A WENO-type slope-limiter for a family of piecewise polynomial methods
For computational fluid dynamics practitioners using high-order finite volume methods, this limiter enhances accuracy without sacrificing robustness.
The paper introduces a WENO-type slope-limiter for PPM and PQM that improves accuracy at smooth extrema while controlling oscillations near sharp features. The new limiter enables third-order convergence for PPM and fifth-order for PQM on smooth problems, outperforming existing monotone limiters.
A new, high-order slope-limiting procedure for the Piecewise Parabolic Method (PPM) and the Piecewise Quartic Method (PQM) is described. Following a Weighted Essentially Non-Oscillatory (WENO)-type paradigm, the proposed slope-limiter seeks to reconstruct smooth, non-oscillatory piecewise polynomial profiles as a non-linear combination of the natural and monotone-limited PPM and PQM interpolants. Compared to existing monotone slope-limiting techniques, this new strategy is designed to improve accuracy at smooth extrema, while controlling spurious oscillations in the neighbourhood of sharp features. Using the new slope-limited PPM and PQM interpolants, a high-order accurate Arbitrary-Lagrangian-Eulerian framework for advection-dominated flows is constructed, and its effectiveness is examined using a series of one- and two-dimensional benchmark cases. It is shown that the new WENO-type slope-limiting techniques offer a significant improvement in accuracy compared to existing strategies, allowing the PPM- and PQM- based schemes to achieve fully third- and fifth-order accurate convergence, respectively, for sufficiently smooth problems.