基于流体静力学重构的天然气流动模型的Well-Balanced间断伽辽金方法
A Well-Balanced Discontinuous Galerkin Method Based on Hydrostatic Reconstruction for Real Gas in Pipelines
DOI: 10.12677/AAM.2021.1012469, PDF,    国家自然科学基金支持
作者: 郭 威, 陈子铭, 李 刚*：青岛大学，数学与统计学院，山东 青岛
关键词: 天然气流动模型；间断伽辽金方法；源项；高阶精度；Real Gas in Pipelines； Discontinuous Galerkin Methods； Source Term； High Order Accuracy
摘要: 在本文研究中，我们针对天然气科学与工程领域中天然气流动模型建立了高阶well-balanced间断伽辽金有限元方法。管道中的天然气流动模型精确保持速度为零的定常状态。为了从数值角度上保持该定常状态，我们提出了well-balanced数值流通量以及一种崭新的源项离散，最终建立了高阶间断伽辽金有限元方法。此方法能够在离散状态下精确保持速度为零的定常状态。严格的理论分析以及广泛的数值结果均验证了本方法保持良好的特性。此外，数值实验还验证了该方法对于小扰动具有精确捕捉能力和良好的分辨率。我们相信该方法在天然气科学与工程领域中具有潜在应用前景。
Abstract: In this research, we propose high order well-balanced discontinuous Galerkin methods for real gas in pipelines in the fields of the natural gas science and engineering. The model of real gas in pipelines preserves the steady state exactly. In order to maintain the steady state at the discrete level, we propose to construct the well-balanced numerical fluxes as well as a novel source term approximation. In this article, by means of hydrostatic reconstruction, we build a high order discontinuous Galerkin method, which exactly preserves the steady state, and is characterized by a discharge equal to zero (analogue to hydrostatic equilibrium). Rigorous theoretical analysis as well as extensive numerical results, all validate that the current method preserves the well-balanced property. In addition, numerical experiments are carried out to validate the ability to capture small perturbation of steady state, and high resolutions. We believe that the resulting method has potential applications in the fields of natural gas science and engineering.
文章引用：郭威, 陈子铭, 李刚. 基于流体静力学重构的天然气流动模型的Well-Balanced间断伽辽金方法[J]. 应用数学进展, 2021, 10(12): 4404-4414. https://doi.org/10.12677/AAM.2021.1012469

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