Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to t...Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.展开更多
When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly M...When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly Matched Layers （PML） are deduced and their Crank-Nicolson scheme are presented in this paper. We use the second-, sixth-, and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives. Two numerical models, a homogeneous isotropic medium and a multi-layer model with a cave, are designed to investigate how the absorbing boundary width and the algorithms determine PML effects. Numerical results show that, for PML, the low-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin, whereas, high-order algorithms always have good absorption when the boundary is thick. Finally, we discuss the reflection coefficient and point out its shortcomings, which is why we use the SNR to quantitatively scale the PML effects,展开更多
Due to the complexity of compressible flows,nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient.In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3...Due to the complexity of compressible flows,nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient.In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers,the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5,6 and 8 are analyzed by numerical simulations.It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level.The most rapidly amplified 3-D disturbances are Klebanoff type(K-type)disturbances which have the same frequency as the 2-D disturbance.Among these K-type 3-D disturbances,the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher.Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages,the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.展开更多
文摘Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
基金supported jointly by the 973 Program (Grant No.2007CB209505)the National Natural Science Fund (Grant No.40704019,40674061)+1 种基金the School Basic Research Fund of Tsinghua University (JC2007030)PetroChina Innovation Fund (Grant No.060511-1-1)
文摘When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly Matched Layers （PML） are deduced and their Crank-Nicolson scheme are presented in this paper. We use the second-, sixth-, and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives. Two numerical models, a homogeneous isotropic medium and a multi-layer model with a cave, are designed to investigate how the absorbing boundary width and the algorithms determine PML effects. Numerical results show that, for PML, the low-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin, whereas, high-order algorithms always have good absorption when the boundary is thick. Finally, we discuss the reflection coefficient and point out its shortcomings, which is why we use the SNR to quantitatively scale the PML effects,
基金supported by the State Key Program of National Natural Science Foundation of China(Grant No.11332007)
文摘Due to the complexity of compressible flows,nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient.In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers,the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5,6 and 8 are analyzed by numerical simulations.It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level.The most rapidly amplified 3-D disturbances are Klebanoff type(K-type)disturbances which have the same frequency as the 2-D disturbance.Among these K-type 3-D disturbances,the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher.Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages,the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.
