Publicación: Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method
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2022-01-21
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info:eu-repo/semantics/openAccess
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MDPI
Resumen
The applications of the Eikonal and stationary heat transfer equations in broad fields of science and engineering are the motivation to present an implementation, not only valid for structured domains but also for completely irregular domains, of the meshless Generalized Finite Difference Method (GFDM). In this paper, the fully non-linear Eikonal equation and the stationary heat transfer equation with variable thermal conductivity and source term are solved in 2D. The explicit formulae for derivatives are developed and applied to the equations in order to obtain the numerical schemes to be used. Moreover, the numerical values that approximate the functions for the considered domain are obtained. Numerous examples for both equations on irregular 2D domains are exposed to underline the effectiveness and practicality of the method.
Descripción
La versión registrada de este artículo, publicado por primera vez en Mathematics. 2022; 10(3):332, está disponible en línea en el sitio web del editor: https://doi.org/10.3390/math10030332
The copyrighted version of this article, first published in Mathematics. 2022; 10(3):332, is available online at the publisher's website: https://doi.org/10.3390/math10030332
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Palabras clave
generalized finite difference method, eikonal equation, heat transfer equation, meshless methods, Newton–Raphson
Citación
Flores J, García Á, Negreanu M, Salete E, Ureña F, Vargas AM. Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method. Mathematics. 2022; 10(3):332. https://doi.org/10.3390/math10030332
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Facultades y escuelas::E.T.S. de Ingenieros Industriales
Departamento
Ingeniería de Construcción y Fabricación