一种改进型内嵌特征压缩机制的智能间断指示器

A Modified Characteristic-Compression Embedded Discontinuity Indicator Based on Artificial Intelligence

高精度高分辨率数值格式是模拟高速含激波复杂流动最有效的计算方法之一,而其中对于激波等间断结构的捕捉和辨识,是设计鲁棒的高精度高分辨率数值格式的关键问题之一。借助先验的数理知识及人工神经网络(artificial neural network,ANN)方法,构造了一种改进型内嵌“特征压缩”机制的智能间断指示器,以提高高精度格式框架下间断捕捉的精准度。该间断指示器模型是通过借助先验的数学物理知识进行预建模,然后借助数据驱动方法学习模型中的待定参数而得到。这使得间断指示器模型形式简洁,在训练过程中具有小样本依赖的优势,还使训练后的模型具备计算复杂度低、数理可解释等优秀性质,且其一维形式可以自然地推广到高维非结构网格下的方程组中。已证明该间断指示器模型包含两种间断捕捉机制,即基于特征压缩的激波捕捉机制和基于大梯度跳跃的膨胀波起点、接触间断捕捉机制。一系列数值实验结果验证了所构造的间断指示器对于流场不同间断类型的捕捉精准性。

The high-order and high-resolution numerical schemes are one of the most effective computational methods for simulating high-speed complex flows with shock waves,and the detection of discontinuous structures such as shock waves is one of the key problems in designing robust,high-resolution and high-order numerical schemes.Based on the prior mathematical knowledge and the artificial neural network(ANN)method,a modified characteristic-compression embedded discontinuity indicator was developed to improve the accuracy of discontinuity capturing in the framework of high-order schemes.The present indicator was obtained by pre-modeling based on the prior mathematical knowledge and then learning the undetermined parameters in the model through data-driven methods.This makes the discontinuity indicator concise,and has the advantage of small sample dependency during the training process,and makes the trained model have excellent properties such as low computational complexity and mathematical interpretation.Its one-dimensional form can be naturally generalized to multi-dimensional system of equations on unstructured grids.The present indicator was proved to contain two types of discontinuity capture mechanisms,namely,shock wave capture mechanism based on characteristic compression,and expansion wave origin/contact wave capture mechanism based on large gradient jump.A number of numerical results verified the accuracy of the proposed indicator for capturing different types of discontinuities in high-speed complex flows.