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Second-Order Decoupled Linear Energy-Law Preserving gPAV Numerical Schemes for Two-Phase Flows in Superposed Free Flow and Porous Media

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Abstract

We propose second-order numerical methods based on the generalized positive auxiliary variable (gPAV) framework for solving the Cahn–Hilliard–Navier–Stokes–Darcy model in superposed free flow and porous media. In the gPAV-reformulated system, we introduce an auxiliary variable according to the modified energy law and take account into the interface conditions between the two subdomains. By implicit-explicit temporal discretization, we develop fully decoupled linear gPAV-CNLF and gPAV-BDF2 numerical methods effected with the Galerkin finite element method. The fully discrete schemes satisfy a modified energy law irrespective of time step size. Plentiful numerical experiments are performed to validate the methods and demonstrate the robustness. The application in filtration systems, the influence of viscous instability, general permeability, curve interface, and different densities are discussed in details to further illustrate the compatibility and applicability of our developed gPAV numerical methods.

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Funding

The first author is partially supported by the NSFC, PR China grant 12371406, Natural Science Foundation of Guangdong Province, PR China 2023A1515010697. The work of the second author was partially supported by the National Science Foundation grants DMS-2310340.

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  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710129, Shaanxi, People’s Republic of China

    Yali Gao

  2. Department of Mathematics, The State University of New York at Buffalo, Buffalo, NY, 14260, USA

    Daozhi Han

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  1. Yali Gao
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Correspondence to Daozhi Han.

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Gao, Y., Han, D. Second-Order Decoupled Linear Energy-Law Preserving gPAV Numerical Schemes for Two-Phase Flows in Superposed Free Flow and Porous Media. J Sci Comput 100, 36 (2024). https://doi.org/10.1007/s10915-024-02576-4

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