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

authored by: Mostafa Abbaszadeh, Maryam Parvizi, Amirreza Khodadadian, Thomas Wick, Mehdi Dehghan
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.
Organisation(s): Institute of Applied Mathematics
External Organisation(s): Amirkabir University of Technology
University of Birmingham
Keele University
TU Wien (TUW)
Type: Article
Journal: Computers and Mathematics with Applications
Volume: 179
Pages: 197-211
No. of pages: 15
ISSN: 0898-1221
Publication date: 01.02.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Computational Theory and Mathematics, Computational Mathematics
Electronic version(s): https://doi.org/10.1016/j.camwa.2024.12.011 (Access: Closed)

BibTeX

@article{15b80b435ca2430f8ce5364a47e56459,
title = "A reproducing kernel particle method (RKPM) algorithm for solving the tropical Pacific Ocean model",
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.",
keywords = "Error analysis, Meshless Galerkin method, Ocean wave dynamics, Reproducing kernel particle method (RKPM), Tropical Pacific Ocean",
author = "Mostafa Abbaszadeh and Maryam Parvizi and Amirreza Khodadadian and Thomas Wick and Mehdi Dehghan",
note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Ltd",
year = "2025",
month = feb,
day = "1",
doi = "10.1016/j.camwa.2024.12.011",
language = "English",
volume = "179",
pages = "197--211",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Ltd.",
}