Comparison between continuous and discontinuous boundary elements in the multidomain dual reciprocity method for the solution of the two-dimensional Navier-Stokes equations

Engineering Analysis with Boundary Elements

Volumn 25, Issue 1, 2001, Pages 57-69

  Florez, W F ^a,b   Power, H ^a  

^a WESSEX INSTITUTE OF TECHNOLOGY   (United Kingdom)

^b UNIVERSIDAD PONTIFICIA BOLIVARIANA   (Colombia)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; INTEGRAL EQUATIONS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING;

DUAL RECIPROCITY BOUNDARY ELEMENT METHOD (DERBEM); MULTIDOMAIN DECOMPOSITION TECHNIQUES;

BOUNDARY ELEMENT METHOD;

EID: 0035095836     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(00)00051-5     Document Type: Article

References (30)

1. Brebbia C.A. The boundary element method for engineers. 1984;Pentech Press.
2. Brebbia C.A., Dominguez J. Boundary elements an introductory course. 1992;Computational Mechanics Publications, Southampton.
3. Cheng A, Grilli HD, Lafe O. Dual reciprocity BEM based on complete set global shape functions. In: BEM XV. Southampton: Computational Mechanics Publications, 1993. p. 343-58.
4. Davis T, Duff IS. Unsymmetric pattern MultiFrontal package (UMFRACK). Technical Report, University of Florida, USA, and Rutherford Appleton Laboratory, UK, 1997.
5. Dennis J.E., Schnabel R.B. Numerical methods for unconstrained optimization and nonlinear equations. 1980;Prentice-Hall, Englewood Cliffs, NJ.
6. Florez WF, Power H. DRM multi-domain mass conservative interpolation approach for the BEM solution of the Navier-Stokes equations. Computers and Mathematics with Applications, in press.
7. Ghia U. High re solutions for incompressible flow using the Navier-Stokes equations and a multi-grid method. J Comput Phys. 48:1982;387-411.
8. Goldberg M.A., Chen C.S. Discrete projection methods for integral equations. 1997;Computational Mechanics Publications, Southampton.
9. Higdon J.J.L. Stokes flow in arbitrary two-dimensional domains: shear flow over ridges and cavities. J Fluid Mech. 1985;195-226.
10. Ingham D.B., Kelmanson M.A. Boundary integral equation analyses of singular, potential and biharmonic problems. vol. 15:1984;Spinger, Berlin.
11. Kansa E.J., Carlson R.E. Radial basis functions: a class of grip-free, scattered data approximations. Comput Fluid Dyn J. 3:(4):1995;479-496.
12. Kelmanson M.A. Boundary integral equation solution of viscous flows with free surfaces. J Engng Math. 17:1983;329-343.
13. Ladyzhenskaya O.A. The mathematical theory of viscous incompressible flow. 1963;Gordon and Breach, New York.
14. Paige C., Saunders M. LSQR: sparse linear equations and least squares problems. ACM Trans Math Software. 8:(2):1982;195-209.
15. Partridge P., Sensale B. Hybrid approximation functions in the dual reciprocity boundary element method. Commun Numer Meth Engng. 13:1997;83-94.
16. Partridge P.W., Brebbia C.A., Wrobel L.C. The dual reciprocity boundary element method. 1992;Computational Mechanics Publications, Southampton.
17. Popov V, Power H. The DRM-MD integral equation method for the numerical solution of convection-diffusion equation. In: Boundary element research in Europe. Southampton: Computational Mechanics Publications, 1999. p. 67-81.
18. Power H., Partridge P.W. The use of stokes fundamental solution for the boundary only formulation of the three-dimensional Navier-Stokes equations for moderate Reynolds numbers. Int J Numer Meth Engng. 37:1994;1825-1840.
19. Power H., Wrobel L.C. Boundary integral methods in fluid mechanics. 1995;Computational Mechanics Publications, Southampton.
20. Pozrikidis C. The flow of a liquid film along a periodic wall. J Fluid Mech. (188):1988;275-300.
21. Press W.H., Teulkolski S.A., Flannery B.P., Vetterling W.T. Numerical recipes. 1992;Cambridge University Press, Cambridge, UK.
22. Rabinowitz P. Numerical methods for non-linear algebraic equations. 1968;Gordon and Breach, London.
23. Saad Y. SPARSKIT: a basic tool kit for sparse matrix computations, ver. Technical Report, University of Illinois, USA, 1994.
24. Sarler B., Kuhn G. Primitive variable dual reciprocity boundary element method solution of incompressible Navier-Stokes equations. Engng Anal BE. 23:1999;443-455.
25. Skerget L., Hribersek M. Iterative methods in solving Naviers-Stokes equations by the boundary element method. Int J Numer Meth Fluids. 39:1996;115-139.
26. Skerget L., Hribersek M., Kuhn G. Computational fluid dynamics by boundary-domain integral method. Int J Numer Meth Engng. 46:1999;1291-1311.
27. Taigbenu A.E. The Green element method. Int J Numer Meth Engng. 1995;2241-2263.
28. Taigbenu A.E., Onyejekwe O.O. Green element simulations of the transient nonlinear unsaturated flow equation. Appl Math Mod. (19):1995;675-684.
29. Telles J.C. A self-adaptive coordinate transformation for efficient numerical evaluation of general boundary element integrals. Int J Numer Meth Engng. 24:1987;959-973.
30. Wu Z. Hermite-Birkhoff interpolation of scattered data by radial basis functions. Approx Theory Appl. 8:1992;1-10.