Iterative domain decomposition meshless method modeling of incompressible viscous flows and conjugate heat transfer

Engineering Analysis with Boundary Elements

Volumn 30, Issue 6, 2006, Pages 465-478

  Divo, Eduardo ^a   Kassab, Alain ^b  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

^b University of Central Florida   (United States)

Author keywords

Conjugate heat transfer; Meshless methods; Parallel computing

Indexed keywords

FINITE ELEMENT METHOD; HEAT TRANSFER; INTERPOLATION; PARALLEL PROCESSING SYSTEMS; RADIAL BASIS FUNCTION NETWORKS; VISCOUS FLOW;

CONDUCTING SOLIDS; CONJUGATE HEAT TRANSFER; HELMHOLTZ POTENTIAL; MESHLESS METHODS;

ITERATIVE METHODS;

EID: 33646769608     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2006.02.002     Document Type: Article

References (30)

1. Belytscho T., Lu Y.Y., and Gu L. Element-free Galerkin methods. Int J Numer Methods 37 (1994) 229-256
2. Atluri S.N., and Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 22 (1998) 117-127
3. Melenk J.M., and Babuska I. The partition of unity finite element method: basic theory and application. Comput Meth Appl Mech Eng 139 (1996) 289-316
4. Kansa E.J. Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics I-surface approximations and partial derivative estimates. Comput Math Appl 19 (1990) 127-145
5. Kansa E.J. Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics II-solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 19 (1990) 147-161
6. Kansa E.J., and Hon Y.C. Circumventing the Ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput Math Appl 39 (2000) 123-137
7. Franke R. Scattered data interpolation: test of some methods. Math Comput 38 (1982) 181-200
8. Mai-Duy N., and Tran-Cong T. Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of poisson's equation. Eng Anal Bound Elem 26 (2002) 133-156
9. Cheng A.H.-D., Golberg M.A., Kansa E.J., and Zammito G. Exponential convergence and H-c multiquadric collocation method for partial differential equations. Numer Meth. PDE 19 5 (2003) 571-594
10. Gottlieb D., and Orzag S.A. Numerical analysis of spectral methods: theory and applications (1977), Society for Industrial and Applied Mathematics, Bristol, England
11. Maday Y., and Quateroni A. Spectral and pseudo-spectral approximations of the Navier-Stokes equations. SIAM J Numer Anal 19 4 (1982) 761-780
12. Patera A. A spectral element method of fluid dynamics: laminar flow in a channel expansion. J Comput Phys 54 (1984) 468-488
13. Macaraeg M., and Street C.L. Improvement in spectral collocation discretization through a multiple domain technique. Appl Numer Math 2 (1986) 95-108
14. Hwar C.K., Hirsch R., Taylor T., and Rosenberg A.P. A pseudo-spectral matrix element method for solution of three-dimensional incompressible flows and its parallel implementation. J Comput Phys 83 (1989) 260-291
15. Powell M.J.D. The theory of radial basis function approximation. In: Light W. (Ed). Advances in numerical analysis vol. II (1992), Oxford Science Publications, Oxford 143-167
16. Dyn N., Levin D., and Rippa S. Numerical procedures for surface fitting of scattered data by radial basis functions. SIAM J Sci Stat Comput 7 2 (1986) 639-659
17. Brebbia C.A., Partridge P., and Wrobel L.C. The dual reciprocity boundary element method (1992), Computational Mechanics and Elsevier, Southampton, UK
18. Golberg M., Chen C.S., and Bowman H. Some recent results and proposals for the use of radial basis functions in the BEM. Eng Anal Bound Elem 23 (1999) 285-296
19. Rahaim C.P., and Kassab A.J. Pressure correction DRBEM solution for heat transfer and fluid flow in incompressible viscous fluids. Eng Anal Bound Elem 18 4 (1996) 265-272
20. Hardy RL. Multiquadric equations of topography and other irregular surfaces. J Geophys Res 176:1905-15.
21. Kassab A., Divo E., Heidmann J., Steinthorsson E., and Rodriguez F. BEM/FVM conjugate heat transfer analysis of a three-dimensional film cooled turbine blade. Int J Numer Meth Heat Fluid Flow 13 5 (2003) 581-610
22. In: Kassab A.J., and Aliabadi M.H. (Eds). Advances in boundary elements: coupled field problems (2001), WIT Press, Southampton
23. Rahaim C.P., Kassab A.J., and Cavalleri R. A coupled dual reciprocity boundary element/finite volume method for transient conjugate heat transfer. AIAA J Thermophys Heat Transfer 14 1 (2000) 27-38
24. He M., Bishop P., Kassab A.J., and Minardi A. A coupled FDM/BEM solution for the conjugate heat transfer problem. Numer Heat Transfer Part B Fundam 28 2 (1995) 139-154
25. Li H, Kassab AJ. A coupled FVM/BEM solution to conjugate heat transfer in turbine blades. AIAA Paper 94-1981, presented at the AIAA/ASME sixth joint thermophysics conference, Colorado Springs, Colorado; June 20-23, 1994.
26. Divo E.A., Kassab A.J., and Rodriguez F. Parallel domain decomposition approach for large-scale 3d boundary element models in linear and non-linear heat conduction. Numer Heat Transfer Part B Fundam 44 5 (2003) 417-437
27. Divo E, Kassab AJ, Mitteff E, Quintana L. A parallel domain decomposition technique for meshless methods applications to large-scale heat transfer problems. ASME Paper: HT-FED2004-56004.
28. Divo E., and Kassab A.J. A meshless method for conjugate heat transfer problems. Eng Anal 29 2 (2005) 136-149
29. Harlow F.H., and Welch J.E. Numerical calculation of time dependent viscous incompressible flow of fluids with a free surface. Phys Fluids 8 (1965) 2182-2189
30. Patankar S.V. Numerical heat transfer and fluid flow (1980), Hemisphere, New York