New fifth order WENO scheme based on mapping functions

LIU Bo; LI Shiyao; CHEN Jiayu; CHENG Qihao; SHI Xiaotian

doi:10.7527/S1000-6893.2021.26155

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2022 , Vol. 43 >Issue 12: 126155 - 126155

DOI: https://doi.org/10.7527/S1000-6893.2021.26155

Fluid Mechanics and Flight Mechanics

New fifth order WENO scheme based on mapping functions

LIU Bo ,
LI Shiyao ,
CHEN Jiayu ,
CHENG Qihao ,
SHI Xiaotian

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1. China Academy of Aerospace Aerodynamics, Beijing 100074, China;
2. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
3. School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China;
4. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China;
5. School of Civil Engineering, Tianjin University, Tianjin 300350, China;
6. School of Mathematics, Tianjin University, Tianjin 300350, China

Received date: 2021-07-26

Revised date: 2021-08-17

Online published: 2021-09-22

Supported by

National Key Research and Development Program of China(2019YFA0405300); National Natural Science Foundation of China (11872348, 11802297)

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Abstract

Differential formats with high accuracy and high resolution are critical for numerical simulation of complex flow fields. To overcome the degradation defects of WENO-JS and WENO-Z at the first and second order extreme points of the flux function, a new mapping function (Pe) is designed and applied to the fifth order WENO scheme based on the idea of weighted coefficient reconstruction. The analyses of Approximate Dispersion Relations (ADR) indicate a smaller dispersion error and numerical dissipation of WENO-Pe than WENO-JS, WENO-Z, and other mapping function-based WENO schemes. We conduct numerical simulation in the new scheme and other schemes for 1D cases of the deformed Gaussian wave problem, Sod excitation tube problem, Lax excitation tube problem, and Shu-Osher problem, and 2D cases of the Riemann problem, Rayleigh-Taylor shock-density instability problem, and double Mach reflection problem. The results show that WENO-Pe has stronger ability to capture intermittency and higher resolution with the same order, thereby suitable for numerical simulation of complex flow fields.

Key words： WENO; high precision; high resolution; mapping function; Euler equation

Cite this article

LIU Bo , LI Shiyao , CHEN Jiayu , CHENG Qihao , SHI Xiaotian . New fifth order WENO scheme based on mapping functions[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(12) : 126155 -126155 . DOI: 10.7527/S1000-6893.2021.26155

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