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

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.

Citation

Benkhaldoun, F., Halassi, A., Ouazar, D., Seaid, M., & Taik, A. (2017). A stabilized meshless method for time-dependent convection-dominated flow problems. Mathematics and Computers in Simulation, 137, 159-176. https://doi.org/10.1016/j.matcom.2016.11.003

• Journal Article Type: Article
• Acceptance Date: Nov 2, 2016
• Online Publication Date: Nov 17, 2016
• Publication Date: 2017-07
• Deposit Date: Oct 29, 2019
• Publicly Available Date: Nov 20, 2024
• Journal: Mathematics and Computers in Simulation
• Print ISSN: 0378-4754
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 137
• Pages: 159-176
• DOI: https://doi.org/10.1016/j.matcom.2016.11.003
• Public URL: https://durham-repository.worktribe.com/output/1316562