V. R. LESSARD, A multigrid and upwind viscous flow solver on three-dimensional overlapped and embedded grids, AIAA J., 29 (1991), pp. 903-910.
7. O. BAYSAL AND G. W. YEN, Kinematic domain decomposition to simulate flow past moving objects, 29th Aerospace Science Meeting, AIAA paper 91-0725, 1991.
8. J. A. BENEK, J. L. STEGER, AND P. G. BUNING, A 3-D Chimera Grid Embedding Technique, AIAA paper 85-1523, 1985.
9. J. U. BRACKBILL AND J. S. SALTZMAN, Adaptive zoning for singular problems in two dimensions, J. Comput. Phys., 46 (1982), pp. 342-368.
10. A. A. CHARAKHCH'YAN AND S. A. IVANENKO, A variational form of the Winslow grid generator, J. Comput. Phys., 136 (1997) pp. 385-398.
11. G. CHESSHIRE AND W. D. HENSHAW, Composite overlapping meshes for the solution of partial differential equations, J. Comput. Phys., 90 (1990), pp. 1-64.
12. P. DARIPA, A new theory for one-dimensional adaptive grid generation and its applications, SIAM J. Numer. Anal., 28 (1991), pp. 1635-1660.
13. D. L. DAVIS AND H. D. THOMPSON, The Impact of Computational Zone Interfacing on Calculated Scramjet Performance, AIAA paper 92-0390, 1992.
14. I. DEMIRDZIC AND M. PERIC, Finite volume methods for prediction of fluid flow in arbitrary shaped domains with moving boundaries, Internat. J. Numer. Methods Fluids, 10 (1990), pp. 771-790.
15. E. P. DEUQUE, R. BISWAS, AND R. C. STRAWN, A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Application to Helicoptor Rotor Flows, in Proceedings of the 13th Applied Aeronautics Conference, San Diego, AIAA 95-1766, 1995, pp. 13-21.
16. P. R. EISEMAN, Adaptive grid generation, Comput. Methods Appl. Mech. Engrg., 64 (1987), pp. 321-376.
17. J. H. FRIEDMAN, J. L. BENTLEY, AND R. A. FINKEL, An algorithm, for finding best matches in logarithmic expected time, ACM Trans. Math. Software, 3 (1977), pp. 209-226.
18. S. D. GILMORE AND S. I. GUCERI, Three dimensional solidification - A numerical approach, Num. Heat Trans., 89 (1988), pp. 673-707.
19. D. F. HAWKEN, J. J. GOTTLIEB, AND J. S. HANSEN, Review of some adaptive node-movement techniques in finite element and finite-difference solutions of partial differential equations, J. Comput. Phys., 95 (1991), pp. 254-302.
20. D. F. HAWKEN, Review of adaptive-grid techniques for solution of partial differential equations, Prog. Aerospace Sci., 24 (1987), pp. 29-49.
21. C. C. HSU AND C. L. LEE, On a zonal method for transonic turbulent flow past a wing fuselage configuration, in Proceedings of the International AIAA Congress, 1991, pp. 279-287.
22. K. H. KAO AND M. S. LIOU, Grid adaption using chimera composite overlapping meshes, AIAA J., 32 (1994) pp. 942-949.
23. H. J. KIM AND J. F. THOMPSON, Three-dimensional adaptive grid generation using parabolic partial differential equations, AIAA J., 28 (1990), pp. 470-477.
24. P. M. KNUPP AND S. STEINBERG, The Fundamentals of Grid Generation, CRC Press, Boca Raton, FL, 1994.
25. M. LACROIX, Analysis of mixed convection melting of a pure metal, Num. Heat Trans., 17 (1990), pp. 401-416.
26. M. LACROIX AND V. R. VOLLER, Finite difference solutions of solidification phase change problems: Transformed versus fixed grids, Num. Heat Trans., 17 (1990), pp. 25-41.
27. R. L. LIJEWSKI AND N. E. SUHS, Time-accurate computational fluid dynamics approach to transonic store separation trajectory prediction, J. Aircraft, 31 (1994), pp. 886-891.
28. V. D. LISEIKIN The construction of structured adaptive grids - A review, Comput. Math. Math. Phys., 36 (1996), pp. 1-32.
29. R. MEAKIN, On the spatial and temporal accuracy of overset grid methods for moving body problems, 12th AIAA Applied Aeronautics Conference, AIAA-94-1925, 1994, pp. 858-871.
30. Y. MOON AND M. S. LIOU, Conservative Treatment of Boundary Interfaces for Overlaid Grids and Multi-Level Grid Adaptions, AIAA paper 89-1980, 1989.
31. S. V. PATANKAR, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, New York, 1996.
32. C. Y. PERNG AND R. L. STREET, A coupled multigrid-domain splitting technique for simulating incompressible flows in geometrically complex domains, Internat. J. Numer. Methods Fluids, 13 (1991), pp. 269-286.
33. W. H. PRESS, S. A. TEUKOLSKY, W. T. VETTERLING, AND B. P. FLANNERY, Numerical Recipes in C, Cambridge University Press, New York, 1992.
34. W. H. PRESS, S. A. TEUKOLSKY, W. T. VETTERLING, AND B. P. FLANNERY, Numerical Recipes in FORTRAN, Cambridge University Press, New York, 1992.
35. M. M. RAI, A conservative treatment of zonal boundaries for Euler equation calculations, J. Comput. Phys., 62 (1986), pp. 472-503.
36. M. M. RAI, An implicit conservative zonal-boundary scheme for Euler equation calculations, Computers in Fluids, 14 (1986), pp. 295-319.
37. R. J. RENKA, Algorithm 751 tripack: A constrained two-dimensional Delaunay triangulation package, ACM Trans. Math. Software, 22 (1986), pp. 1-8.
38. D. F. ROGERS AND J. A. ADAMS, Mathematical Elements for Computer Graphics, McGraw-Hill, New York, 1990.
39. R. K. SAHOO, Composite Adaptive Grid Generation, Migration and Parallel Algorithms for Computational Materials Processing, Ph.D. dissertation, State University of New York, Stony Brook, NY, 1998.
40. R. K. SAHOO AND V. PRASAD, Application of composite adaptive grid generation and migration (CAGGM) scheme to phase-change materials processes, Num. Heat Trans., to appear.
41. J. SAHU AND C. J. NIETUBICZ, Application of chimera technique to projectiles in relative motion, J. Spacecraft Rockets, 32 (1995), pp. 795-800.
42. J. S. SALTZMAN Variational method for generating meshes on surfaces in three dimensions, J. Comput. Phys., 63 (1986), pp. 1-19.
43. W. SHYY, Computational modeling for fluid flow and interfacial transport, Elsevier Science, New York, 1993.
44. J. L. STEGER, F. C. DOUGHERTY, AND J. A. BENEK, A chimera grid scheme : Advances in grid generation, ASME Fluid Engrg. Conf., 5 (1983), pp. 9-69.
45. J. F. THOMPSON, Z. U. A. WARSI, AND C. W. MASTIN, Numerical Grid Generation, Elsevier Science, New York, 1985.
46. J. L. STEGER AND J. A. BENEK, On the use of composite grid schemes in computational aerodynamics, Comput. Methods Appl. Mech. Engrg., 64 (1987), pp. 301-320.
47. P. D. THOMAS AND J. F. MIDDLECOFF, Direct control of the grid point distribution in meshes generated by elliptic equations, AIAA J., 18 (1980), pp. 652-657.
48. J. F. THOMPSON, A general three-dimensional elliptic grid generation system on a composite block structure, Comput. Methods Appl. Mech. Engrg., 64 (1987) pp. 377-411.
49. J. F. THOMPSON AND J. H. FERZIGER, An adaptive multigrid technique for the incompressible Navier-Stokes equations, J. Comput. Phys., 82 (1989), pp. 94-121.
50. J. WRIGHT, A Pressure-Based Composite Grid Method for the Complex Fluid Flows, Ph.D. thesis, University of Florida, Gainesville, FL, 1992.
51. J. WRIGHT AND W. SHYY, A pressure-based composite grid method for the incompressible Navier-Stokes equations, J. Comput. Phys., 107 (1992), pp. 225-238.
52. S. C. YANG, Numerical Simulation of Transonic Flows over a Complex Configuration, Ph.D. thesis, University of Florida, Gainesville, FL, 1990.
53. G. H. YEOH, M. BEHNIA, G. DE VAHL DAVI, AND E. LEONARDI, A numerical study of three-dimensional natural convection during freezing of water, Internat. J. Numer. Methods. Engrg., 30 (1990), pp. 899-914.
54. H. ZHANG, A Multizone Adaptive Grid Generation Technique for Simulations of Moving and Free Boundary Problems, Ph.D. dissertation, Polytechnic University, Brooklyn, NY, 1993.
55. H. ZHANG AND M. K. MOALLEMI, A multizone adaptive grid generation technique for simulation of moving and free boundary problems, Num. Heat Trans., 27 B (1995), pp. 255-276.