欧拉方程数值求解的高精度通量分裂方法

doi:10.3969/j.issn.1000-1093.2019.12.020

兵工学报 ›› 2019, Vol. 40 ›› Issue (12): 2545-2550.doi: 10.3969/j.issn.1000-1093.2019.12.020

欧拉方程数值求解的高精度通量分裂方法

郑秋亚¹，苏宁亚¹，梁益华²

（1.长安大学理学院，陕西西安 710064； 2.中国航空计算技术研究所航空气动力数值模拟重点实验室，陕西西安 710068)

收稿日期:2018-12-19 修回日期:2018-12-19 上线日期:2020-02-14
通讯作者: 郑秋亚（1964—），女，教授，硕士生导师 E-mail:muzizh_2006@126.com
作者简介:苏宁亚（1995—），男，硕士研究生。E-mail: sunny_chd@126.com
基金资助:
航空科学基金项目（2015ZA31002）

High Accuracy Flux Splitting Method for Numerical Solution of Euler Equation

ZHENG Qiuya¹, SU Ningya¹, LIANG Yihua²

(1.School of Science, Chang'an University, Xi'an 710064, Shaanxi， China; 2.Aeronautical Laboratory of Computational Fluid Dynamics, Aeronautics Computing Technique Research Institute, Xi'an 710068, Shaanxi， China)

Received:2018-12-19 Revised:2018-12-19 Online:2020-02-14

摘要/Abstract

摘要： 针对欧拉方程，提出一种将总能对流迎风和分压(E-CUSP)格式与加权本质无振荡(WENO)格式相耦合的新格式。在空间方向上，通过对低耗散E-CUSP格式的通量，采用高精度WENO格式进行重构；在时间方向上，使用4阶总变差递减（TVD）的Runge-Kutta方法进行推进，由此得到求解欧拉方程的高精度通量分裂方法。考虑E-CUSP格式与WENO重构进行耦合得到新格式，使其空间精度进一步提高。通过对激波管问题进行数值模拟发现，新的格式相对于E-CUSP格式对激波和接触间断捕捉的效果更加精准。数值结果表明：耦合得到的新格式具有更高的准确性和稳健性。

关键词: 欧拉方程, 通量分裂方法, 计算流体力学, 总能对流迎风和分压格式, 加权本质无振荡格式

Abstract: A new scheme to couple the energy-convective upwind and split pressure (E-CUSP) scheme with the weighted essentially non-oscillatory (WENO) scheme is proposed for Euler equation. In the spatial direction, the flux of low dissipation E-CUSP scheme is reconstructed using high-precision WENO scheme. Fourth-order total variation reduction Runge-Kutta method is used for propulsion in time direction. On this base, a high accuracy flux splitting method for solving Euler equation is proposed. It is found through numerical simulation of shock tube that the proposed scheme can be used to simulate the shock tube problem and capture the shock wave and contact discontinuity more accurately compared to E-CUSP scheme. The numerical results show that the proposed scheme has higher accuracy and robustness. Key

Key words: Eulerequation, fluxsplittingmethod, computationalfluiddynamics, energy-convectiveupwindandsplitpressurescheme, weightedessentiallynon-oscillatoryscheme

中图分类号:

O351.2

郑秋亚，苏宁亚，梁益华. 欧拉方程数值求解的高精度通量分裂方法[J]. 兵工学报, 2019, 40(12): 2545-2550.

ZHENG Qiuya, SU Ningya, LIANG Yihua. High Accuracy Flux Splitting Method for Numerical Solution of Euler Equation[J]. Acta Armamentarii, 2019, 40(12): 2545-2550.

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欧拉方程数值求解的高精度通量分裂方法

High Accuracy Flux Splitting Method for Numerical Solution of Euler Equation

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