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

verfasst von: 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.
Organisationseinheit(en): Institut für Angewandte Mathematik
Externe Organisation(en): Amirkabir University of Technology
University of Birmingham
Keele University
Technische Universität Wien (TUW)
Typ: Artikel
Journal: Computers and Mathematics with Applications
Band: 179
Seiten: 197-211
Anzahl der Seiten: 15
ISSN: 0898-1221
Publikationsdatum: 01.02.2025
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Modellierung und Simulation, Theoretische Informatik und Mathematik, Computational Mathematics
Elektronische Version(en): https://doi.org/10.1016/j.camwa.2024.12.011 (Zugang: Geschlossen)

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.",
}