ENO格式在计算一维激波管问题中的优化研究  

Investigate of Optimization in ENO Schemes on Computing One-dimensional Shock Tube Problem

作　　者：刘晓[1] 张肇弛 胡伊琳 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]华中师范大学数学与统计学学院,武汉430079

出　　处：《河南师范大学学报（自然科学版）》2015年第2期20-24,共5页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(41374158);河南省教育厅科学技术研究重点项目(13A110547)

摘　　要：ENO格式在捕捉激波间断问题中需要计算3个模板多项式,而这些模板多项式仅在间断附近有较大差别,在其它较为平滑的位置差别很小.针对这一特点,对ENO格式进行优化,达到既节约计算时间又不影响计算效果的目的.之后,以一维激波管问题为例,在压强梯度大于预设临界值的位置用标准ENO格式计算,而在平滑的位置上,直接用预设模板多项式计算.结果表明：优化后的计算时间比原来减少30%～50%.此外,预设模板多项式的选择依据格式的迎风性,直接用标准ENO三模板的最左端或最右端模板作为最终结果.Three stencil polymerizations are needed to capture discontinuous in shock problems by using the ENO scheme.However,they have dramatic differences just near the discontinuities.Based on this character,we optimize the ENO scheme in this paper so that we can reach the purposes of both saving the computing time and nearly having no effect on the computing results.Based on this idea,we take one-dimensional shock tube as an example and compute the results with the standard ENO scheme where the pressure gradient is greater than the default critical value and with the preinstall polymerization at the smooth position.The results show that the computing time of the optimized schemes is shorter than the original schemes by 30%-50%.In addition,the preinstall polymerization at the leftmost or rightmost stencil is selected as the final result directly according to the upwind character.

关 键 词：ENO格式 一维激波管 EULER方程 格式优化 压强梯度 

分 类 号：O241.6[理学—计算数学]