一种高精度的修正Hermite-ENO格式

doi:10.19596/j.cnki.1001-246x.7819

计算物理 ›› 2019, Vol. 36 ›› Issue (2): 141-152.DOI: 10.19596/j.cnki.1001-246x.7819

一种高精度的修正Hermite-ENO格式

郭子滔, 冯仁忠

北京航空航天大学数学与系统科学学院, 数学、信息与行为教育部重点实验室, 北京 100191

收稿日期:2017-12-21 修回日期:2018-02-16 出版日期:2019-03-25 发布日期:2019-03-25
作者简介:郭子滔(1994-),男,硕士,主要研究领域为计算流体力学,E-mail:gzt940726@qq.com
基金资助:
国家自然科学基金（91630203）及民机专项（MJ-F-2012-04）资助项目

A High Order Accuracy Corrected Hermite-ENO Scheme

GUO Zitao, FENG Renzhong

LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

Received:2017-12-21 Revised:2018-02-16 Online:2019-03-25 Published:2019-03-25

摘要/Abstract

摘要： 设计一种基于三单元具有六阶精度的修正Hermite-ENO格式（CHENO），求解一维双曲守恒律问题.CHENO格式利用有限体积法进行空间离散，在空间层上，使用ENO格式中的Newton差商法自适应选择模板.在重构半节点处的函数值及其一阶导数值时，利用Taylor展开给出修正Hermite插值使其提高到六阶精度，并设计了间断识别法与相应的处理方法以抑制间断处的虚假振荡；在时间层上采用三阶TVD Runge-Kutta法进行函数值及一阶导数值的推进.其主要优点是在达到高阶精度的同时具有紧致性.数值实验表明对一维双曲守恒律问题的求解达到了理论分析结果，是有效可行的.

关键词: 双曲守恒律, ENO和WENO格式, 修正Hermite插值, 间断识别法

Abstract: A kind of sixth order accuracy ENO scheme with 3 units based on corrected Hermite polynomials, named CHENO scheme, is proposed for one-dimensional hyperbolic conservation laws. Space discrete of CHENO scheme is based on finite volume formulation. In space layer, it chooses templates with Newton difference method in ENO scheme. Reconstruction of function and its first derivative in the half node based on Hermite interpolation are corrected to improve accuracy to sixth order by Taylor expansion. We proposed a discontinuous recognition method to control oscillation in discontinuous points. In time layer, both function and its first derivative of CHENO scheme are evolved in time by using 3rd TVD Runge-Kutta schemes. Major advantage of CHENO scheme is higher order accuracy and compactness. Numerical experiments on one-dimensional hyperbolic conservation laws validated feasibility of CHENO scheme.

Key words: hyperbolic conservation laws, ENO and WENO schemes, corrected Hermite interpolation, discontinuous recognition method

中图分类号:

O241.82

郭子滔, 冯仁忠. 一种高精度的修正Hermite-ENO格式[J]. 计算物理, 2019, 36(2): 141-152.

GUO Zitao, FENG Renzhong. A High Order Accuracy Corrected Hermite-ENO Scheme[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(2): 141-152.

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一种高精度的修正Hermite-ENO格式

A High Order Accuracy Corrected Hermite-ENO Scheme

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