Performance of multiquadric collocation method in solving Lid-driven cavity flow problem with low reynolds number

CMES - Computer Modeling in Engineering and Sciences

Volumn 15, Issue 3, 2006, Pages 137-146

  Chantasiriwan, S ^a  

^a THAMMASAT UNIVERSITY   (Thailand)

Author keywords

Meshless; Multiquadrics; Navier stokes; Radial basis function

Indexed keywords

BENCHMARKING; FLOW OF FLUIDS; LINEAR SYSTEMS; NAVIER STOKES EQUATIONS; NONLINEAR SYSTEMS; PROBLEM SOLVING; REYNOLDS NUMBER;

LID DRIVEN CAVITY FLOW PROBLEM; MESHLESS; MULTIQUADRIC COLLOCATION; VELOCITY VORTICITY FORMULATION;

RADIAL BASIS FUNCTION NETWORKS;

EID: 33845397945     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. Ahrem, R.; Beckert, A.; Wendland, H. (2006): A meshless spatial coupling scheme for large-scale fluid-structure-interaction problems. CMES: Computer Modeling in Engineering & Sciences, vol. 12, pp. 121-136.
2. Andreaus, U.; Batra, R. C.; Porfiri, M. (2005): Vibrations of cracked Euler-Bernoulli beams using Meshless Local Petrov-Galerkin (MLPG) method CMES: Computer Modeling in Engineering & Sciences, vol. 9, pp. 111-131.
3. 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, pp. 491-513.
4. Chantasiriwan, S. (2004): Cartesian grid methods using radial basis functions for solving Poisson, Helmholtz and diffusion-convection equations. Engr. Anal. with Bound. Elem., vol. 28, pp. 1417-1425.
5. Chantasiriwan, S. (2005): Solutions of partial differential equations with random Dirichlet boundary conditions by multiquadric collocation method. Engr. Anal. with Bound. Elem., vol. 29, pp. 1124-1129.
6. Ching, H. K.; Chen, J. K. (2006): Thermomechanical analysis of functionally graded composites under laser heating by the MLPG method. CMES: Computer Modeling in Engineering & Sciences, vol. 13, pp. 199-217.
7. Cho, H. A.; Golberg, M. A.; Muleshkov, A. S.; Li, X. (2004): Trefftz methods for time dependent partial differential equations. Computers, Materials and Continua, vol. 1, pp. 1-37.
8. Choi, S.; Marcozzi, M. D. (2004): On the application of MQ-RBF to the valuation of derivative securities. CMES: Computer Modeling in Engineering & Sciences, vol. 5, pp. 201-212.
9. Ding, H.; Shu, C.; Yeo, K. S.; Xu, D. (2006): Nu merical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method. Comp. Meth. Appl. Mech. Engr., vol. 195, pp. 516-533.
10. Gao, L.; Liu, K.; Liu, Y. (2006): Applications of - MLPG method in dynamic fracture problems. CMES: Computer Modeling in Engineering & Sciences, vol. 12, pp. 181-195.
11. Ghia, U.; Ghia, K. N.; Shin, C. T. (1982): High-Re solutions for incompressible flow using the Navier-Stokes equations and a multi-grid method. J. Comp. Phys., vol. 48, pp. 387-411.
12. Han, Z. D.; Atluri, S. N. (2004): Meshless local Petrov-Galerkin (MLPG) approaches for solving 3D problems in elasto-statics. CMES: Computer Modeling in Engineering & Sciences, vol. 6, pp. 169-188.
13. Han, Z. D.; Rajendran, A. M.; Atluri, S. N. (2005): Meshless Local Petrov-Galerkin (MLPG) approaches for solving nonlinear problems with large deformations and rotations. CMES: Computer Modeling in Engineering & Sciences, vol. 10, pp. 1-12.
14. Hansen, E. B. (1997): Root structure and numerical solution of the equation sin z = cz. Appl. Math. Lett., vol. 10, pp. 33-38.
15. Hardy, R. L. (1971): Multiquadric equation of topography and other irregular surfaces. J. Geophys. Res., vol. 76, pp. 1905-1915.
16. Hon, Y. C.; Ling, L.; Liew, K. M. (2005): Numerical analysis of parameters in a laminated beam model by radial basis functions. Computers, Materials and Continua, vol. 2, pp. 39-49.
17. Kansa, E. J. (1990): Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics - II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comp. Math. with Appl., vol. 19, pp. 147-161.
18. Lian, Y. S.; Liou, M. S. (2005): Mining of data from evolutionary algorithms for improving design optimization. CMES: Computer Modeling in Engineering & Sciences, vol. 8, pp. 61-72.
19. Ling, L. (2004): A univariate quasi-multiquadric interpolation with better smoothness. Comp. Math. with Appl., vol. 48, pp. 897-912.
20. Ma, Q. W. (2005): MLPG method based on Rankine source solution for simulating nonlinear water waves. CMES: Computer Modeling in Engineering & Sciences, vol. 9, pp. 193-209.
21. Mai-Cao, L.; Tran-Cong, T. (2005): A meshless IRBFN-based method for transient problems. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 149-171.
22. Mai-Duy, N. (2004): Indirect RBFN method with scattered points for numerical solution of PDEs. CMES: Computer Modeling in Engineering & Sciences, vol. 6, pp. 209-226.
23. Mai-Duy, N.; Tran-Cong, T. (2001): Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks. Int. J. Numer. Meth. Fl., vol. 37, pp. 65-86.
24. Mai-Duy, N.; Tran-Cong, T. (2006): Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engr. Anal. with Bound. Elem., vol. 30, pp. 77-87.
25. Pecher, R.; Elston, S.; Raynes, P. (2006): Meshfree solution of Q-tensor equations of nematostatics using the MLPG method. CMES: Computer Modeling in Engineering & Sciences, vol. 13, pp. 91-101.
26. Sarler, B. (2005): A radial basis collocation approach in computational fluid dynamics. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 185-193.
27. Sellountos, E. J.; Vavourakis, V.; Polyzos, D. (2005): A new singular/hypersingular MLPG (LBIE) method for 2D elastostatics. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 35-47.
28. Shankar, P. N. (1993): The eddy structure in Stokes flow in a cavity. J. Fluid Mech., vol. 250, pp. 371-383.
29. Shen, S.; Atluri, S. N. (2004): Multiscale simulation based on the meshless local Petrov-Galerkin (MLPG) method. CMES: Computer Modeling in Engineering & Sciences, vol. 5, pp. 235-255.
30. Shen, S.; Atluri, S. N. (2005): A tangent stiffness MLPG method for atom/continuum multiscale simulation. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 49-67.
31. Shu, C.; Ding, H.; Yeo, K. S. (2005): Computation of incompressible Navier-Stokes equations by local RBF-based differential quadrature method. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 195-205.
32. Sladek, J.; Sladek, V.; Wen, P. H.; Aliabadi, M. H. (2006): Meshless Local Petrov-Galerkin (MLPG) method for shear deformable shells analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 13, pp.103-117.
33. Soric, J.; Li, Q.; Jarak, T.; Atluri, S. N. (2004): Meshless Local Petrov-Galerkin (MLPG) formulation for analysis of thick plates. CMES: Computer Modeling in Engineering & Sciences, vol. 6, pp. 349-357.
34. Tolstykh, A. I.; Shirobokov, D. A. (2005): Using radial basis functions in a "finite difference mode". CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 207-222.
35. Vavourakis, V.; Sellountos, E. J.; Polyzos, D. (2006): A comparison study on different MLPG (LBIE) formulations. CMES: Computer Modeling in Engineering & Sciences, vol. 13, pp. 171-183.
36. Wang, S. Y.; Wang, M. Y. (2006): Structural shape and topology optimization using an implicit free boundary parametrization method. CMES: Computer Modeling in Engineering & Sciences, vol. 13, pp. 119-147.
37. Young, D. L.; Lane, S. C.; Lin, C. Y.; Chiu, C. L.; Chen, K. C. (2004): Solutions of 2D and 3D Stokes laws using multiquadrics method. Engr. Anal. with Bound. Elem., vol. 28, pp. 1233-1243.