A new finite volume approach for transport models and related applications with balancing source terms

Autor(es)

Abreu, E. ; Lambert, W. ; Perez, J. ; Santo, A.

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICS AND COMPUTERS IN SIMULATION; v. 137, p. 27-pg., 2017-07-01.

Resumo

We develop a new finite volume scheme for numerically solving transport models associated with hyperbolic problems and balance laws. The numerical scheme is obtained via a Lagrangian Eulerian approach that retains the fundamental principle of conservation of the governing equations as it is linked to the classical finite volume framework. As features of the novel algorithm we highlight: the new scheme is locally conservative in balancing the flux and source term gradients and preserves a component wise structure at a discrete level for systems of equations. The novel approach is applied to several nontrivial examples to evidence that we are calculating the correct qualitatively good solutions with accurate resolution of small perturbations around the stationary solution. We discuss applications of the new method to classical and nonclassical nonlinear hyperbolic conservation and balance laws such as the classical inviscid Burgers equation, two-phase and three-phase flow problems in porous media as well as numerical experiments for nonlinear shallow water equations with friction terms. In addition, we consider the case of the source term which is discontinuous as a function of space x. We also extend the Lagrangian Eulerian framework to the two-dimensional scalar conservation law, along with pertinent numerical experiments to show the performance of the new method. (C) 2017 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 11/23628-0 - Sistemas de Leis de Balanço em Problemas de Dinâmica de Fluidos em Meios Porosos: Modelagem Matemática e Aproximação Numérica
• Beneficiário: Abel Alvarez Bustos
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 14/03204-9 - Computando aproximações qualitativamente corretas de equações diferenciais parciais em fenômenos de transporte em meios porosos
• Beneficiário: Eduardo Cardoso de Abreu
• Modalidade de apoio: Auxílio à Pesquisa - Regular