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Analysis of a stabilized element-free Galerkin method for magnetohydrodynamic flow at very large Hartmann numbers

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  • Li, Xiaolin
  • Dong, Haiyun

Abstract

A stabilized element-free Galerkin (EFG) method is designed to simulate magnetohydrodynamic (MHD) flow at very large Hartmann numbers. By transforming the MHD flow to two decoupled convection-diffusion problems, residual-based formulas are devised to improve the performance of the standard EFG method damaged by large Hartmann numbers. Error of the stabilized EFG method is discussed in theory. Numerical examples show that this meshless method can produce efficacious solutions for MHD problems with very large Hartmann numbers such as 1016.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:495:y:2025:i:c:s009630032500061x
    DOI: 10.1016/j.amc.2025.129334
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    References listed on IDEAS

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    1. Ding, Rui & Shen, Quan & Yao, Yuan, 2022. "The element-free Galerkin method for the dynamic Signorini contact problems with friction in elastic materials," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    2. Ma, Xiao & Zhou, Bo & Xue, Shifeng, 2022. "A Hermite interpolation element-free Galerkin method for functionally graded structures," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    3. Li, Yancheng & Liu, Cong & Li, Wei & Chai, Yingbin, 2023. "Numerical investigation of the element-free Galerkin method (EFGM) with appropriate temporal discretization techniques for transient wave propagation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    4. 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.
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