Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws. The family of minmod limiters serves as the prototype example. Here, we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et. al. 1982. The van Albada (vA) limiter is smoother near extrema, and consequently, in many cases, it outperforms the results obtained using the standard minmod limiter. In particular, we prove that the vA limiter ensures 1D TVD stability and demonstrate that it yields noticeable improvement in computation of one- and two-dimensional systems.

翻译：斜率限制器在保持非线性守恒律高分辨率方法的非振荡特性中起着关键作用。最小值限制器族是典型示例。本文基于van Albada等人（1982）提出的斜率限制器，重新审视高分辨率中心格式的非振荡行为问题。van Albada（vA）限制器在极值附近更为平滑，因此在许多情况下，其性能优于使用标准最小值限制器获得的结果。特别地，我们证明了vA限制器可确保一维TVD稳定性，并展示了其在计算一维和二维系统时带来的显著改善。