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Article Dans Une Revue Mathematics and Computers in Simulation Année : 2017

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

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.

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hal-03872879 , version 1 (25-11-2022)

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Fayssal Benkhaldoun, A. Halassi, Driss Ouazar, Mohammed Seaid, Ahmed Taik. A stabilized meshless method for time-dependent convection-dominated flow problems. Mathematics and Computers in Simulation, 2017, 137, pp.159-176. ⟨10.1016/j.matcom.2016.11.003⟩. ⟨hal-03872879⟩
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