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

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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. (C) 2018 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)215-233
Number of pages19
JournalApplied Mathematics and Computation
Volume348
Early online date10 Dec 2018
DOIs
Publication statusPublished - 1 May 2019

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Magnetohydrodynamic Flow
Meshless
Magnetohydrodynamics
Collocation Method
Ducts
Local Refinement
Collocation
Laminar flow
Explicit Time Integration
Interpolation
Transient Flow
Boundary layers
Mesh Refinement
Interpolation Method
Laminar Flow
Magnetic fields
Cartesian
Electrodes
Electrode
Fluids

Cite this

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title = "An explicit meshless point collocation method for electrically driven magnetohydrodynamics (MHD) flow",
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. (C) 2018 Elsevier Inc. All rights reserved.",
author = "G.C. Bourantas and V.C. Loukopoulos and G.R. Joldes and A. Wittek and K. Miller",
year = "2019",
month = "5",
day = "1",
doi = "10.1016/j.amc.2018.11.054",
language = "English",
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journal = "Applied Mathematics and Computation",
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TY - JOUR

T1 - An explicit meshless point collocation method for electrically driven magnetohydrodynamics (MHD) flow

AU - Bourantas, G.C.

AU - Loukopoulos, V.C.

AU - Joldes, G.R.

AU - Wittek, A.

AU - Miller, K.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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. (C) 2018 Elsevier Inc. All rights reserved.

AB - 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. (C) 2018 Elsevier Inc. All rights reserved.

U2 - 10.1016/j.amc.2018.11.054

DO - 10.1016/j.amc.2018.11.054

M3 - Article

VL - 348

SP - 215

EP - 233

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -