Modified picard with multigrid method for two-phase flow problems in rigid porous media

Oliveira, Michely Laís de ; Pinto, Marcio Augusto Villela ; Rodrigo, Carmen (Universidad de Zaragoza) ; Gaspar, Francisco José (Universidad de Zaragoza)

Resumen: Two‐phase flow problems in porous media can be found in several areas, such as Geomechanics, Hydrogeology, Engineering and Biomedicine, for example. Typically, these processes are mathematically modeled by a highly nonlinear system of coupled partial differential equations. The nonlinearity of the system makes the design and implementation of robust numerical solvers a challenging task. In this work we consider the flow of two immiscible and incompressible fluids within a non‐deformable porous medium. A mixed pressure‐saturation formulation is adopted, allowing the transition from the unsaturated to saturated zones and maintaining numerical mass conservation. A cell‐centered finite volume method and an implicit Euler scheme are considered for the spatial and time discretization of the problem. In this work, we propose a solution method for two‐phase flow problems which is based on the combination of the modified Picard linearization method and a very simple cell‐centered multigrid algorithm that performs efficiently even for heterogeneous random media. This is shown in the numerical experiments, where two test problems are presented to demonstrate the robustness of the proposed solver.

Idioma: Inglés

DOI: 10.1002/nme.7397

Año: 2024

Publicado en: International Journal for Numerical Methods in Engineering 125, 5 (2024), e7397 [13 pp.]
ISSN: 0029-5981

Factor impacto JCR: 2.9 (2024)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 26 / 136 = 0.191 (2024) - Q1 - T1
Categ. JCR: ENGINEERING, MULTIDISCIPLINARY rank: 44 / 175 = 0.251 (2024) - Q2 - T1

Factor impacto CITESCORE: 6.1 - Applied Mathematics (Q1) - Engineering (all) (Q1) - Numerical Analysis (Q1)

Factor impacto SCIMAGO: 1.075 - Applied Mathematics (Q1) - Numerical Analysis (Q1) - Engineering (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E2-417R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2019-105574GB-I00
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/PGC2018-099536-A-I00

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)