基于映射函数的新型五阶WENO格式

doi:10.7527/S1000-6893.2021.26155

流体力学与飞行力学

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基于映射函数的新型五阶WENO格式

刘博¹, 李诗尧^2,3, 陈嘉禹^4,5, 程启豪⁶, 时晓天¹

1. 中国航天空气动力技术研究院, 北京 100074;
2. 中国科学院力学研究所高温气体动力学国家重点实验室, 北京 100190;
3. 中国科学院大学工程科学学院, 北京 100049;
4. 天津大学水利工程仿真与安全国家重点实验室, 天津 300072;
5. 天津大学建筑工程学院, 天津 300350;
6. 天津大学数学学院, 天津 300350

收稿日期:2021-07-26 修回日期:2021-08-17 发布日期:2021-09-22
通讯作者: 时晓天,E-mail:xxtshi@163.com E-mail:xxtshi@163.com
基金资助:
国家重点研发计划（2019YFA0405300）；国家自然科学基金（11872348，11802297）

New fifth order WENO scheme based on mapping functions

LIU Bo¹, LI Shiyao^2,3, CHEN Jiayu^4,5, CHENG Qihao⁶, SHI Xiaotian¹

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:2021-07-26 Revised:2021-08-17 Published:2021-09-22
Supported by:
National Key Research and Development Program of China(2019YFA0405300); National Natural Science Foundation of China (11872348, 11802297)

摘要/Abstract

摘要： 研究高精度和高分辨率的差分格式对于复杂流场的数值模拟有重要意义。为了克服WENO-JS格式和WENO-Z在通量函数的一阶和二阶极值点处降阶的缺陷，基于重构权重系数的思想，设计一族映射函数并应用到五阶WENO格式中。近似色散关系表明，WENO-Pe的色散误差和数值耗散均小于WENO-JS、WENO-Z以及其他基于映射函数的WENO格式。新格式与其他格式数值模拟变形的高斯波问题，Sod激波管、Lax激波管、激波密度干扰问题等一维算例，Riemann问题、Rayleigh-Taylor不稳定性问题、双马赫反射问题等二维算例的结果表明：在精度阶相同的情况下，WENO-Pe格式拥有更良好的捕捉间断能力，分辨率更高，适合应用于复杂流场的数值模拟。

关键词: WENO, 高精度, 高分辨率, 映射函数, 欧拉方程

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

中图分类号:

刘博, 李诗尧, 陈嘉禹, 程启豪, 时晓天. 基于映射函数的新型五阶WENO格式[J]. 航空学报, 2022, 43(12): 126155-126155.

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.

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于映射函数的新型五阶WENO格式

New fifth order WENO scheme based on mapping functions

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