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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Abreu, Eduardo [1] ; Perez, John [2]
Total Authors: 2
[1] Univ Estadual Campinas, Dept Appl Math, BR-13083970 Campinas, SP - Brazil
[2] ITM Univ Inst, Calle 73 76A-354 Via Volador, Medellin - Colombia
Total Affiliations: 2
Document type: Journal article
Source: COMPUTERS & MATHEMATICS WITH APPLICATIONS; v. 77, n. 9, p. 2310-2336, MAY 1 2019.
Web of Science Citations: 0

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)

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 type: Regular Research Grants