Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 197-211 |
Seitenumfang | 15 |
Fachzeitschrift | Computers and Mathematics with Applications |
Jahrgang | 179 |
Frühes Online-Datum | 27 Dez. 2024 |
Publikationsstatus | Veröffentlicht - 1 Feb. 2025 |
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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Modellierung und Simulation
- Informatik (insg.)
- Theoretische Informatik und Mathematik
- Mathematik (insg.)
- Computational Mathematics
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in: Computers and Mathematics with Applications, Jahrgang 179, 01.02.2025, S. 197-211.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A reproducing kernel particle method (RKPM) algorithm for solving the tropical Pacific Ocean model
AU - Abbaszadeh, Mostafa
AU - Parvizi, Maryam
AU - Khodadadian, Amirreza
AU - Wick, Thomas
AU - Dehghan, Mehdi
N1 - Publisher Copyright: © 2024 Elsevier Ltd
PY - 2025/2/1
Y1 - 2025/2/1
N2 - 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.
AB - 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.
KW - Error analysis
KW - Meshless Galerkin method
KW - Ocean wave dynamics
KW - Reproducing kernel particle method (RKPM)
KW - Tropical Pacific Ocean
UR - http://www.scopus.com/inward/record.url?scp=85213017833&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2024.12.011
DO - 10.1016/j.camwa.2024.12.011
M3 - Article
AN - SCOPUS:85213017833
VL - 179
SP - 197
EP - 211
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
ER -