@Article{EAJAM-13-3,
author = {Chertock, Alina and Shaoshuai, Chu and Kurganov, Alexander},
title = {Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {3},
pages = {576--609},
abstract = {<p style="text-align: justify;">We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ
the recently proposed local characteristic decomposition based central-upwind numerical fluxes, the three-stage third-order strong stability preserving Runge-Kutta time integrator, and the fifth-order WENO-Z interpolation. The adaptive strategy is implemented
by applying the limited interpolation only in the parts of the computational domain
where the solution is identified as rough with the help of a smoothness indicator. We
develop and use a new simple and robust local smoothness indicator (LSI), which is applied to the solutions computed at each of the three stages of the ODE solver. The new
LSI and adaptive A-WENO schemes are tested on the Euler equations of gas dynamics.
We implement the proposed LSI using the pressure, which remains smooth at contact
discontinuities, while our goal is to detect other rough areas and apply the limited interpolation mostly in the neighborhoods of the shock waves. We demonstrate that the
new adaptive schemes are highly accurate, non-oscillatory, and robust. They outperform
their fully limited counterparts (the A-WENO schemes with the same numerical fluxes
and ODE solver but with the WENO-Z interpolation employed everywhere) while being
less computationally expensive.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2022-313.160123},
url = {https://global-sci.com/article/82429/adaptive-high-order-a-weno-schemes-based-on-a-new-local-smoothness-indicator}
}