论文标题
DG离散性双曲线问题的过滤单调化方法
A filtering monotonization approach for DG discretizations of hyperbolic problems
论文作者
论文摘要
我们引入了一种过滤技术，用于双曲问题的不连续的盖尔金近似值。遵循其他作者已经针对汉密尔顿 - 雅各比方程提出的方法，我们旨在减少在使用高阶空间空间离散化时不连续性的情况下出现的虚假振荡。使用过滤器函数实现此目标，该滤波在解决方案时保持高阶方案，如果不是，则可以切换到单调的低阶近似值。该方法已在$ deal.ii $数字库的框架中实现，其网格适应能力也用于减少使用低阶近似的区域。许多数值实验证明了所提出的滤波技术的潜力。
We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not. The method has been implemented in the framework of the $deal.II$ numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. A number of numerical experiments demonstrate the potential of the proposed filtering technique.
