A learned conservative semi-Lagrangian finite volume scheme for transport simulations
A learned conservative semi-Lagrangian finite volume scheme for transport simulations
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DOI：
10.1016/j.jcp.2023.112329
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发表时间：
2023-02
期刊：
影响因子：
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通讯作者：
Yongsheng Chen;Wei Guo;Xinghui Zhong
中科院分区：
文献类型：
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作者：
Yongsheng Chen;Wei Guo;Xinghui Zhong
半拉格朗日（Semi-Lagrangian，SL）格式是求解输运方程的主要数值工具，具有许多优点，已被广泛应用于计算流体力学、等离子体物理模拟、数值天气预报等领域。在这项工作中，我们开发了一种新的机器学习辅助方法来加速传统的SL有限体积（FV）计划。所提出的方案避免了昂贵的上游细胞的跟踪，但试图学习SL离散化的数据，将特定的感应偏置的神经网络，显着简化了算法的实现，并导致提高效率。此外，该方法提供了尖锐的冲击过渡和精度水平，通常需要一个更精细的网格与传统的运输求解器。数值试验表明了该方法的有效性和效率。
Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather prediction, among others. In this work, we develop a novel machine learning-assisted approach to accelerate the conventional SL finite volume (FV) schemes. The proposed scheme avoids the expensive tracking of upstream cells but attempts to learn the SL discretization from the data by incorporating specific inductive biases in the neural network, significantly simplifying the algorithm implementation and leading to improved efficiency. In addition, the method delivers sharp shock transitions and a level of accuracy that would typically require a much finer grid with traditional transport solvers. Numerical tests demonstrate the effectiveness and efficiency of the proposed method.