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.
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