The introduction of 'hydrostatic extraction' scheme, or 'standard stratification approximation', into spectral model gained some advantages compared with commonly used schemes. However, computational i...The introduction of 'hydrostatic extraction' scheme, or 'standard stratification approximation', into spectral model gained some advantages compared with commonly used schemes. However, computational instability may occur for high vertical resolution versions if the stratification parameter C0 taken as a constant. In this paper, the possible cause leading to the instability is discussed and an improved scheme presented where C0 is generalized to be a function of both height and latitudes. Hence the reference atmosphere gets closer to the real atmosphere and the temperature deviation field to be expanded becomes smoother everywhere. Test by real case forecasts shows good computational stability of the new scheme and better prediction performance than-usual schemes of spectral model.展开更多
There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equations of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic...There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equations of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical fluid dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.Chen et al (1987) introduced the hydrostatic extraction scheme into a global spectral model, which attained preliminary success at low resolution. Zhang and Sheng et al (1990) developed and improved the hydrostatic extraction scheme in a global spectral model, in which C0, the parameter that represents the stratification of the reference atmosphere, changes not only with height, but also with latitude. The scheme has been incorporated BMRC's global spectral model (IAPB). Four 5-day forecasts have been performed to test the IAPB with the hydrostatic extraction scheme. Objective verifications demonstrate a positive effect of the hydrostatic extration scheme on BMRC's model, particularly at upper levels, over the tropics and the Antartic region.展开更多
Some current methods for the calculation of the geogenetic depth are based on the hydrostatic model, it is induced that the depth in certain underground place is equal to the pressure divided by the specific weight of...Some current methods for the calculation of the geogenetic depth are based on the hydrostatic model, it is induced that the depth in certain underground place is equal to the pressure divided by the specific weight of rock, on the assumption that the rock is hydrostatic and overlain by no other force but gravity. However, most of rock is in a deformation environment and non hydrostatic state, especially in an orogenic belt, so that the calculated depth may be exaggerated in comparison with the actual depth according to the hydrostatic formula. In the finite slight deformation and elastic model, the relative actual depth value from the 3 axis strain data was obtained with the measurement of strain including that of superimposed tectonic forces but excluding that of time factor for the strain. If some data on the strain speed are obtained, the depth would be more realistically calculated according to the rheological model because the geological body often experiences long term creep strains.展开更多
In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order recons...In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control volume.This is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous terms.The presented method is fully conservative by construction,since the transported quantity or the vector field is integrated for each cell over the deformed vol-ume obtained at the foot of the characteristics that arises from all the vertexes defining the computational element.The semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing equations.Furthermore,a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance,hence yielding a stability condition which depends only on the explicit discretization of the viscous terms.A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment,which is assumed to be passive.The accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solu-tion whenever is known.The new numerical scheme can reach up to fourth order of accu-racy on general orthogonal meshes composed by Voronoi polygons.展开更多
Within the framework of an equivalent single-layer beam theory incorporating moderately large deformations at contact surface,a nonlinear hydroelastic fluid-structure interaction(FSI)model is developed to investigate ...Within the framework of an equivalent single-layer beam theory incorporating moderately large deformations at contact surface,a nonlinear hydroelastic fluid-structure interaction(FSI)model is developed to investigate the buckling and postbuckling behavior of foam sandwich beams in viscous flow.The sandwich beam is assumed to consist of two orthotropic face sheets and a metal foam core,with a symmetric porosity distribution along the thickness direction.For the first time,the nonlinear pressure distribution of incompressible viscous flow along the beam length is derived based on the exponential variation of velocity components through the thickness,the nonlinear impermeability condition,the continuity equation,and the Navier-Stokes equation.Then,Timoshenko beam equations with von Karman’s geometric nonlinearity are solved via the Galerkin method,to present the closed-form expressions of static equilibrium paths(in both prebuckling and postbuckling regimes),buckling compressive load(N_(a,cr)),and critical upstream speed(U_(∞,cr)).The numerical results indicate that the critical values are highly sensitive to the decay rate,therefore its accurate determination is crucial for understanding the effect of viscous flow on the mechanical behavior of foam sandwich beams.Furthermore,the findings reveal that the linear hydroelastic FSI model by neglecting the geometric nonlinearities is inadequate for predicting the buckling behavior.展开更多
基金This work has been carried out under the support of the Medium-range Numerical Weather Forecast research project
文摘The introduction of 'hydrostatic extraction' scheme, or 'standard stratification approximation', into spectral model gained some advantages compared with commonly used schemes. However, computational instability may occur for high vertical resolution versions if the stratification parameter C0 taken as a constant. In this paper, the possible cause leading to the instability is discussed and an improved scheme presented where C0 is generalized to be a function of both height and latitudes. Hence the reference atmosphere gets closer to the real atmosphere and the temperature deviation field to be expanded becomes smoother everywhere. Test by real case forecasts shows good computational stability of the new scheme and better prediction performance than-usual schemes of spectral model.
文摘There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equations of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical fluid dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.Chen et al (1987) introduced the hydrostatic extraction scheme into a global spectral model, which attained preliminary success at low resolution. Zhang and Sheng et al (1990) developed and improved the hydrostatic extraction scheme in a global spectral model, in which C0, the parameter that represents the stratification of the reference atmosphere, changes not only with height, but also with latitude. The scheme has been incorporated BMRC's global spectral model (IAPB). Four 5-day forecasts have been performed to test the IAPB with the hydrostatic extraction scheme. Objective verifications demonstrate a positive effect of the hydrostatic extration scheme on BMRC's model, particularly at upper levels, over the tropics and the Antartic region.
文摘Some current methods for the calculation of the geogenetic depth are based on the hydrostatic model, it is induced that the depth in certain underground place is equal to the pressure divided by the specific weight of rock, on the assumption that the rock is hydrostatic and overlain by no other force but gravity. However, most of rock is in a deformation environment and non hydrostatic state, especially in an orogenic belt, so that the calculated depth may be exaggerated in comparison with the actual depth according to the hydrostatic formula. In the finite slight deformation and elastic model, the relative actual depth value from the 3 axis strain data was obtained with the measurement of strain including that of superimposed tectonic forces but excluding that of time factor for the strain. If some data on the strain speed are obtained, the depth would be more realistically calculated according to the rheological model because the geological body often experiences long term creep strains.
基金support of MIUR-PRIN Project 2017,No.2017KKJP4X“Innovative numerical methods for evolutionary partial differential equations and applications”.
文摘In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control volume.This is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous terms.The presented method is fully conservative by construction,since the transported quantity or the vector field is integrated for each cell over the deformed vol-ume obtained at the foot of the characteristics that arises from all the vertexes defining the computational element.The semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing equations.Furthermore,a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance,hence yielding a stability condition which depends only on the explicit discretization of the viscous terms.A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment,which is assumed to be passive.The accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solu-tion whenever is known.The new numerical scheme can reach up to fourth order of accu-racy on general orthogonal meshes composed by Voronoi polygons.
文摘Within the framework of an equivalent single-layer beam theory incorporating moderately large deformations at contact surface,a nonlinear hydroelastic fluid-structure interaction(FSI)model is developed to investigate the buckling and postbuckling behavior of foam sandwich beams in viscous flow.The sandwich beam is assumed to consist of two orthotropic face sheets and a metal foam core,with a symmetric porosity distribution along the thickness direction.For the first time,the nonlinear pressure distribution of incompressible viscous flow along the beam length is derived based on the exponential variation of velocity components through the thickness,the nonlinear impermeability condition,the continuity equation,and the Navier-Stokes equation.Then,Timoshenko beam equations with von Karman’s geometric nonlinearity are solved via the Galerkin method,to present the closed-form expressions of static equilibrium paths(in both prebuckling and postbuckling regimes),buckling compressive load(N_(a,cr)),and critical upstream speed(U_(∞,cr)).The numerical results indicate that the critical values are highly sensitive to the decay rate,therefore its accurate determination is crucial for understanding the effect of viscous flow on the mechanical behavior of foam sandwich beams.Furthermore,the findings reveal that the linear hydroelastic FSI model by neglecting the geometric nonlinearities is inadequate for predicting the buckling behavior.
