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Optimal Switching Time Control Constrained by Immiscible Two-Phase Porous Media Flow Based on the Discontinuous Galerkin Method

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Abstract

This paper presents a gradient-based approach for solving a switching time control problem under the two-phase porous media flow within petroleum extraction. The primary goal is to find an optimal switching time strategy that will maximize the net present value over a predetermined production period. To achieve this aim, a combination of Lagrangian techniques and variational methods is used to handle the proposed optimal control system, followed by the state equations, adjoint equations and the control strategy. The fully implicit discontinuous Galerkin methods are then used to solve the state and adjoint equations in the optimal control problem. Then the optimal switching directions for adjusting the timing of the switching instants to achieve optimality are obtained. The proposed numerical schemes are finally applied to several numerical examples, which further demonstrate that our propose methods are effective and feasible for the purpose of maximizing the net present value.

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Funding

Projects supported by the National Natural Science Foundation of China Grant Nos.12131014,12001325.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China

    Decheng Kong, Hongxing Rui & Wenju Zhao

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  1. Decheng Kong
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  2. Hongxing Rui
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Correspondence to Hongxing Rui.

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Kong, D., Rui, H. & Zhao, W. Optimal Switching Time Control Constrained by Immiscible Two-Phase Porous Media Flow Based on the Discontinuous Galerkin Method. J Sci Comput 99, 72 (2024). https://doi.org/10.1007/s10915-024-02538-w

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