A Meshless Radial Point Interpolation Method for Solving Fractional Navier-Stokes Equations

被引：2

作者：

Dabiri, Arman ^{[1
]}

Moghaddam, Behrouz Parsa ^{[2
]}

Taghizadeh, Elham ^{[3
]}

Galhano, Alexandra ^{[4
]}

机构：

[1] Southern Illinois Univ, Dept Mech & Mechatron, Edwardsville, IL 62026 USA

[2] Islamic Azad Univ, Dept Math, Lahijan Branch, Lahijan 4416939515, Iran

[3] Islamic Azad Univ, Dept Math, Cent Tehran Branch, Tehran 1955847781, Iran

[4] Univ Lusofona Porto, Fac Ciencias Nat Engn & Tecnol, Rua Augusto Rosa 24, P-4000098 Porto, Portugal

来源：

AXIOMS | 2024年 / 13卷 / 10期

关键词：

fractional calculus; time-fractional incompressible Navier-Stokes equations; radial point interpolation; shape parameters; meshless method; DIFFERENTIAL-EQUATIONS; SCHEME; WEAK;

D O I：

10.3390/axioms13100695

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper aims to develop a meshless radial point interpolation (RPI) method for obtaining the numerical solution of fractional Navier-Stokes equations. The proposed RPI method discretizes differential equations into highly nonlinear algebraic equations, which are subsequently solved using a fixed-point method. Furthermore, a comprehensive analysis regarding the effects of spatial and temporal discretization, polynomial order, and fractional order is conducted. These factors' impacts on the accuracy and efficiency of the solutions are discussed in detail. It can be shown that the meshless RPI method works quite well for solving some benchmark problems accurately.

引用

页数：16

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