Accurate prediction of Shock-Wave/Boundary Layer Interaction(SWBLI)flows has been a persistent challenge for linear eddy viscosity models.A major limitation lies in the isotropic representation of the Reynolds stress,...Accurate prediction of Shock-Wave/Boundary Layer Interaction(SWBLI)flows has been a persistent challenge for linear eddy viscosity models.A major limitation lies in the isotropic representation of the Reynolds stress,as assumed under the Boussinesq approximation.Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor.However,it remains uncertain whether this approach is effective for SWBLI flows,which involve compressibility and discontinuity.To address this issue,this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows.The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport(SST)model and reveal the impacts of anisotropy on the prediction of quantities of interest,such as separation and reattachment positions,wall static pressure,skin friction,and heat flux.The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model.Furthermore,a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty.The findings indicate that eigenspace perturbation primarily affects turbulent shear stress,while the prediction error of the SST model is more related to turbulent kinetic energy.展开更多
In this paper we consider approximate eigenvalues and approximate eigenspaces for the generalized Rayleigh quotient, and present some residual bounds. Our obtained bounds will improve the existing ones.
针对非圆相干信号的解相干问题,给出了一种新的特征空间算法(eigenspace-direction of arrival,ES-DOA)。利用信号源的非圆特性,虚拟地扩展了阵元个数,使阵列信息增至扩展前的两倍,对信号源数目的估计突破了M-1(M为阵元数)的限制;将信...针对非圆相干信号的解相干问题,给出了一种新的特征空间算法(eigenspace-direction of arrival,ES-DOA)。利用信号源的非圆特性,虚拟地扩展了阵元个数,使阵列信息增至扩展前的两倍,对信号源数目的估计突破了M-1(M为阵元数)的限制;将信息量加倍后的协方差矩阵加以重构,给出一种新的特征空间算法进行解相干,最大限度地利用了噪声子空间与信号子空间的信息,避免了空间平滑思想的阵列孔径损失及最大似然算法运算量过大的问题;该方法还对信号源功率进行了估计,提高了对小能量信号的估计成功概率。仿真结果表明,该方法对波达方向估计具有很好的鲁棒性。展开更多
The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices...The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.展开更多
基金supported by the National Natural Science Foundation of China(Nos.92252201 and 11721202)。
文摘Accurate prediction of Shock-Wave/Boundary Layer Interaction(SWBLI)flows has been a persistent challenge for linear eddy viscosity models.A major limitation lies in the isotropic representation of the Reynolds stress,as assumed under the Boussinesq approximation.Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor.However,it remains uncertain whether this approach is effective for SWBLI flows,which involve compressibility and discontinuity.To address this issue,this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows.The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport(SST)model and reveal the impacts of anisotropy on the prediction of quantities of interest,such as separation and reattachment positions,wall static pressure,skin friction,and heat flux.The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model.Furthermore,a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty.The findings indicate that eigenspace perturbation primarily affects turbulent shear stress,while the prediction error of the SST model is more related to turbulent kinetic energy.
基金Acknowledgments. The authors thank the referees for their helpful comments. The work was supported in part by National Natural Science Foundations of China （No. 10671077, 10971075）, Guangdong Provincial Natural Science Foundations （No. 09150631000021, 06025061） and Research Fund for the Doctoral Program of Higher Education of China （No. 20104407110001）.
文摘In this paper we consider approximate eigenvalues and approximate eigenspaces for the generalized Rayleigh quotient, and present some residual bounds. Our obtained bounds will improve the existing ones.
文摘针对非圆相干信号的解相干问题,给出了一种新的特征空间算法(eigenspace-direction of arrival,ES-DOA)。利用信号源的非圆特性,虚拟地扩展了阵元个数,使阵列信息增至扩展前的两倍,对信号源数目的估计突破了M-1(M为阵元数)的限制;将信息量加倍后的协方差矩阵加以重构,给出一种新的特征空间算法进行解相干,最大限度地利用了噪声子空间与信号子空间的信息,避免了空间平滑思想的阵列孔径损失及最大似然算法运算量过大的问题;该方法还对信号源功率进行了估计,提高了对小能量信号的估计成功概率。仿真结果表明,该方法对波达方向估计具有很好的鲁棒性。
文摘The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.
