Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

Computational Mechanics

Volumn 47, Issue 2, 2011, Pages 137-159

  Loukopoulos, V C ^a   Bourantas, G C ^b   Skouras, E D ^a,c   Nikiforidis, G C ^b  

^a UNIVERSITY OF PATRAS   (Greece)

^b UNIVERSITY OF PATRAS   (Greece)

^c INSTITUTE OF CHEMICAL ENGINEERING SCIENCES   (Greece)

Author keywords

LBIE; Local meshless point collocation; MLPG; Moving least squares; Unsteady MHD; Wall conductivity

Indexed keywords

BOUNDARY INTEGRAL EQUATIONS; INTEGRAL EQUATIONS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

LBIE; LOCAL BOUNDARY INTEGRAL EQUATIONS; MAGNETOHYDRODYNAMICS FLOWS; MESHLESS LOCAL PETROV-GALERKIN METHOD; MLPG; MOVING LEAST SQUARES; MOVING LEAST SQUARES APPROXIMATION; POINT COLLOCATION;

LEAST SQUARES APPROXIMATIONS;

EID: 79951551309     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-010-0535-8     Document Type: Article

References (40)

1. J Hartmann 1937 Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field Math Fys Med 6 15
2. RR Gold 1953 Magnetohydrodynamic pipe flow Part 1 J Fluid Mech 21 577 590
3. JA Shercliff 1953 Steady motion of conducting fluids in pipes under transverse magnetic fields Proc Camb Phil Soc 49 136 144 0050.19404 10.1017/S0305004100028139 52261
4. B Singh J Lal 1978 MHD axial flow in a triangular pipe under transverse magnetic field Ind J Pure Appl Math 9 101 115 468614
5. B Singh J Lal 1979 MHD axial flow in a triangular pipe under transverse magnetic field parallel to a side of the triangle Ind J Technol 17 184 189 0413.76094 (Pubitemid 10455535)
6. B Singh J Lal 1982 Finite element method in MHD channel flow problems Int J Numer Methods Eng 18 1104 1111 0489.76119 10.1002/nme.1620180714
7. B Singh J Lal 1984 Finite element method of MHD channel flow with arbitrary wall conductivity J Math Phys Sci 18 501 516 0574.76117
8. LRT Gardner GA Gardner 1995 A two-dimensional bi-cubic B-spline finite element used in a study of MHD duct flow Comput Methods Appl Mech Eng 124 365 375 10.1016/0045-7825(94)00760-K
9. M Tezer-Sezgin S Köksal 1989 Finite element method for solving MHD flow in a rectangular duct Int J Numer Methods Eng 28 445 459 0669.76140 10.1002/nme.1620280213
10. Z Demendy T Nagy 1997 A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers Acta Mech 123 135 149 0902.76058 10.1007/BF01178406 (Pubitemid 127539008)
11. KE Barrett 2001 Duct flow with a transverse magnetic field at high Hartmann numbers Int J Numer Methods Eng 50 1893 1906 0998.76045 10.1002/nme.101 (Pubitemid 32329293)
12. C Bozkaya M Tezer-Sezgin 2007 Fundamental solution for coupled magnetohydrodynamic flow equations J Comput Appl Math 203 125 144 1172.76383 10.1016/j.cam.2006.03.013 2313825 (Pubitemid 46349471)
13. B Singh PK Agarwal 1984 Numerical solution of a singular integral equation appearing in MHD ZAMP 35 760 769 0559.76109 10.1007/BF00945441
14. M Tezer-Sezgin 1994 BEM solution of MHD flow in a rectangular duct Int J Numer Methods Fluids 18 937 952 0814.76063 10.1002/fld.1650181004
15. HW Liu SP Zhu 2002 The dual reciprocity boundary element method for magnetohydrodynamic channel flows ANZIAM J 44 305 322 1017.76059 10.1017/S1446181100013961 1933303 (Pubitemid 44229221)
16. M Tezer-Sezgin SH AydIn 2002 Dual reciprocity BEM for MHD flow using radial basis functions Int J Comput Fluid Dyn 16 49 63 1082.76580 10.1080/10618560290004026 1885032
17. A Carabineanu A Dinu I Oprea 1995 The application of the boundary element method to the magnetohydrodynamic duct flow ZAMP 46 971 981 0836.76053 10.1007/BF00917881 1365073 (Pubitemid 126005293)
18. AI Nesliturk M Tezer-Sezgin 2005 The finite element method for MHD flow at high Hartmann numbers Comput Methods Appl Mech Eng 194 1201 1224 1091.76036 10.1016/j.cma.2004.06.035 2116608 (Pubitemid 40133566)
19. B Singh J Lal 1984 Finite element method for unsteady MHD flow through pipes with arbitrary wall conductivity Int J Numer Methods Fluids 4 291 302 0547.76119 10.1002/fld.1650040307 (Pubitemid 14565564)
20. NB Salah A Soulaimani WG Habashi 2001 A finite element method for magnetohydrodynamic Comput Methods Appl Mech Eng 190 5867 5892 1044.76030 10.1016/S0045-7825(01)00196-7 (Pubitemid 32808585)
21. L Seungsoo GS Dulikravich 1991 Magnetohydrodynamic steady flow computation in three dimensions Int J Numer Methods Fluids 13 917 936 0741.76049 10.1002/fld.1650130709
22. TWH Sheu RK Lin 2004 Development of a convection-diffusion-reaction magnetohydrodynamic solver on non-staggered grids Int J Numer Methods Fluids 45 1209 1233 1060.76619 10.1002/fld.738 2072226 (Pubitemid 39047759)
23. C Bozkaya M Tezer-Sezgin 2006 Boundary element method solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme Int J Numer Methods Fluids 51 567 584 1089.76040 10.1002/fld.1131 2227588 (Pubitemid 43899190)
24. T Belytschko Y Krongauz D Organ M Fleming P Krysl 1996 Meshless methods; an overview and recent developments Comput Meth Appl Mech Eng 139 3 47 0891.73075 10.1016/S0045-7825(96)01078-X (Pubitemid 126382692)
25. GC Bourantas ED Skouras VC Loukopoulos GC Nikiforidis 2009 An accurate, stable and efficient domain-type meshless method for the solution of MHD flow problems J Comput Phys 228 8135 8160 05615476 10.1016/j.jcp.2009.07.031 2573349
26. SLL Verardi JM Machado Y Shiyou 2003 The application of interpolating MLS approximations to the analysis of MHD flows Fin Elem Anal Design 39 1173 1187 10.1016/S0168-874X(02)00163-4
27. M Dehghan D Mirzaei 2009 Meshless local boundary integral equation (LBIE) method for the unsteady magnetohydrodynamic (MHD) flow in rectangular and circular pipes Comput Phys Commun 180 1458 1466 10.1016/j.cpc.2009.03.007 2678417
28. M Dehghan D Mirzaei 2009 Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity Appl Numer Math 59 1043 1058 1159.76034 10.1016/j.apnum.2008.05.001 2495137
29. Liu GR, Gu YT (2005) An introduction to Meshfree methods and their programming. Springer, Berlin
30. NR Aluru 2000 A point collocation method based on reproducing kernel approximations Int J Numer Methods Eng 47 1083 1121 0960.74078 10.1002/(SICI)1097-0207(20000228)47:6<1083::AID-NME816>3.0.CO;2-N (Pubitemid 30542455)
31. Dragos L (1975) Magneto-fluid dynamics. Academic Press, England
32. Liu GR (2002) Mesh free methods, moving beyond the finite elements method. CRC Press, Boca Raton
33. P Lancaster K Salkauskas 1981 Surface generated by moving least squares methods Math Comp 37 141 158 0469.41005 10.1090/S0025-5718-1981-0616367-1 616367
34. JG Wang GR Liu 2002 A point interpolation meshless method based on radial basis functions Int J Numer Methods Eng 54 1623 1648 1098.74741 10.1002/nme.489 (Pubitemid 34842350)
35. YS Kim DW Kim SK Jun JH Lee 2007 Meshfree point collocation method for the stream-vorticity formulation of 2D incompressible Navier-Stokes equations Comput Methods Appl Mech Eng 196 3095 3109 1173.76386 10.1016/j.cma.2007.01.018 2330770 (Pubitemid 46804390)
36. DW Kim YS Kim 2003 Point collocation methods using the fast moving least square reproducing kernel approximation Int J Numer Methods Eng 56 1445 1464 1054.76066 10.1002/nme.618 (Pubitemid 36339865)
37. GC Bourantas ED Skouras GC Nikiforidis 2009 Adaptive support domain implementation on the moving least squares approximation for mfree methods applied on elliptic and parabolic pde problems using strong-form description Comput Model Eng Sci 43 1 25 2536222
38. DW Kim WK Liu 2006 Maximum principle and convergence analysis for the meshfree point collocation method Siam J Numer Anal 44 515 539 1155.65090 10.1137/04060809X 2218958 (Pubitemid 46622335)
39. YT Gu GR Liu 2006 Meshless techniques for convection dominated problems Comput Mech 38 171 182 1138.76402 10.1007/s00466-005-0736-8 2229263
40. M Tezer-Sezgin SH AydIn 2006 Solution of magnetohydrodymanic flow problems using the boundary element method Eng Anal Bound Elem 30 411 418 1187.76703 10.1016/j.enganabound.2005.12.001 (Pubitemid 44308081)