针对高阶间断伽辽金数值格式的Gibbs现象智能去噪方法

Intelligent denoising methods for Gibbs phenomenon of high⁃order discontinuous Galerkin numerical scheme

在使用高阶间断伽辽金方法进行高速可压缩流场计算时,激波附近会出现影响数值精度甚至导致计算失败的非物理数值振荡,这类似于图像处理领域不断堆积的Gibbs噪声。如何抑制激波振荡或消除Gibbs现象并确保计算过程稳定,已经成为了高阶间断伽辽金方法研究领域的一个挑战。针对这一问题,利用机器学习技术,提出了一种由图注意力机制和图卷积网络构成的Gibbs现象智能去噪模型,该模型能够抑制间断伽辽金方法计算中激波附近的振荡,在确保间断伽辽金方法计算顺利进行的同时提升了捕捉激波的效果。该模型使用间断伽辽金方法计算中产生的Gibbs噪声数据构造训练数据集,在图卷积滤波器的指导下进行图神经网络训练。对跨声速和超声速来流条件的NACA0012翼型进行了数值模拟,结果表明在间断伽辽金方法计算过程中嵌入所构建的Gibbs现象智能去噪模型,能够消除Gibbs现象,有效抑制激波振荡。

The high-order discontinuous Galerkin(DG)method for the high-speed compressible flow field calculations will cause non-physical numerical oscillation near the shock wave,affecting numerical accuracy and even leading to calculation failure,similar to the accumulation of Gibbs noise in the image processing field.In the high-order DG methods,restraining shock oscillation or eliminating the Gibbs phenomenon to ensure the stability of the calculation process has become a challenge.A Gibbs phenomenon intelligent denoising model composed of graph attention mechanism and graph convolutional network is proposed by using machine learning technology.This model can restrain the oscillation near the shock wave in DG calculation,while ensuring the convergence of DG calculation and improving the effectiveness of shock wave capturing.After constructing a training dataset from Gibbs noise data generated by DG calculation,this model trains the graph neural network under the guidance of graph convolutional filters.In the numerical simulation experiment of NACA0012 airfoil under transonic and supersonic inflow conditions,the Gibbs phenomenon intelligent denoising model is embedded in the DG calculation.The experimental results show that the Gibbs phenomenon has been eliminated and shock oscillation has been effectively restrained.