A Relaxation Projection Analytical-Numerical Approach in Hysteretic Two-Phase Flows in Porous Media

Author(s)

Abreu, Eduardo ^[1] ; Bustos, Abel ^[2] ; Ferraz, Paola ^[1] ; Lambert, Wanderson ^[3]

Affiliation

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

^[2] Pontificia Univ Javeriana Cali, 118-250 Ave Canasgordas, Cali - Colombia

^[3] Alfenas Fed Univ, ICT MG Rod BR 267, Km 533, Alfenas - Brazil

• Document type: Journal article
• Source: JOURNAL OF SCIENTIFIC COMPUTING; v. 79, n. 3, p. 1936-1980, JUN 2019.
• Web of Science Citations: 0

Abstract

Hysteresis phenomenon plays an important role in fluid flow through porous media and exhibits convoluted behavior that are often poorly understood and that is lacking of rigorous mathematical analysis. We propose a twofold approach, by analysis and computing to deal with hysteretic, two-phase flows in porous media. First, we introduce a new analytical projection method for construction of the wave sequence in the Riemann problem for the system of equations for a prototype two-phase flow model via relaxation. Second, a new computational method is formally developed to corroborate our analysis along with a representative set of numerical experiments to improve the understanding of the fundamental relaxation modeling of hysteresis for two-phase flows. Using the projection method we show the existence by analytical construction of the solution. The proposed computational method is based on combining locally conservative hybrid finite element method and finite volume discretizations within an operator splitting formulation to address effectively the stiff relaxation hysteretic system modeling fundamental two-phase flows in porous media. (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