×

zbMATH — the first resource for mathematics

The two-level element free Galerkin method for MHD flow at high Hartmann numbers. (English) Zbl 1223.76128
Summary: A new element free Galerkin method, namely the two-level element free Galerkin method, is presented for solving the governing equations of steady magnetohydrodynamic duct flow. Because this element free Galerkin method makes use of the nodal point configurations which do not require a mesh, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometric problems. Another distinguished feature of the proposed method is the resolving capability of high gradients near the layer regions without local or adaptive refinements. Numerical results indicate that, no matter how large the Hartmann number is, this method has the ability to produce satisfactory results for the velocity and the magnetic field simultaneously. That is to say, the presented method has some excellent properties such as better stability and accuracy.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76M12 Finite volume methods applied to problems in fluid mechanics
65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Software:
Mfree2D
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Singh, B.; Lal, J., Indian J. pure appl. math., 9, 101, (1978)
[2] Singh, B.; Lal, J., Indian J. tech., 17, 184, (1979)
[3] Singh, B.; Lal, J., Internat. J. numer. methods engrg., 18, 1104, (1982)
[4] Singh, B.; Lal, J., Internat. J. numer. methods fluids, 4, 291, (1984)
[5] Tezer-Sezgin, M.; Koksal, S., Internat. J. numer. methods engrg., 28, 445, (1989)
[6] Demendy, Z.; Nagy, T., Acta mech., 123, 135, (1997)
[7] Barrett, K.E., Int. J. numer. methods engrg., 50, 1893, (2001)
[8] Tezer-Sezgin, M., Internat. J. numer. methods fluids, 18, 937, (1994)
[9] Liu, G.R., Mesh free methods: moving beyond the finite element method, (2003), CRC Press Boca Raton, FL · Zbl 1031.74001
[10] Xiong, Z.; Yan, L., Meshless methods, (2004), Tsinghua University Press Beijing
[11] Belytschko, T.; Lu, Y.Y.; Gu, L., Int. J. numer. methods engrg., 37, 229, (1994) · Zbl 0796.73077
[12] Belytschko, T.; Krongauz, Y.; Organ, D., Comput. methods appl. mech. engrg., 139, 3, (1996) · Zbl 0891.73075
[13] Belytschko, T.; Krongauz, Y.; Fleming, M., J. comput. appl. math., 74, 111, (1996)
[14] Liu, W.K.; Li, S.; Belytschko, T., Comput. methods appl. mech. engrg., 143, 113, (1997)
[15] Hughes, T.J.R., Comput. methods appl. mech. engrg., 127, 387, (1995)
[16] Hughes, T.J.R.; Feijoo, G.R.; Luca, M.; Jean-Baptiste, Q., Comput. methods appl. mech. engrg., 166, 1-2, 3, (1998)
[17] Masud, A.; Khurram, R.A., Comput. methods appl. mech. engrg., 193, 1997, (2004)
[18] Ayub, M.; Masud, A., Numer. heat transfer, 43, 6, 601, (2003)
[19] Masud, A., On a stabilized finite element formulation for incompressible navier – stokes equations, ()
[20] Masud, A.; Hughes, T.J.R., Comput. methods appl. mech. engrg., 1991, 4341, (2002)
[21] Masud, A.; Bergman, L.A., Comput. methods appl. mech. engrg., 194, 1513, (2005)
[22] Franca, L.P.; Nesliturk, A.; Stynes, M., Comput. methods appl. mech. engrg., 166, 35, (1998)
[23] Franca, L.P.; Nesliturk, A., Int. J. numer. methods engrg., 52, 433, (2001)
[24] Nesliturk, A.I.; Tezer-Sezgin, M., Comput. methods appl. mech. engrg., 194, 1201, (2005)
[25] Nesliturk, A.I.; Tezer-Sezgin, M., Comput. appl. math., 192, 339, (2006)
[26] Gravemeie, V.; Wall, W.A.; Ramm, E., Comput. methods appl. mech. engrg., 193, 1323, (2004)
[27] Gravemeier, V.; Wall, W.A.; Ramm, E., Int. J. numer. methods fluids, 48, 1067, (2005)
[28] Gravemeier, V., Arch. comput. methods engrg., (2006)
[29] John, V., ()
[30] Verardi, S.L.L.; Machado, J.M.; Yang, S.Y., Finite elem. anal. des., 39, 1173, (2003)
[31] Verardi, S.L.L.; Cardoso, J.R., IEEE trans. magn., 34, 5, 3134, (1998)
[32] Hughes, W.F.; Young, F.J., The electromagneto-dynamics of fluids, (1966), Wiley New York
[33] Sherchiff, J.A., J. fluid mech., 1, 644, (1956)
[34] Lu, Y.Y.; Belytschko, T.; Gu, L., Comput. methods appl. mech. engrg., 113, 397, (1994)
[35] Chu, Y.A.; Moran, B., Modelling simul. mater. sci. engrg., 3, 455, (1995)
[36] Belytschko, T.; Organ, D.; Krongauz, Y., Comput. mech., 17, 186, (1995)
[37] Masud, A.; Khurram, R.A., Comput. methods appl. mech. engrg., 195, 1750, (2006)
[38] Jie, O.Y.; Zhang, L.; Zhang, X.H., Numer. math.: J. chin. univ., 27, 100, (2005)
[39] Donea, J.; Huerta, A., Finite element methods for flow problems, (2003), Wiley New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.