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High-Order Bound-Preserving Local Discontinuous Galerkin Methods for Incompressible and Immiscible Two-Phase Flows in Porous Media

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Abstract

In this paper, we develop high-order bound-preserving (BP) local discontinuous Galerkin methods for incompressible and immiscible two-phase flows in porous media, and employ implicit pressure explicit saturation (IMPES) methods for time discretization, which is locally mass conservative for both phases. Physically, the saturations of the two phases, \(S_w\) and \(S_n\), should belong to the range of [0, 1]. Nonphysical numerical approximations may result in instability of the simulation. Therefore, it is necessary to construct a BP technique to obtain physically relevant numerical approximations. However, the saturation does not satisfy the maximum principle, so most of the existing BP techniques cannot be applied directly. The main idea is to apply the positivity-preserving techniques to both \(S_w\) and \(S_n\), respectively, and enforce \(S_w+S_n = 1\) simultaneously. Numerical examples are given to demonstrate the high-order accuracy of the scheme and effectiveness of the BP technique.

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, China

    Xiuhui Guo, Hui Guo & Lulu Tian

  2. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Yang Yang

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Hui Guo and Lulu Tian were supported by National Key R &D Program of China (2023YFA1009003), National Nature Science Foundation of China (12131014, 12371416), the Natural Science Foundation of Shandong Province (ZR2021MA001) and the Fundamental Research Funds for the Central Universities (22CX03025A). Yang Yang was supported by the Simons Foundation 961585.

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Guo, X., Guo, H., Tian, L. et al. High-Order Bound-Preserving Local Discontinuous Galerkin Methods for Incompressible and Immiscible Two-Phase Flows in Porous Media. J Sci Comput 99, 71 (2024). https://doi.org/10.1007/s10915-024-02532-2

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