Several improved adaptive mapped weighted essentially non-oscillatory scheme for hyperbolic conservation law

TL;DR

This paper introduces new adaptive mapped WENO schemes with improved mapping functions that enhance accuracy for hyperbolic conservation laws, outperforming existing schemes in one- and two-dimensional tests.

Contribution

The paper proposes novel adaptive mapped WENO schemes by modifying the mapping function's central region, leading to improved accuracy over classical schemes.

Findings

New schemes outperform classical WENO schemes in accuracy.

Theoretical analysis confirms improved mapping function properties.

Numerical tests demonstrate better performance in 1D and 2D problems.

Abstract

The decisive factor for the calculation accuracy of the mapped weighted essentially non-oscillatory scheme is the width of the center region of the mapping function. Through analysis of the classical mapped WENO schemes, the results show the width of the central range of the mapping function determined by the local operator in its denominator. Substituting the local operator in WENO-AIM with a symmetric one and an asymmetric function, we get two new adaptive mapped WENO schemes, WENO-AIMS and WENO-AIMA. Similarly, we improve WENO-RM260 and WENO-PM6 by using these local operators, and composed adaptive WENO-RM260 and adaptive WENO-PM6. Theoretical and numerical results show the present adaptive mapped WENO schemes composed in this paper perform better than WENO-AIM, WENO-RM260, and WENO-PM6 for one- and two-dimensional problems.