This article considers the application of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering for the non-linear stabilization of discontinuous Galerkin (DG) discretizations via entropy correction. Upon constructing discrete filters from continuous convolution SIAC kernels, the schemes are made to be conservative and are then appended to the DG method in a semi-discrete fashion. Performance of these tunable SIAC filters is compared to the local averaging typically employed in the entropy correction of finite element methods, and their capabilities are demonstrated for energy conservation as well as a shock regularization strategy based on an artificial viscosity estimate. Relaxation Runge-Kutta time integration methods are further employed in order to ensure a fully-discrete energy preserving procedure, with impacts of the overall solution accuracy being investigated for calculations of the one- and two-dimensional Burgers equation.

翻译：本文探讨了光滑性增强精度保持（SIAC）滤波在间断伽辽金（DG）离散格式非线性稳定化中的应用，其实现途径为熵修正。通过由连续卷积SIAC核构造离散滤波器，所构建的格式保持守恒性，并以半离散方式附加至DG方法。将这些可调谐SIAC滤波器的性能与有限元方法熵修正中通常采用的局部平均方法进行了对比，并通过能量守恒以及基于人工黏性估计的激波正则化策略展示了其能力。进一步采用松弛龙格-库塔时间积分方法以确保全离散格式的能量守恒过程，并针对一维与二维Burgers方程的计算，研究了整体求解精度的影响。