Revisting high-resolution schemes with van-Albada slope limiter

Slope limiters play an essential 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 limiter is smoother near extrema, and consequently, it outperforms 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.