In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubi...In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.展开更多
In this study, strength softening models are developed for exploring rainfall-induced landslide mechanism based on Mohr Coulomb strength theory with both saturation degree and temporal evolution into consideration. Ac...In this study, strength softening models are developed for exploring rainfall-induced landslide mechanism based on Mohr Coulomb strength theory with both saturation degree and temporal evolution into consideration. According to the ratio of two time scales available, the model can be classified into three categories, i.e., instant softening model, delay softening model, and coupling softening model. Corresponding evolution functions are specified to represent these kinds of softening processes and then applied to simulate landslide of homogeneous slopes triggered by rainfall, therefrom, useful conclusions can be drawn in the end.展开更多
We investigate under what conditions transient simulation could be used to integrate backward in time so that the initial field could be recovered from later histories. In this paper we use realistic examples and find...We investigate under what conditions transient simulation could be used to integrate backward in time so that the initial field could be recovered from later histories. In this paper we use realistic examples and find that, in long histories, traces of the initial field would be present only in the exact analytical solutions. We conclude that the recovery of initial field is possible only if the equations could be solved analytically or only short time periods are involved. In practice, it is not possible to detect those traces by measurements or observations. If numerical procedures are used, truncation and discretization errors are always present. Fine-tuning of system parameters used or transforming time into another pseudo time frame may allow numerical integration to be carried out backward in time. But numerical instability is still a problem. Large spurious increases found by numerical procedures are most likely due to numerical inaccuracy and instability.展开更多
The paper deals with the application of 3 -D visible technology to reservoir management. Making use of this method for expanding - spread data point in reservoir management, can discard the false and retain the true d...The paper deals with the application of 3 -D visible technology to reservoir management. Making use of this method for expanding - spread data point in reservoir management, can discard the false and retain the true during data recording. As a result, The quality of data recording is ensured. In reservoir description, the reservoir characteristics, such as space distribution,physical change and fluid distribution may be identified by restoring palaeostructures, building - up 3-D facics tract model and 3-D fracture system model. Seismic interpretation, geologic modeling and numerical simulation are well integrated so that they can be promote reservoir performance management to develop into the intensive management pattern.展开更多
文摘In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.
基金supported by the National Natural Science Funds of China (10932012)
文摘In this study, strength softening models are developed for exploring rainfall-induced landslide mechanism based on Mohr Coulomb strength theory with both saturation degree and temporal evolution into consideration. According to the ratio of two time scales available, the model can be classified into three categories, i.e., instant softening model, delay softening model, and coupling softening model. Corresponding evolution functions are specified to represent these kinds of softening processes and then applied to simulate landslide of homogeneous slopes triggered by rainfall, therefrom, useful conclusions can be drawn in the end.
文摘We investigate under what conditions transient simulation could be used to integrate backward in time so that the initial field could be recovered from later histories. In this paper we use realistic examples and find that, in long histories, traces of the initial field would be present only in the exact analytical solutions. We conclude that the recovery of initial field is possible only if the equations could be solved analytically or only short time periods are involved. In practice, it is not possible to detect those traces by measurements or observations. If numerical procedures are used, truncation and discretization errors are always present. Fine-tuning of system parameters used or transforming time into another pseudo time frame may allow numerical integration to be carried out backward in time. But numerical instability is still a problem. Large spurious increases found by numerical procedures are most likely due to numerical inaccuracy and instability.
文摘The paper deals with the application of 3 -D visible technology to reservoir management. Making use of this method for expanding - spread data point in reservoir management, can discard the false and retain the true during data recording. As a result, The quality of data recording is ensured. In reservoir description, the reservoir characteristics, such as space distribution,physical change and fluid distribution may be identified by restoring palaeostructures, building - up 3-D facics tract model and 3-D fracture system model. Seismic interpretation, geologic modeling and numerical simulation are well integrated so that they can be promote reservoir performance management to develop into the intensive management pattern.
