Development of RBF-DQ method for derivative approximation and its application to simulate natural convection in concentric annuli

Computational Mechanics

Volumn 29, Issue 6, 2002, Pages 477-485

  Wu, Y L ^a   Shu, C ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Approximation of derivatives; Concentric annuli; DQ; Natural convection; PDEs; RBFs

Indexed keywords

APPROXIMATION THEORY; INTERPOLATION; NATURAL CONVECTION; NAVIER STOKES EQUATIONS; PROBLEM SOLVING;

CONCENTRIC ANNULI;

RADIAL BASIS FUNCTION NETWORKS;

EID: 0036868714     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0357-4     Document Type: Article

References (16)

1. Bellman R, Kashef BG, Casti J (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J Comput Phys. 10:40-52
2. Shu C, Richards BE (1992) Application of generalised differential quadrature to solve two-dimension incompressible Navier-Stokes equations. Int. J. Numer Methods Fluids 15: 791-798
3. Shu C, Chew YT (1997) Fourier expansion-based differential quadrature and its application to Helmholtz eigenvalue problems. Commun. in Numer Methods in Eng 13:643-653
4. Shu C (2000) Differential Quadrature and its Application in Engineering. Springer-Verlag, London
5. Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophysics Res. 176:1905-1915
6. Kansa ET (1990) Multiquadrics - A scattered data approximation scheme with applications to computational fluid dynamics: Surface approximations and partial derivative estimates. Comput. Math. Appl. 19(6-8): 127-145
7. Kansa ET (1990) Multiquadrics - A scattered data approximation scheme with applications to computational fluid dynamics: Solutions to parabolic, hyperbolic, and elliptic partial differential equations, Comput. Math. Appl. 19(6-9): 147-161
8. Zhang X, Song KZ, Lu MW, Liu X (2000) Meshless methods based on collocation with radial basis functions. Computational Mechanics 26(4): 333-343
9. Kansa EJ, Hon YC (2000) Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput. Math. Applic. 39:123-127
10. Franke C, Schaback R (1998) Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput. 93:73-83
11. Fasshauer GE (1997) Solving Partial Differential Equations by Collocation with Radial Basis Functions: Surface Fitting and Multiresolution Methods. Vanderbilt University Press, pp. 131-138
12. Hon YC, Schaback R (2001) On unsymmetric collocation by radial basis functions. Appl. Math. Comput. 119:177-186
13. Jumarhon B, Amini S, Chen K (2000) The Hermite collocation method using radial basis functions. Engineering Analysis with Boundary Elements 24:607-611
14. Madych WR, Nelson SA (1989) Multivariate interpolation and conditionally positive definite function. Approx. Theory Appl. 4:77-89
15. Shu C (1999) Application of differential quadrature method to simulate natural convection in a concentric annulus. Int. J. Numer. Methods. Fluids 30:977-993
16. Kuehn TH, Goldstein RJ (1976) An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders. J. Fluid Mech. 74:695-716.