Simulation of multiphase porous media flows with minimising movement and finite volume schemes

• Published in: European journal of applied mathematics Vol. 30; no. 6; pp. 1123 - 1152
• Main Authors: CANCÈS, CLÉMENT, GALLOUËT, THOMAS, LABORDE, MAXIME, MONSAINGEON, LÉONARD
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 01.12.2019; Cambridge University Press (CUP)
• Subjects: Analysis of PDEs; Applied mathematics; Augmented Lagrangian methods; Computer simulation; Constrained optimization; Finite volume method; Finite volume schemes; Flows in porous media; Gradient flow; Lagrange multipliers; Mathematics; Mathématiques; Multiphase flow; Multiphase porous media; Multiphase porous media flows; Numerical Analysis; Numerical results; Partial differential; Partial differential equations; Physical, chemical, mathematical & earth Sciences; Physique, chimie, mathématiques & sciences de la terre; Porous materials; Porous media; Stability; Wasserstein gradient flow; Augmented Lagrangian method; Multiphase porous media flows; Finite Volumes AMS subjects classification; Wasserstein gradient flow; minimizing movement scheme
• ISSN: 0956-7925; 1469-4425; 1469-4425
• DOI: 10.1017/S0956792518000633

The Wasserstein gradient flow structure of the partial differential equation system governing multiphase flows in porous media was recently highlighted in Cancès et al. [ Anal. PDE 10 (8), 1845–1876]. The model can thus be approximated by means of the minimising movement (or JKO after Jordan, Kinderlehrer and Otto [ SIAM J. Math. Anal. 29 (1), 1–17]) scheme that we solve thanks to the ALG2-JKO scheme proposed in Benamou et al. [ ESAIM Proc. Surv. 57 , 1–17]. The numerical results are compared to a classical upstream mobility finite volume scheme, for which strong stability properties can be established.