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Upwinding meshfree point collocation method for steady MHD flow with arbitrary orientation of applied magnetic field at high Hartmann numbers. (English) Zbl 1271.76239
Summary: In this paper, a meshfree point collocation method, with an upwinding scheme, is presented to obtain the numerical solutions of the coupled equations in velocity and magnetic field for the fully developed magnetohydrodynamic (MHD) flow through an insulated straight duct of rectangular section. The moving least-square (MLS) approximation is employed to construct the shape functions in conjunction with the framework of the point collocation method. Computations have been carried out for different applied magnetic field orientations and a wide range of values of Hartmann number from 5 to 10\(^6\). As the adaptive upwinding local support domain is introduced in the meshless point collocation method, numerical results show that the method may compute MHD problems not only at low and moderate values but also at high values of the Hartmann number with high accuracy and good convergence.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76W05 Magnetohydrodynamics and electrohydrodynamics
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[1] Singh, B.; Lal, J., Finite element method in magnetohydrodynamic channel flow problems, Int J numer methods eng, 18, 1104-1111, (1982) · Zbl 0489.76119
[2] Singh, B.; Lal, J., FEM for MHD channel flow with arbitrary wall conductivity, J math phys sci, 18, 501-516, (1984) · Zbl 0574.76117
[3] Singh, B.; Lal, J., Finite element method for unsteady MHD flow through pipes with arbitrary wall conductivity, Int J numer methods fluids, 4, 291-302, (1984) · Zbl 0547.76119
[4] Tezer-Sezgin, M.; Köksal, S., Finite element method for solving MHD flow in a rectangular duct, Int J numer methods eng, 28, 445-459, (1989) · Zbl 0669.76140
[5] Tezer-Sezgin, M.; Bozkaya, C., Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field, Comput mech, 41, 769-775, (2008) · Zbl 1241.76323
[6] Demendy, Z.; Nagy, T., A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers, Acta mech, 123, 135-149, (1997) · Zbl 0902.76058
[7] Verardi, S.L.L.; Machado, J.M.; Cardoso, J.R., The element-free Galerkin method applied to the study of fully developed magnetohydrodynamic duct flows, IEEE trans magn, 38, 941-944, (2002)
[8] Nesliturk, A.I.; Tezer-Sezgin, M., The finite element method for MHD flow at high Hartmann numbers, Comput methods appl mech eng, 194, 1201-1224, (2005) · Zbl 1091.76036
[9] Zhang, L.; Ouyang, J.; Zhang, X.H., The two-level element free Galerkin method for MHD flow at high Hartmann numbers, Phys lett A, 372, 5625-5638, (2008) · Zbl 1223.76128
[10] Oñate, E.; Idelsohn, S.; Zienkiewicz, O.C.; Taylor, R.L.; Sacco, C., A stabilized finite point method of analysis of fluid mechanics problems, Comput methods appl mech eng, 139, 315-346, (1996) · Zbl 0894.76065
[11] Oñate, E.; Perazzo, F.; Miquel, J., A finite point method for elasticity problems, Comput struct, 79, 2151-2163, (2001)
[12] Kansa, E.J., Multiquadrics – a scattered data approximation scheme with applications to computational fluid-dynamics, Comput math appl, 19, 127-145, (1990) · Zbl 0692.76003
[13] Yongsik, K.; Do Wan, K.; Sukky, J.; Jin Ho, L., Meshfree point collocation method for the stream-vorticity formulation of 2D incompressible navier – stokes equations, Comput methods appl mech eng, 196, 3095-3109, (2007) · Zbl 1173.76386
[14] Randolph, E.B.; Josef, F.B.; Wolfgang, F.; Smith, R.K., Some upwinding techniques for finite element approximations of convection – diffusion equations, Numer math, 58, 185-202, (1990) · Zbl 0713.65066
[15] Xue, S.-C.; Phan-Thien, N.; Tanner, R.I., Upwinding with deferred correction (UPDC): an effective implementation of higher-order convection schemes for implicit finite volume methods, J non-Newtonian fluid mech, 108, 1-24, (2002) · Zbl 1143.76507
[16] Gu, Y.T.; Liu, G.R., Meshless techniques for convection dominated problems, Comput mech, 38, 171-182, (2006) · Zbl 1138.76402
[17] Shercliff, J.A., Steady motion of conducting fluids in pipes under transverse magnetic fields, Proc camb phil soc, 49, 136-144, (1953) · Zbl 0050.19404
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