Discrete energy balance equation via a symplectic second-order method for two-phase flow in porous media

Giselle Sosa Jones and Catalin Trenchea

Applied Mathematics and Computation, 2024, vol. 480, issue C

Abstract: We propose and analyze a second-order partitioned time-stepping method for a two-phase flow problem in porous media. The algorithm is a refactorization of Cauchy's one-leg θ-method: the implicit backward Euler method on [tn,tn+θ], and a linear extrapolation on [tn+θ,tn+1]. In the backward Euler step, the decoupled equations are solved iteratively, with the iterations converging linearly. In the absence of the chain rule for time-discrete setting, we approximate the change in the free energy by the product of a second-order accurate discrete gradient (chemical potential) and the one-step increment of the state variables. Similar to the continuous case, we also prove a discrete Helmholtz free energy balance equation, without numerical dissipation. In the numerical tests we compare this symplectic implicit midpoint method (θ=1/2) with the classic backward Euler method, and two implicit-explicit time-lagging schemes. The midpoint method outperforms the other schemes in terms of rates of convergence, long-time behavior and energy approximation, for both small and large values of the time step.

Keywords: Symplectic time integrators; Two-phase flow in porous media; Helmholtz free energy (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:480:y:2024:i:c:s0096300324003709

DOI: 10.1016/j.amc.2024.128909

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