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

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Author(s):	Abreu, Eduardo ^[1] ; Perez, John ^[2] ; Santo, Arthur ^[1] Total Authors: 3
Affiliation:	^[1] Univ Estadual Campinas, Inst Math Stat & Sci Comp, Campinas, SP - Brazil ^[2] ITM Inst Univ, Fac Ciencias Exactas & Aplicadas, Medellin - Colombia Total Affiliations: 2
Document type:	Journal article
Source:	UIS INGENIERIAS; v. 17, n. 1, p. 191-200, JAN-JUN 2018.
Web of Science Citations:	2
Abstract
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. (AU)

FAPESP's process:	16/23374-1 - Conservation laws, balance laws and related PDEs with discontinuous and nonlocal fluxes in applied sciences: numerical analysis, theory and applications
Grantee:	Eduardo Cardoso de Abreu
Support Opportunities:	Regular Research Grants