Revisting high-resolution schemes with van-Albada slope limiter
Numerical Analysis
2023-10-31 v2 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2304.00437,
title = {Revisting high-resolution schemes with van-Albada slope limiter},
author = {Jingcheng Lu and Eitan Tadmor},
journal= {arXiv preprint arXiv:2304.00437},
year = {2023}
}