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A stabilized meshless method for time-dependent convection-dominated flow problems

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  • Benkhaldoun, Fayssal
  • Halassi, A.
  • Ouazar, Driss
  • Seaid, Mohammed
  • Taik, Ahmed

Abstract

Meshless methods for convection-dominated flow problems have the potential to reduce the computational effort required for a given order of solution accuracy compared to mesh-based methods. The state of the art in this field is more advanced for elliptic partial differential equations than for time-dependent convection–diffusion problems. In this paper, we introduce a new meshless method that it based on combining the modified method of characteristics with the radial basis functions during the solution reconstruction. The method belongs to a class of fractional time-stepping schemes in which a predictor stage is used for the discretization of convection terms and a corrector stage is used for the treatment of diffusion terms. Special attention is given to the application of this method to solve convection-dominated flow problems in two-dimensional domains. Numerical results are shown for several test examples including the incompressible Navier–Stokes equations and the computed results support our expectations for a stable and highly accurate meshless method.

Suggested Citation

  • Benkhaldoun, Fayssal & Halassi, A. & Ouazar, Driss & Seaid, Mohammed & Taik, Ahmed, 2017. "A stabilized meshless method for time-dependent convection-dominated flow problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 159-176.
    • Handle: RePEc:eee:matcom:v:137:y:2017:i:c:p:159-176
    DOI: 10.1016/j.matcom.2016.11.003
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    Cited by:

    1. Zhijuan Meng & Xiaofei Chi & Lidong Ma, 2022. "A Hybrid Interpolating Meshless Method for 3D Advection–Diffusion Problems," Mathematics, MDPI, vol. 10(13), pages 1-21, June.

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