Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

Year:    2023

Author:    Alina Chertock, Shaoshuai Chu, Alexander Kurganov

East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 3 : pp. 576–609

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2022-313.160123

East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 3 : pp. 576–609

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:    Local smoothness indicator scheme adaption strong stability preserving Runge-Kutta methods hyperbolic systems of conservation laws A-WENO schemes.

Author Details

Alina Chertock

Shaoshuai Chu

Alexander Kurganov