Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method

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 (GF...

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Detalles Bibliográficos
Autores: Flores, Jesús, García, Ángel, Negreanu, Mihaela, Salete Casino, Eduardo, Ureña, Francisco, Vargas Ureña, Antonio Manuel
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/25122
Acceso en línea:https://hdl.handle.net/20.500.14468/25122
Access Level:acceso abierto
Palabra clave:33 Ciencias Tecnológicas::3310 Tecnología industrial
generalized finite difference method
eikonal equation
heat transfer equation
meshless methods
Newton–Raphson
Descripción
Sumario: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.