Lagrangian-Eulerian approximation methods for balance laws and hyperbolic conservation laws

• Autores: Eduardo Abreu, Jhon Pérez, Arthur Santo
• Localización: Revista UIS Ingenierías, ISSN-e 2145-8456, ISSN 1657-4583, Vol. 17, Nº. 1, 2018 (Ejemplar dedicado a: Revista UIS Ingenierías), págs. 191-200
• Idioma: inglés
• DOI: 10.18273/revuin.v17n1-2018018
• Títulos paralelos:
  • Métodos de aproximación Lagrangiano-Eulerianos para leyes de equilibrio y leyes de conservación hiperbólicas
• Enlaces
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• Resumen
  • español

    Un nuevo volumen finito de control es presentado en un enfoque Lagrangiano-Euleriano (ver artículos [1, 28]), en este, un dominio de espacio-tiempo es estudiado con el fin de diseñar un esquema localmente conservativo. Tal esquema tiene en cuenta el delicado balance no linear, entre las aproximaciones numéricas del flujo hiperbólico y el término fuente, en problemas de ley de balance ligados con leyes de conservación puramente hiperbólicas. Además, combinando algunas ideas de este nuevo enfoque, hacemos una construcción formal de un nuevo algoritmo para resolver importantes problemas de leyes de conservación en dos dimensiones espaciales. Un conjunto pertinente de experimentos numéricos para diferentes modelos es presentado para mostrar evidencia que soluciones cualitativamente correctas son aproximadas. 

  • English

    A new finite control volume in a Lagrangian-Eulerian framework is presented (see papers [1, 28]), in which a local space-time domain is studied, in order to design a locally conservative scheme. Such scheme accounts for the delicate nonlinear balance between the numerical approximations of the hyperbolic flux and the source term for balance law problems linked to the purely hyperbolic character of conservation laws. Furthermore, by combining the ideas of this new approach, we give a formal construction of a new algorithm for solving several nonlinear hyperbolic conservation laws in two space dimensions. Here, a set of pertinent numerical experiments for distinct models is presented to evidence that we are calculating the correct qualitatively good solutions. 

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