标题： 关于应用于带有新颖单调性参数的有限体积法的 troubled-cell 指标的研究 显示英文标题

标题： A study of troubled-cell indicators applied to finite volume methods using a novel monotonicity parameter

摘要： 我们为求解双曲守恒律的有限体积法（FVM）框架引入了一个针对间断伽辽金（DG）方法开发的 troubled-cell 指示器。 该指示器仅依赖于目标单元及其相邻单元的单元平均数据。 一旦识别出 troubled-cells，我们仅在这些单元上应用限制器，而不是在整个计算网格上应用。 我们通过定义一个单调性参数$\mu$来量化激波附近解的质量。 使用 MUSCL 重构的有限体积求解器对二维欧拉方程组的各种数值模拟结果验证了 troubled-cell 指示器以及仅在 troubled-cells 上进行限制方法的有效性。 结果显示，仅在 troubled-cells 上进行限制优于在所有单元上限制，因为它可以提高收敛速度而不牺牲解的精度。 显示英文摘要

摘要： We adapt a troubled-cell indicator developed for discontinuous Galerkin (DG) methods to the finite volume method (FVM) framework for solving hyperbolic conservation laws. This indicator depends solely on the cell-average data of the target cell and its immediate neighbours. Once the troubled-cells are identified, we apply the limiter only in these cells instead of applying in all computational cells. We introduce a novel technique to quantify the quality of the solution in the neighbourhood of the shock by defining a monotonicity parameter $\mu$. Numerical results from various two-dimensional simulations on the hyperbolic systems of Euler equations using a finite volume solver employing MUSCL reconstruction validate the performance of the troubled-cell indicator and the approach of limiting only in the troubled-cells. These results show that limiting only in the troubled-cells is preferable to limiting everywhere as it improves convergence without compromising on the solution accuracy.