The dual reciprocity boundary element method for magnetohydrodynamic channel flows

ANZIAM Journal

Volumn 44, Issue 2, 2002, Pages 305-322

  Liu, Huan Wen ^a   Zhu, Song Ping ^b  

^a GUANGXI UNIVERSITY FOR NATIONALITIES   (China)

^b UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745116201     PISSN: 14461811     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1446181100013961     Document Type: Article

References (40)

1. C. A. Brebbia, J. C. F. Tells and L. C. Wrobel (eds.), Boundary element techniques (Springer, Berlin, 1984).
2. T. R. Bridges and L. C. Wrobel, "A dual reciprocity formulation for elasticity problems with body forces using augmented thin plate splines", Comm. Numer. Methods Eng. 12 (1996) 209-220.
3. I. L. Brunton and A. J. Pullan, "A semi-analytic boundary element method for parabolic problem", Eng. Anal. Boundary Elements 18 (1996) 253-264.
4. C. J. Coleman, D. L. Tullock and N. Phan-Thien, "An effective boundary element method for inhomogeneous partial differential equations", TAMP 42 (1991) 730-745.
5. J. Duchon, "Splines minimizing rotation-invariant semi-norms in Sobolev spaces", in Constructive theory of Junctions of several variables (Proc. Conf., Math. Res. Inst., Obenvolfach, I976), Lecture Notes in Math. 571, (Springer, Berlin, 1977) 85-100.
6. L. R. T. Gardner and G. A. Gardner, "A two dimensional bi-cubic B-spline finite element: used in a study of MHD-duct flow", Comput. Methods Appl. Mech. Eng. 124 (1995) 365-375.
7. M. A. Golberg, "The method of fundamental solutions for Poisson's equation", Eng. Anal. Boundary Elements 16 (1995) 205-213.
8. M. A. Golberg, C. S. Chen and S. Karur, "Improved multiquadric approximation for partial differential equations". Eng. Anal. Boundary Elements 18 (1996) 9-17.
9. R. R. Gold, "Magnetohydrodynamic pipe flow, part. I", J. Fluid Mech. 13 (1962) 505-512.
10. M. Itagaki and C. A. Brebbia, "Generation of higher order fundamental solutions to the two-dimensional modified Helmholtz equation", Eng. Anal. Boundary Elements 11 (1993) 87-90.
11. A. D. Kerr, "An extension of the Kantorovich method", Quart. Appl. Math. 26 (1968) 219.
12. H.-W. Liu, "Numerical modeling of the propagation of ocean waves", Ph. D. Thesis, University of Wollongong, Australia, 2001.
13. H.-W. Liu, S.-P. Zhu and T. R. Marchant, "A perturbation DRBEM model for weakly nonlinear wave runups around islands", accepted in principle.
14. W. R. Madych and S. A. Nelson, "Multivariate interpolation and conditionally positive definite functions II", Math. Comp. 54 (1990) 211-230.
15. D. Nardini and C. A. Brebbia, A new approach to free vibration analysis using boundary elements (Comput. Mech., Southampton, and Springer, Berlin, 1982).
16. A. C. Neves and C. A. Brebbia, "The multiple reciprocity boundary element method in elasticity: A new approach for transforming domain integrals to the boundary", Int. J. Numer. Methods Eng. 31 (1991) 709-727.
17. A. J. Nowak and C. A. Brebbia, 'The multiple-reciprocity method. A new approach for transforming BEM domain integrals to the boundary". Eng. Anal. Boundary Elements 6 (1989) 164-168.
18. A. J. Nowak and C. A. Brebbia, "Solving Helmholtz equation by multiple reciprocity method", in Computer and experiments in fluid flow (eds. G. M. Carlomagno and C. A. Brebbia), (Comput. Mech., Southampton, 1989) 265-270.
19. P. W. Partridge and C. A. Brebbia, "Computer implementation of the BEM dual reciprocity method for the solution of Poisson-type equations", Software Engrg. Workstations 5 (1989) 199-206.
20. P. W. Partridge, C. A. Brebbia and L. C. Wrobel, The dual reciprocity boundary element method (Comput. Mech., Southampton, and Elsevier Appl. Sci., London, 1992).
21. P. W. Partridge and L. C. Wrobel, "The dual reciprocity method for spontaneous ignition", Int. J. Numer. Methods Eng. 30 (1990) 953-963.
22. M. J. D. Powell, "The uniform convergence of thin plate splines in two dimensions", in Univ. of Cambridge Numer. Anal. Report DAMTP 1993/NA 16.
23. M. J. D. Powell, "The theory of radial basis function approximation in 1990", in Advances in numerical analysis. Vol. II (Lancaster, 1990), (Oxford Univ. Press, New York, 1992) 105-210.
24. J. A. Shercliff, "Steady motion of conducting fluid in pipes under transverse magnetic fields", Math. Proc. Cambridge Philos. Soc. 49 (1953) 136-144.
25. B. Singh and J. Lal, "Magnetohydrodynamic axial flow in a triangular pipe under transverse magnetic field", Indian J. Pure Appl. Math. 9 (1978) 101-115.
26. B. Singh and J. Lal, "MHD axial flow in a triangular pipe under transverse magnetic field parallel to a side of the triangle", Indian J. Tech. 17 (1979) 184-189.
27. B. Singh and J. Lal, "Finite element method in magnetohydrodynamic channel flow problems", Int. J. Numer. Methods Eng. 18 (1982) 1104-1111.
28. B. Singh and J. Lal, "Finite element method for MHD channel flow with arbitrary wall conductivity", J. Math. Phys. Sci. 18 (1984) 501-516.
29. B. Singh and J. Lal, "Finite element method for unsteady MHD flow through pipes with arbitrary wall conductivity", Int. J. Numer. Methods Fluids 4 (1984) 291-302.
30. M. Tezer-Sezgin, "BEM solution of MHD flow in a rectangular duct". Int. J. Numer. Methods Fluids 18 (1994) 937-952.
31. M. Tezer-Sezgin and S. Dost, "Boundary element method for MHD channel flow with arbitrary wall conductivity", Appl. Math. Modeling 18 (1994) 429-436.
32. M. Tezer-Sezgin and S. Dost, "Boundary element solution of inhomogeneous modified Helmholtz equation", Scientia Iranica 1 (1994) 157-166.
33. M. Tezer-Sezgin and S. Koksal, "Finite element method for solving MHD flow in a rectangular duct". Int. J. Numer. Methods Eng. 28 (1989) 445-459.
34. Z. Wu and R. Shaback, "Local error estimates for radial basis function interpolation of scattered data", 1MA J. Num. Anal. 13 (1993) 13-27.
35. Y. L. Zhang and S.-P. Zhu, "On the choice of interpolation functions used in the dual-reciprocity boundary-element method", Eng. Anal. Boundary Elements 13 (1994) 387-396.
36. R. Zheng, C. J. Coleman and N. Phan-Thien, "A boundary element approach for non-homogeneous potential problems", Comp. Mech. 7 (1991) 279-288.
37. S.-P. Zhu and H.-W. Liu, "On the application of the multiquadric bases in conjunction with the LTDRM method to solve nonlinear diffusion equations", Appl. Math. Comput. 96 (1998) 161-175.
38. S.-P. Zhu, H.-W. Liu and X.-P. Lu, "A combination of the LTDRM and the ATPS in solving linear diffusion problems". Eng. Anal. Boundary Elements 21 (1998) 285-289.
39. S.-P. Zhu, P. Satravaha and X.-P. Lu, "Solving linear diffusion equations with the dual reciprocity method in Laplace space". Eng. Anal. Boundary Elements 13 (1994) 1-10.
40. S.-P. Zhu and Y. L. Zhang, "Improvement on dual reciprocity boundary element method for equations with convective terms", Comm. Numer. Methods Eng. 10 (1994) 361-371.