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An explicit meshless point collocation method for electrically driven magnetohydrodynamics (MHD) flow

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  • Bourantas, G.C.
  • Loukopoulos, V.C.
  • Joldes, G.R.
  • Wittek, A.
  • Miller, K.

Abstract

In this paper, we develop a meshless collocation scheme for the numerical solution of magnetohydrodynamics (MHD) flow equations. We consider the transient laminar flow of an incompressible, viscous and electrically conducting fluid in a rectangular duct. The flow is driven by the current produced by electrodes placed on the walls of the duct. The method combines a meshless collocation scheme with the newly developed Discretization Corrected Particle Strength Exchange (DC PSE) interpolation method. To highlight the applicability of the method, we discretize the spatial domain by using uniformly (Cartesian) and irregularly distributed nodes. The proposed solution method can handle high Hartmann (Ha) numbers and captures the boundary layers formed in such cases, without the presence of unwanted oscillations, by employing a local mesh refinement procedure close to the boundaries. The use of local refinement reduces the computational cost. We apply an explicit time integration scheme and we compute the critical time step that ensures stability through the Gershgorin theorem. Finally, we present numerical results obtained using different orientation of the applied magnetic field.

Suggested Citation

  • Bourantas, G.C. & Loukopoulos, V.C. & Joldes, G.R. & Wittek, A. & Miller, K., 2019. "An explicit meshless point collocation method for electrically driven magnetohydrodynamics (MHD) flow," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 215-233.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:215-233
    DOI: 10.1016/j.amc.2018.11.054
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    Cited by:

    1. Badday, Alaa Jabbar & Harfash, Akil J., 2022. "Magnetohydrodynamic instability of fluid flow in a porous channel with slip boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Li, Xiang & Yu, Peng & Niu, Xiao-Dong & Li, De-Cai & Yamaguchi, Hiroshi, 2021. "A magnetic field coupling lattice Boltzmann model and its application on the merging process of multiple-ferrofluid-droplet system," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    3. Li, Xiaolin & Dong, Haiyun, 2025. "Analysis of a stabilized element-free Galerkin method for magnetohydrodynamic flow at very large Hartmann numbers," Applied Mathematics and Computation, Elsevier, vol. 495(C).

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