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冲击波强间断的高分辨率低耗散的精确捕捉数值计算方法

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强间断是爆炸冲击波的典型特征之一,如何高效且高分辨率地求解爆炸冲击波强间断是实现爆炸冲击问题精确数值模拟的关键.本文基于传统5阶加权本质无振荡(weighted essentially non-oscillatory,WENO)格式提出一种具有更高分辨率、更低耗散的5阶WENO格式.通过引入一种紧凑形式的局部光滑度量对子模板的光滑度进行定量表征,并设计新的全局光滑度量以衡量整体模板的光滑度,能够充分利用各子模板的光滑信息,有效降低强间断附近的耗散.针对现有格式的权值调控系数受网格步长直接限制的缺陷,提出一种能够摆脱网格步长依赖的自适应权值调控系数,使得非线性权值能够随流场变化自动调控.此外,该权值调控系数适当地提高欠光滑模板的权重,避免在网格较粗糙的情况下将欠光滑部分误识别为强间断,从而提高格式分辨率.最后,通过精度测试与典型的具有强间断特性的数值算例表明新计算方法可明显降低强间断附近的耗散,提高传统WENO格式的分辨率,从而实现对爆炸冲击波的锐利捕捉以及冲击波碰撞后复杂流场旋涡结构的高分辨率识别,为爆炸冲击问题的数值模拟仿真和冲击波强间断面的预测提供支撑.
A high-resolution and low-dissipation numerical method for accurate capture of shock waves
The impact problem attracts considerable attention in the field of national defense and security.One major problem of the numerical simulation is accurately capturing and tracking strong discontinuities.Thus,it is necessary to develop a high-resolution and low-dissipation numerical calculation method.In this paper,we improved the traditional fifth-order weighted essential nonoscillating(WENO)scheme and proposed a high-resolution and low-dissipation WENO scheme.A local smooth indicator with a compact form was introduced to quantitatively characterize the smoothness of the subtemplates,making scaling formats to higher levels easier.Furthermore,we developed a new global indicator to measure the overall smoothness of the template,which can substantially reduce dissipation near the strong discontinuity.Compared with the traditional one,the new global indicator contains more complete information,which is one of the elements for improving the resolution.The complete information is important for improving the resolution;however,it is usually underestimated in a relatively rough zone with no discontinuity.The resolution of the scheme can be considerably improved if their contribution to the reconstruction flux is correctly increased while avoiding amplifying spurious numerical oscillations.The contribution of such relatively rough templates is governed by the coefficient of a weight expression term.It is empirically determined and constrained by the grid step size in traditional formats.As a result,an adaptive regulatory component in the weight is presented,which can automatically modify the weight with changes in the flow field and eliminate the dependence on the grid step size.This improvement is another element for improving the resolution.Finally,several typical numerical tests demonstrated that the new method can considerably reduce the dissipation near the discontinuity and improve the resolution of the classic WENO scheme.This advantage is particularly evident in the capture of vortices.

strong discontinuitysmooth indicatorhigh resolutionlow dissipation

宁建国、苏璇、许香照

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北京理工大学爆炸科学与技术国家重点实验室,北京 100081

强间断 光滑度量因子 高分辨率 低耗散

国家自然科学基金爆炸科学与技术国家重点实验室自主研究课题青年基金项目

12032006QNKT23-18

2024

中国科学(技术科学)
中国科学院

中国科学(技术科学)

CSTPCD北大核心
影响因子:0.752
ISSN:1674-7259
年,卷(期):2024.54(5)