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

Chertock, Alina1; Chu, Shaoshuai2; Kurganov, Alexander2,3,4

2023-04-01

10.4208/eajam.2022-313.160123

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS   影响因子和分区

2079-7362

2079-7370

We develop new adaptive alternative weighted essentially non-oscillatory (AWENO) 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.

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

SCI

英语

通讯

NSF["DMS-1818684","DMS- 2208438"] ; NSFC["12111530004","12171226"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]

Mathematics

Mathematics, Applied

WOS:000971272700001

GLOBAL SCIENCE PRESS

Web of Science

1.North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China

Chertock, Alina,Chu, Shaoshuai,Kurganov, Alexander. Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator[J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2023,13(3).

Chertock, Alina,Chu, Shaoshuai,&Kurganov, Alexander.(2023).Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator.EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,13(3).

Chertock, Alina,et al."Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator".EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 13.3(2023).