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Local meshless method for convection dominated steady and unsteady partial differential equations

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Abstract

In this paper, we propose a mildly shock-capturing stabilized local meshless method (SLMM) for convection-dominated steady and unsteady PDEs. This work is extension of the numerical procedure, which was designed only for steady state convection-dominated PDEs (Siraj-ul-Islam and Singh in Int J Comput Methods 14(6):1750067, 2017). The proposed meshless methodology is based on employing different type of stencils embodying the already known flow direction. Numerical experiments are performed to compare the proposed method with the finite-difference method on special grid (FDSG) and other numerical methods. Numerical results confirm that the new approach is accurate and efficient for solving a wide class of one- and two- dimensional convection-dominated PDEs having sharp corners and jump discontinuities. Performance of the SLMM is found better in some cases and comparable in other cases, than the mesh-based numerical methods.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Computer Science, South Asian University, New Delhi, India

    Vikendra Singh & R. K. Mohanty

  2. Department of Basic Sciences, Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan

    Siraj-ul-Islam

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  1. Vikendra Singh
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  2. Siraj-ul-Islam
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  3. R. K. Mohanty
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Correspondence to Vikendra Singh or Siraj-ul-Islam.

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Singh, V., Siraj-ul-Islam & Mohanty, R.K. Local meshless method for convection dominated steady and unsteady partial differential equations. Engineering with Computers 35, 803–812 (2019). https://doi.org/10.1007/s00366-018-0632-4

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  • DOI: https://doi.org/10.1007/s00366-018-0632-4

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