Solutions of 2D and 3D stokes laws using multiquadrics method

Engineering Analysis with Boundary Elements

Volumn 28, Issue 10 SPEC. ISS., 2004, Pages 1233-1243

  Young, D L ^a   Jane, S C ^a   Lin, C Y ^a   Chiu, C L ^a   Chen, K C ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Circular cavity; Cubic cavity; Iterative solution; Meshless; Multiquadrics method; Square cavity; Stokes flow; Three dimensional; Two dimensional; Velocity vorticity formulation

Indexed keywords

INCOMPRESSIBLE FLOW; ITERATIVE METHODS; MATHEMATICAL MODELS; POISSON EQUATION; PROBLEM SOLVING; VORTEX FLOW;

CIRCULAR CAVITY; CUBIC ACTIVITY; ITERATIVE SOLUTIONS; MULTIQUADRICS METHODS; SQUARE CAVITY; STOKES FLOW; VELOCITY VORTICITY FORMULATIONS;

COMPUTATIONAL FLUID DYNAMICS;

EID: 3142773581     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2003.04.002     Document Type: Article

References (22)

1. Kansa E.J. Multiquadrics - a scattered data approximation scheme with application to computational fluid-dynamics. I. Surface approximations and partial derivative estimates. Comput Math Appl. 19:(8/9):1990;127-145.
2. 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:(8/9):1990;147-161.
3. Madych W.R., Nelson S. Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation. J. Approx Theory. 1992.
4. Cheng AH-D, Golberg MA, Kansa EJ, Zammito G. Exponential convergence and H-c multiquadric collocation method for partial differential equations. Numer Meth Part Differ Eq. 2003;19(5):571-94.
5. Hon Y.C., Cheung K.F., Mao X.Z., Kansa E.J. Multiquadric solution for shallow water equations. J Hydraul Engng. 125:(5):1999;524-533.
6. Kansa E.J., 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. Kansa E.J., Carlson R.E. Improved accuracy of multiquadric interpolation using variable shape parameters. Comput Math Appl. 24:(12):1992;99-120.
8. Hon Y.C., Mao X.Z. An efficient numerical scheme for Burger's equation. Appl Math Comput. 95:1998;37-50.
9. Fedoseyev A.I., Friedman M.J., Kansa E.J. Continuation for nonlinear elliptic partial differential equations discretized by the multiquadrics method. Int J Bifurcation Chaos. 10:(2):2000;481-492.
10. Beatson R.K., Cherrie J.B., Mouat C.T. Fast fitting of radial basis functions: method based on preconditioned GMRES iteration. Adv Comput Math. 11:1999;253-270.
11. Beatson R.K., Newsam G.N. Fast evaluation of radial basis functions - I. Comput Math Appl. 24:(12):1992;7-19.
12. Beatson R.K., Newsam G.N. Fast evaluation of radial basis functions: moment-based methods. SIAM J Sci Comput. 19:(5):1998;1428-1449.
13. Beatson R.K., Newsam G.N. Fast solution of the radial basis function interpolation equations: domain decomposition methods. SIAM J Sci Comput. 22:(5):2000;1717-1740.
14. Mai-Duy N., Tran-Cong T. Numerical solution of Navier-Stokes equations using multiquadrics radial basis function networks. Int J Numer Meth Fluids. 37:2001;65-86.
15. Mai-Duy N., Tran-Cong T. Numerical solution of differential equations using multiquadrics radial basis function networks. Neural Netw. 14:2001;185-199.
16. Burggraf O.R. Analytical and numerical studies of the structure of steady separated flows. J Fluid Mech. 124:1966;113-151.
17. Young D.L., Lin Q.H. Application of finite element method to 2-D flows. Proceedings of the Third National Conference On Hydraulic Engineering, Taipei, Taiwan. 1986;. p. 223-42.
18. Young D.L., Yang S.K. Simulation of two-dimensional steady Stokes flows by the velocity-vorticity boundary element method. Proceedings of the 20th National Conference of Mechanics, Taipei, Taiwan. 1996;. p. 422-9.
19. Eldho T.I., Young D.L. Solution of the velocity-vorticity Navier-Stokes equations using dual reciprocity boundary element method. Proceedings of the Fourteenth Engineering Mechanics Conference, ASCE, Texas, USA. 2000.
20. Hwu T.Y., Young D.L., Chen Y.Y. Chaotic advections for Stokes flows in circular cavity. J Engng Mech. 123:1997;774-782.
21. Tsai C.C., Young D.L., Cheng A.H.-D. Meshless BEM for three-dimensional Stokes flows. CMES: Comput Model Engng Sci. 3:(1):2002;117-128.
22. Young D.L., Liu Y.H., Eldho T.I. Three-dimensional Stokes flow solution using combined boundary element and finite element methods. Chin J Mech. 15:1999;169-176.