Abstract The construction of limiter functions is a crucial factor in total-variation-diminishing (TVD) schemes to achieve high resolution and numerical stability. In this paper, three symmetrical limiter functions are constructed by introducing the MAX function into the classical van Albada, van Leer, and PR-κ limiters. The analysis and numerical results demonstrate that the MUSCL scheme equipped with the proposed limiters satisfies the sufficient conditions for second-order convergence in smooth regions and exhibits lower dissipation and better resolution than the MUSCL scheme utilizing classic limiters corresponding to both smooth and discontinuous solutions.

中文翻译：

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几种新的双曲守恒定律对称通量限制器的构造与应用

摘要 限制器函数的构建是全变差减小（TVD）方案中实现高分辨率和数值稳定性的关键因素。在本文中，通过将 MAX 函数引入经典的 van Albada、van Leer 和 PR-κ 限制器，构建了三个对称的限制器函数。分析和数值结果表明，配备所提出的限制器的 MUSCL 方案满足平滑区域中二阶收敛的充分条件，并且比使用对应于平滑和不连续解的经典限制器的 MUSCL 方案表现出更低的耗散和更好的分辨率。