使用 SIAC 滤波器的高阶熵修正
High-Order Entropy Correction with SIAC Filters
AI总结：
本文提出利用连续卷积 SIAC 核构造可调守恒滤波器，对半离散 DG 方法进行高阶熵修正，并结合 Relaxation Runge-Kutta 实现全离散能量保持。
摘要：
本文考虑将 Smoothness-Increasing Accuracy-Conserving（SIAC，光滑度增强且精度保持）滤波用于通过熵修正实现间断 Galerkin（DG）离散的非线性稳定。在由连续卷积 SIAC 核构造离散滤波器后，相关格式被设计为守恒的，随后以半离散方式附加到 DG 方法中。文中将这些可调 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进行比较，并展示其在能量守恒以及基于人工黏性估计的激波正则化策略方面的能力。研究进一步采用 Relaxation Runge-Kutta 时间积分方法，以确保全离散的保能量过程；同时针对一维和二维 Burgers 方程的计算，考察其对整体求解精度的影响。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
