ON THE CONSERVATION PROPERTIES IN MULTIPLE SCALE COUPLING AND SIMULATION FOR DARCY FLOW WITH HYPERBOLIC-TRANSPORT IN COMPLEX FLOWS

Autor(es)

Abreu, Eduardo ^[1] ; Diaz, Ciro ^[2] ; Galvis, Juan ^[3] ; Perez, John ^[4]

Afiliação do(s) autor(es)

^[1] Univ Campinas UNICAMP, Dept Appl Math, Inst Math Stat & Sci Comp IMECC, BR-13083970 Campinas, SP - Brazil

^[2] Ryerson Univ, Dept Math, 350 Victoria St, Toronto, ON M5B 2K3 - Canada

^[3] Univ Nacl Colombia, Dept Matemat, Carrera 45 26-85, Edificio Uriel Gutierrez, Bogota - Colombia

^[4] Metropolitan Inst Technol ITM Univ Inst, Calle 73 76A-354 Via Volador, Medellin - Colombia

• Tipo de documento: Artigo Científico
• Fonte: MULTISCALE MODELING & SIMULATION; v. 18, n. 4, p. 1375-1408, 2020.
• Citações Web of Science: 1

Resumo

We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of the following: (1) multiscale heterogeneity structures appearing in the elliptic-pressure-velocity and in the rock geology model and (2) multiscale wave structures resulting from interactions of shock waves and rarefaction from the nonlinear hyperbolic-transport model. For the pressure-velocity Darcy flow problem, we revisit a recent high-order and volumetric residual-based Lagrange multipliers saddle point problem to impose local mass conservation on convex polygons. We clarify and improve conservation properties on applications. For the hyperbolic-transport problem we introduce a new locally conservative Lagrangian-Eulerian finite volume method. For the purpose of this work, we recast our method within the Crandall and Majda treatment of the stability and convergence properties of conservation-form, monotone difference, in which the scheme converges to the physical weak solution satisfying the entropy condition. This multiscale coupling approach was applied to several nontrivial examples to show that we are computing qualitatively correct reference solutions. We combine these procedures for the simulation of the fundamental two-phase flow problem with high-contrast multiscale porous medium, but recalling state-of-the-art paradigms on the notion of solution in related multiscale applications. This is a first step to deal with out-of-reach multiscale systems with traditional techniques. We provide robust numerical examples for verifying the theory and illustrating the capabilities of the approach being presented. (AU)

• Processo FAPESP: 19/20991-8 - Estudo de equações diferenciais parciais algébricas com dominância hiperbólica-parabólica com relaxamento: aspectos teóricos, numéricos e aplicações
• Beneficiário: Eduardo Cardoso de Abreu
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil