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Computational Mechanics

, Volume 52, Issue 6, pp 1445–1462 | Cite as

A meshfree weak-strong (MWS) form method for the unsteady magnetohydrodynamic (MHD) flow in pipe with arbitrary wall conductivity

  • Mehdi DehghanEmail author
  • Rezvan Salehi
Original Paper

Abstract

In this paper a meshfree weak-strong (MWS) form method is considered to solve the coupled equations in velocity and magnetic field for the unsteady magnetohydrodynamic flow throFor this modified estimaFor this modified estimaFor this modified estimaugh a pipe of rectangular and circular sections having arbitrary conducting walls. Computations have been performed for various Hartman numbers and wall conductivity at different time levels. The MWS method is based on applying a meshfree collocation method in strong form for interior nodes and nodes on the essential boundaries and a meshless local Petrov–Galerkin method in weak form for nodes on the natural boundary of the domain. In this paper, we employ the moving least square reproducing kernel particle approximation to construct the shape functions. The numerical results for sample problems compare very well with steady state solution and other numerical methods.

Keywords

Unsteady magnetichydrodynamic flow Meshfree method  Weak-strong form Meshless local Petrov–Galerkin method  Moving least square reproducing kernel particle (MLSRKP) approximation 

Notes

Acknowledgments

The authors are very grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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