Revisting High-Resolution Schemes with van Albada Slope Limiter

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. (Astron Astrophys 108: 76–84, 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 the one-dimensional Total-Variation Diminishing (TVD) stability and demonstrate that it yields noticeable improvement in computation of one- and two-dimensional systems.

Keywords

High resolution / Limiters / Total-Variation Diminishing (TVD) stability / Central schemes

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Funding

Office of Naval Research(N00014-2112773)