Computation of incompressible Navier-Stokes equations by local RBF-based differential quadrature method

CMES - Computer Modeling in Engineering and Sciences

Volumn 7, Issue 2, 2005, Pages 195-205

  Shu, C ^a   Ding, H ^a   Yeo, K S ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Differential quadrature; Incompressible flow; Mesh free; Meshless; Radial basis function; Staggered cylinders

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; INCOMPRESSIBLE FLOW; PARTIAL DIFFERENTIAL EQUATIONS; RADIAL BASIS FUNCTION NETWORKS; REYNOLDS NUMBER;

DIFFERENTIAL QUADRATURE (DQ); MESH-FREE; MESHLESS APPROACH; RADIAL BASIS FUNCTION; STAGGERED CYLINDERS;

NAVIER STOKES EQUATIONS;

EID: 15544371314     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Atluri, S. N. (2004): The Meshless Method(MLPG) for Domain & BIE Discretizations. Tech Science Press, 700 pages.
2. Atluri, S. N.; Han, Z. D.; Rajendran, A. M. (2004): A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed" Approach, CMES: Computer Modeling in Engineering & Sciences, Vol. 6, No. 6, pp. 491-514.
3. Atluri, S. N.; Shengping, S. (2002): The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple& Less-costly Alternative to the Finite Element and Boundary Element Methods, CMES: Computer Modeling in Engineering & Sciences, Vol. 3, No. 1, pp. 11-52.
4. Behr, M.; Hastreiter, D.; Mittal, S.; Tezduyar, T. E. (1995): Incompressible flow past a circular cylinder: dependence of the computed flow field on the location of the lateral boundaries. Comput. Methods Appl. Mech. Engrg. Vol. 123, pp. 309-316.
5. Bellman, R. E.; Kashef, B. G.; Casti, J. (1972): Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations. J. Comput. Phys. Vol. 10, 40-52.
6. Chen, C. S.; Brebbia, C. A.; Power, H. (1998): Dual reciprocity method using for Helmholtz-type operators. Boundary Elements, Vol. 20, pp. 495-504.
7. Chen, W.; Tanaka, M. (2002): A meshless, integration-free, and boundary-only RBF technique. Comput. Math. Appl., Vol. 43, pp. 379-391.
8. Fasshauer, G. E. (1997): Solving partial differential equations by collocation with radial basis functions. Surface fitting and multiresolution methods, eds. A. L. Mehaute, C. Rabut and L. L. Schumaker, pp. 131-138.
9. Forberg, B.; Driscoll, T. A. (2002): Interpolation in the limit of increasingly flat radial basis functions. Comput. Math. Appl., Vol. 43, pp. 413-422.
10. Ghia, U.; Ghia, K. N.; Shin, C. T. (1982): High-Resolutions for incompressible flow using the Navier-Stokes equations and a multi-grid method. Journal of computational physics, Vol. 48, pp. 387-411.
11. Hon, Y. C.; Wu, Z. M. (2000): A quasi-interpolation method for solving stiff ordinary differential equations. International Journal for Numerical Methods in Engineering, Vol. 48, pp. 1187-1197.
12. Kansa, E. J. (1990): Multiquadrics - A scattered data approximation scheme with applications to computational fluid-dynamics -I. Surface approximations and partial derivative estimates. Computers Mathematics ap plication, Vol. 19, No (6-8) pp. 127-145.
13. Lin, H.; Atluri, S. N. (2001): The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations, CMES: Computer Modeling in Engineering & Sciences Vol. 2, No. 2, pp. 117-142.
14. Liu, C.; Zheng, X.; Sung, C. H. (1998): Preconditioned multigrid methods for unsteady incompressible flows. J. Comput. Phys. 139, 35.
15. Mai-Duy, N.; Tran-Cong, T. (2001a): Numerical solution of differential equations using multiquadric radial basis function networks. Neural Networks, Vol. 14, pp. 185-199.
16. Mai-Duy, N.; Tran-Cong, T. (2001b): Numerical solution of Navier-Stokes equations using radial basis function networks. Int. J. Numer. Meth. Fluids, Vol. 37, pp. 65-86.
17. Richards, B. E.; Shu, C. (1992): Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids. 15, 791-798.
18. Shu, C. (2000): Differential Quadrature and its Application in Engineering, Springer-Verlag London Limited.
19. Shu, C.; Ding, H.; Yeo, K. S. (2003): Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. Vol. 192, pp. 941-954.
20. Tezduyar, T. E.; Glowinski, R.; Liou, J. (1988): Petrov-Galerkin methods on multiply connected domains for the vorticity-stream function formulation of the incompressible Navier-Stokes equations. Int. J. numer. Methods fluids, Vol. 8, pp. 1269-1290.
21. Tolstykh; Shirobokov (2003): On using radial basis functions in a 'finite difference mode' with applications to elasticity problems. Computational Mechanics, Vol. 33, pp. 68-79.
22. Wu, Y. L.; Shu, C. (2002): Development of RBF-DQ Method for Derivative Approximation and Its Application to Simulate Natural Convection in Concentric Annuli. Computational Mechanics, Vol. 29, pp. 477-485.