迎风格式在接触间断的数值耗散及其诱导误差
2024,46(1):51-62
韩芳
大连理工大学 航空航天学院, 辽宁 大连 116024，duthanf@mail.dlut.edu.cn
魏雁昕
大连理工大学 航空航天学院, 辽宁 大连 116024
刘君
大连理工大学 航空航天学院, 辽宁 大连 116024
大连理工大学 航空航天学院, 辽宁 大连 116024，duthanf@mail.dlut.edu.cn
魏雁昕
大连理工大学 航空航天学院, 辽宁 大连 116024
刘君
大连理工大学 航空航天学院, 辽宁 大连 116024
摘要：
在不同流场参数条件下对三种迎风格式在接触间断中的数值耗散问题进行了数值实验,并对数值耗散产生的机理进行了分析。数值计算结果和理论分析表明,矢通量分裂格式计算接触间断问题时,若流场静止或流场内存在亚声速区域,密度耗散的产生会诱导出以特征速度运动的数值扰动误差,该误差对数值耗散的大小无影响,但会影响流场的速度及压力参数分布,从而改变流场的结构。在二维问题中,诱导误差相互干扰会产生大量的复杂小尺度结构,给流场结构分析带来困难。同时,在密度参数线性分布的流场中,若空间离散格式重构的对象为对流通量,使用矢通量分裂格式计算流场会产生数值误差,使计算精度难以到达二阶。
在不同流场参数条件下对三种迎风格式在接触间断中的数值耗散问题进行了数值实验,并对数值耗散产生的机理进行了分析。数值计算结果和理论分析表明,矢通量分裂格式计算接触间断问题时,若流场静止或流场内存在亚声速区域,密度耗散的产生会诱导出以特征速度运动的数值扰动误差,该误差对数值耗散的大小无影响,但会影响流场的速度及压力参数分布,从而改变流场的结构。在二维问题中,诱导误差相互干扰会产生大量的复杂小尺度结构,给流场结构分析带来困难。同时,在密度参数线性分布的流场中,若空间离散格式重构的对象为对流通量,使用矢通量分裂格式计算流场会产生数值误差,使计算精度难以到达二阶。
基金项目：
国家自然科学基金资助项目(11872144)
国家自然科学基金资助项目(11872144)
Numerical dissipation of upwind schemes in contact discontinuity and their induced error
HAN Fang
School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China,duthanf@mail.dlut.edu.cn
WEI Yanxin
School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
LIU Jun
School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China,duthanf@mail.dlut.edu.cn
WEI Yanxin
School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
LIU Jun
School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
Abstract：
The numerical experiments of three upwind schemes in contact discontinuity were carried out on the numerical dissipation under different flow field parameters, and the mechanism of numerical dissipation was analyzed. The numerical calculation results and theoretical analysis show that when the flux vector splitting scheme is used for contact discontinuity calculation, if the flow field is static or there exists a subsonic region in the flow field, the generation of density dissipation will induce numerical perturbation errors moving with characteristic velocity. These errors have no effect on the magnitude of numerical dissipation, but it will affect the distribution of velocity and pressure parameters in the flow field, thus changing the structure of the flow field. In two-dimensional flow fields, the mutual interference of the induced errors will produce numerous complex small-scale structures, which bring difficulties to the flow field structure identification. Meanwhile, in the flow field with linear distribution of density parameters, if the object reconstructed by the spatial discrete scheme is convective flux, using the flux vector splitting scheme to calculate the flow field will generate numerical errors, making it difficult to reach the second order of computational accuracy.
The numerical experiments of three upwind schemes in contact discontinuity were carried out on the numerical dissipation under different flow field parameters, and the mechanism of numerical dissipation was analyzed. The numerical calculation results and theoretical analysis show that when the flux vector splitting scheme is used for contact discontinuity calculation, if the flow field is static or there exists a subsonic region in the flow field, the generation of density dissipation will induce numerical perturbation errors moving with characteristic velocity. These errors have no effect on the magnitude of numerical dissipation, but it will affect the distribution of velocity and pressure parameters in the flow field, thus changing the structure of the flow field. In two-dimensional flow fields, the mutual interference of the induced errors will produce numerous complex small-scale structures, which bring difficulties to the flow field structure identification. Meanwhile, in the flow field with linear distribution of density parameters, if the object reconstructed by the spatial discrete scheme is convective flux, using the flux vector splitting scheme to calculate the flow field will generate numerical errors, making it difficult to reach the second order of computational accuracy.
收稿日期：
2021-11-04
2021-11-04
