In this work, we present a novel higher-order smooth artificial viscosity method for the discontinuous Galerkin spectral element method and related high order methods. A neural network is used to detect the need for stabilization. Inspired by techniques from image edge detection, the neural network locates discontinuities inside mesh elements on a sub-cell level. Once the sub-cell positions of the shock fronts have been identified, the use of radial basis functions enables the construction of a high order smooth artificial viscosity field on quadrilateral meshes. We show the superiority of using higher order smooth artificial viscosity over piecewise linear approaches in particular on coarse meshes. The capabilities of the novel method are illustrated with typical applications.

在这项工作中，我们为不连续伽辽金谱元方法和相关的高阶方法提出了一种新的高阶平滑人工粘度方法。神经网络用于检测是否需要稳定。受图像边缘检测技术的启发，神经网络在子单元级别上定位网格元素内部的不连续性。一旦确定了激波前沿的子单元位置，使用径向基函数就可以在四边形网格上构建高阶平滑人工粘度场。我们展示了使用高阶平滑人工粘性优于分段线性方法的优势，特别是在粗网格上。通过典型应用说明了这种新颖方法的能力。