A Predictor–Corrector Meshless Based Scheme for Incompressible Navier–Stokes Flows

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In this paper, a predictor–corrector scheme in meshless radial basis functions for solving incompressible Navier–Stokes equations in vorticity–streamfunction formulation is presented. The method is based on a local collocation formulation and does not require either a grid generation or evaluation of an integral. Predictor–corrector techniques are used to evaluate numerical fluxes in the forward–backward stencil parts and a relaxation scheme is investigated in order to reach high order accuracy. The main advantages of this approach are that no mesh generations nor Riemann problem solvers are required during the solution process. Numerical results are shown for several test examples including problems on driven cavity flows, backward-facing step flows and Rayleigh–Benard convection flows. The main focus is to examine the performance of the proposed meshless method for Navier–Stokes problems with high Reynolds number. The obtained results demonstrate its ability to capture the main solution features.

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Financial support provided by Centre National pour la Recherche Scientifique et Technique through the “Projet EuroMéditerranée 3+3/MedLagoon” is gratefully acknowledged. The authors are grateful to the anonymous reviewers for their valuable comments and helpful suggestions which greatly improved the paper’s quality.

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Correspondence to Abdoul-hafar Halassi Bacar.

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Halassi Bacar, A., Ouazar, D. & Taik, A. A Predictor–Corrector Meshless Based Scheme for Incompressible Navier–Stokes Flows. Int. J. Appl. Comput. Math 6, 18 (2020) doi:10.1007/s40819-020-0769-x

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  • Navier–Stokes equations
  • Radial basis functions
  • Predictor–corrector scheme
  • Driven-cavity flow
  • Backward-facing step flows
  • Rayleigh–Benard convection