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• W2972793628 abstract "In this article we study a globally modified Allen–Cahn–Navier–Stokes system in a three-dimensional domain. The model consists of the globally modified Navier–Stokes equations proposed in (Adv. Nonlinear Stud. 6 (2006) 411–436) for the velocity, coupled with an Allen–Cahn model for the order (phase ) parameter. We discretize these equations in time using the implicit Euler scheme and we prove that the approximate solution is uniformly bounded. We also show that the sequence of the approximate solutions of the globally modified Allen–Cahn–Navier–Stokes system converges, as the parameter N goes to infinity, to the solution of the corresponding discrete two-phase flow system. Using the uniform stability of the scheme and the theory of the multi-valued attractors, we then prove that the discrete attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero." @default.
• W2972793628 created "2019-09-19" @default.
• W2972793628 creator A5015570716 @default.
• W2972793628 creator A5038797984 @default.
• W2972793628 creator A5083853363 @default.
• W2972793628 date "2020-06-08" @default.
• W2972793628 modified "2023-09-27" @default.
• W2972793628 title "Long-time stability of the implicit Euler scheme for a three dimensional globally modified two-phase flow model" @default.
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• W2972793628 doi "https://doi.org/10.3233/asy-191559" @default.
• W2972793628 hasPublicationYear "2020" @default.
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