A fast, robust, and simple Lagrangian-Eulerian solver for balance laws and applications

Autor(es)

Abreu, Eduardo ^[1] ; Perez, John ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Appl Math, BR-13083970 Campinas, SP - Brazil

^[2] ITM Univ Inst, Calle 73 76A-354 Via Volador, Medellin - Colombia

• Tipo de documento: Artigo Científico
• Fonte: COMPUTERS & MATHEMATICS WITH APPLICATIONS; v. 77, n. 9, p. 2310-2336, MAY 1 2019.
• Citações Web of Science: 0

Resumo

In this work, we present an improvement of the Lagrangian-Eulerian space-time tracking forward scheme to deal with balance laws and related applications. This extended algorithm is shown in the most simple setting and it is a result of our previous works. We describe and explain a new strategy of discretization of conservation laws, starting from the scalar case in one space dimension, extending it to systems and to the multi-dimensional setting. The computations are fast, accurate and stable with good resolution. This algorithm is very easy to implement in a computer to address the delicate well-balancing between the first-order hyperbolic flux and the source term. We do not use approximate or exact Riemann solvers, nonlinear reconstructions, or upwind source term discretizations. The scheme is written into the classical theory of monotone schemes, which produces a scheme that converges to entropy solutions linked to the purely hyperbolic counterpart. This method can produce well-balanced approximations of solutions for nonlinear balance laws. Numerical experiments also demonstrate the robustness of the forward tracking to solve related problems involving systems and two-dimensional models. (C) 2018 Elsevier Ltd. All rights reserved. (AU)

• Processo FAPESP: 16/23374-1 - Leis de conservação, leis de equilíbrio e EDPs relacionadas com fluxos descontínuos e não-locais em ciências aplicadas: análise numérica, teoria e aplicações
• Beneficiário: Eduardo Cardoso de Abreu
• Modalidade de apoio: Auxílio à Pesquisa - Regular