A reproducing kernel particle method (RKPM) algorithm for solving the tropical Pacific Ocean model

Abbaszadeh, Mostafa; Parvizi, Maryam; Khodadadian, Amirreza; Wick, Thomas; Dehghan, Mehdi

Abstract

Meshless methods have become increasingly popular for solving a wide range of problems in both solid and fluid mechanics. In this study, we focus on a meshless numerical approach to solve the tropical Pacific Ocean model, which captures the horizontal velocity and layer thickness of ocean waves, using an advanced meshless Galerkin technique known as the reproducing kernel particle method (RKPM). To address the temporal component in this scheme, we apply a Crank-Nicolson finite difference method, resulting in a semi-discrete formulation. For spatial discretization, we use a kernel-based meshless Galerkin method that integrates the strengths of finite element methods with reproducing kernel particle approximations. We conduct a comprehensive stability analysis and provide an a priori estimate for the semi-discrete solution. Furthermore, we derive error estimates for both the semi-discrete and fully discrete solutions. Finally, we validate the theoretical findings and evaluate the method's efficiency through real-world test cases.

Citation

Abbaszadeh, M., Parvizi, M., Khodadadian, A., Wick, T., & Dehghan, M. (in press). A reproducing kernel particle method (RKPM) algorithm for solving the tropical Pacific Ocean model. Computers and Mathematics with Applications, 179, 197-211. https://doi.org/10.1016/j.camwa.2024.12.011

• Journal Article Type: Article
• Acceptance Date: Dec 16, 2024
• Online Publication Date: Dec 27, 2024
• Deposit Date: Mar 19, 2025
• Journal: Computers & Mathematics with Applications
• Print ISSN: 0898-1221
• Electronic ISSN: 1873-7668
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 179
• Pages: 197-211
• DOI: https://doi.org/10.1016/j.camwa.2024.12.011
• Keywords: Tropical Pacific Ocean, Reproducing kernel particle method (RKPM), Meshless Galerkin method, Error analysis, Ocean wave dynamics
• Public URL: https://keele-repository.worktribe.com/output/1043921