Meshless Local Petrov–Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity

Atluri, 2004 Atluri, 1999, A critical assessment of the truly meshless local Petrov–Galerkin (MLPG) and local boundary integral equation (LBIE) methods, Comput. Mech., 24, 348, 10.1007/s004660050457 Atluri, 2002, The meshless local Petrov–Galerkin (MLPG) method: a simple and less-costly alternative to the finite element and boundary element methods, CMES: Comp. Modeling Eng. Sci., 3, 11 Atluri, 2002 Atluri, 1998, A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics, Comput. Mech., 22, 117, 10.1007/s004660050346 Atluri, 1998, A new meshless local Petrov–Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation, Comput. Model. Simul. Eng., 3, 187 Atluri, 2000, The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics, Comput. Mech., 25, 169, 10.1007/s004660050467 Barrett, 2001, Duct flow with a transverse magnetic field at high Hartmann numbers, Int. J. Numer. Meth. Eng., 50, 1893, 10.1002/nme.101 Barry, 2004, A wachspress meshless local Petrov–Galerkin method, Engrg. Anal. Bound. Elem., 28, 509, 10.1016/S0955-7997(03)00104-8 Batra, 2006, Analysis of electrostatic MEMS using meshless local Petrov–Galerkin (MLPG) method, Engrg. Anal. Bound. Elem., 30, 949, 10.1016/j.enganabound.2006.04.008 Bozkaya, 2006, Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme, Int. J. Numer. Meth. Fluids, 51, 567, 10.1002/fld.1131 Bozkaya, 2007, Fundamental solution for coupled magnetohydrodynamic flow equations, J. Comput. Appl. Math., 203, 125, 10.1016/j.cam.2006.03.013 Bozkaya, 2008, Time-domain BEM solution of convection–diffusion-type MHD equations, Int. J. Numer. Meth. Fluids, 56, 1969, 10.1002/fld.1570 Deeks, 2007, A hybrid meshless local Petrov–Galerkin method for unbounded domains, Comput. Methods Appl. Mech. Engrg., 196, 843, 10.1016/j.cma.2006.06.011 Dehghan, 2008, The meshless local Petrov–Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrödinger equation, Engrg. Anal. Bound. Elem., 32, 10.1016/j.enganabound.2007.11.005 Demendy, 1997, A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers, Acta Mech., 123, 135, 10.1007/BF01178406 Gold, 1965, Magnetohydrodynamic pipe flow, Part 1, J. Fluid Mech., 21, 577 Gupta, 1972, Unsteady MHD flow in a rectangular channel under transverse magnetic field, Indian J. Pure Appl. Math., 3, 1038 Hu, 2006, A modified meshless local Petrov–Galerkin method to elasticity problems in computer modeling and simulation, Engrg. Anal. Bound. Elem., 30, 399, 10.1016/j.enganabound.2005.12.002 Li, 2005, A locking-free meshless local Petrov–Galerkin formulation for thick and thin plates, J. Comput. Phys., 208, 116, 10.1016/j.jcp.2005.02.008 Liu, 2006, A simple and less-costly meshless local Petrov–Galerkin (MLPG) method for the dynamic fracture problem, Engrg. Anal. Bound. Elem., 30, 72, 10.1016/j.enganabound.2005.09.002 Long, 2006, A new meshless method based on MLPG for elastic dynamic problems, Engrg. Anal. Bound. Elem., 30, 43, 10.1016/j.enganabound.2005.09.001 Pecher, 2006, Efficient cubature formulae for MLPG and related methods, Int. J. Numer. Meth. Engrg., 65, 566, 10.1002/nme.1458 Qian, 2005, Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov–Galerkin method, Comput. Mech., 35, 214, 10.1007/s00466-004-0617-6 Ramos, 1990, Finite difference and finite element methods for MHD channel flows, Int. J. Numer. Meth. Fluids, 11, 907, 10.1002/fld.1650110614 Salah, 2001, A finite element method for magnetohydrodynamic, Comput. Methods Appl. Mech. Engrg., 190, 5867, 10.1016/S0045-7825(01)00196-7 Sellountos, 2005, A MLPG(LBIE) approach in combination with BEM, Comput. Methods Appl. Mech. Engrg., 164, 859, 10.1016/j.cma.2004.06.007 Seungsoo, 1991, Magnetohydrodynamic steady flow computation in three dimensions, Int. J. Numer. Meth. Fluids, 13, 917, 10.1002/fld.1650130709 Shercliff, 1953, Steady motion of conducting fluids in pipes under transverse magnetic fields, Proc. Camb. Phil. Soc., 49, 136, 10.1017/S0305004100028139 Shercliff, 1956, The flow of conducting fluids in circular pipes under transverse magnetic fields, J. Fluid Mech., 1, 644, 10.1017/S0022112056000421 Shercliff, 1962, Magnetohydrodynamic pipe flow. Part 2. high Hartmann number, J. Fluid Mech., 13, 634, 10.1017/S0022112062231497 Sheu, 2004, Development of a convection–diffusion–reaction magnetohydrodynamic solver on nonstaggered grids, Int. J. Numer. Meth. Fluids, 45, 1209, 10.1002/fld.738 Singh, 1978, MHD axial flow in a triangular pipe under transverse magnetic field, Indian J. Pure Appl. Math., 18, 101 Singh, 1984, Finite element method of MHD channel flow with arbitrary wall conductivity, J. Math. Phys. Sci., 18, 501 Singh, 1982, Finite element method in MHD channel flow problems, Int. J. Numer. Meth. Eng., 18, 1091, 10.1002/nme.1620180714 Singh, 1984, Finite element method for unsteady MHD flow through pipes with arbitrary wall conductivity, Int. J. Numer. Meth. Fluids, 4, 291, 10.1002/fld.1650040307 Sladek, 2007, Heat conduction analysis of 3-D axisymmetric and anisotropic FGM bodies by meshless local Petrov–Galerkin method, Comput. Mech., 39, 323, 10.1007/s00466-006-0031-3 Sladek, 2006, Inverse heat conduction problems by meshless local Petrov–Galerkin method, Engrg. Anal. Bound. Elem., 30, 650, 10.1016/j.enganabound.2006.03.003 Sladek, 2006, Meshless local Petrov–Galerkin method for continuously nonhomogeneous linear viscoelastic solids, Comput. Mech., 37, 279, 10.1007/s00466-005-0715-0 Tezer-Sezgin, 1994, Boundary element method solution of MHD flow in a rectangular duct, Int. J. Numer. Meth. Fluids, 18, 937, 10.1002/fld.1650181004 Tezer-Sezgin, 2008, Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field, Comput. Mech., 41, 769, 10.1007/s00466-006-0139-5 Tezer-Sezgin, 2006, Solution of magnetohydrodynamic flow problems using the boundary element method, Eng. Anal. Bound. Elem., 30, 411, 10.1016/j.enganabound.2005.12.001 Tezer-Sezgin, 1989, Finite element method for solving MHD flow in a rectangular duct, Int. J. Numer. Meth. Eng., 28, 445, 10.1002/nme.1620280213 Vavourakis, 2008, A MLPG(LBIE) numerical method for solving 2D incompressible and nearly incompressible elastostatic problems, Commun. Numer. Meth. Engrg., 24, 281, 10.1002/cnm.965 Verardi, 2002, The element-free Galerkin method applied to the study of fully developed magnetohydrodynamic duct flows, IEEE Trans. Magnetics, 38, 941, 10.1109/20.996242 Verardi, 2003, The application of interpolating MLS approximations to the analysis of MHD flows, Finite Elements Anal. Des., 39, 1173, 10.1016/S0168-874X(02)00163-4 Xiao, 2005, Meshless solutions of 2D contact problems by subdomain variational inequality and MLPG method with radial basis functions, Engrg. Anal. Bound. Elem., 29, 95, 10.1016/j.enganabound.2004.12.004