Due to the decrease in grid size associated with the convergence of meridians toward the poles inspherical coordinates, the time steps in many global climate models with finite-difference method are restrictedto be un...Due to the decrease in grid size associated with the convergence of meridians toward the poles inspherical coordinates, the time steps in many global climate models with finite-difference method are restrictedto be unpleasantly small. To overcome the problem, a reduced grid is introduced to LASG/IAP world oceangeneral circulation models. The reduced grid is implemented successfully in the coarser resolutions versionmodel L30T63 at first. Then, it is carried out in the improved version model LICOM with finer resolutions. Inthe experiment with model L30T63, under time step unchanged though, execution time per single model run isshortened significantly owing to the decrease of grid number and filtering execution in high latitudes. Resultsfrom additional experiments with L30T63 show that the time step of integration can be quadrupled at most inreduced grid with refinement ratio 3. In the experiment with model LICOM and with the model’s original timestep unchanged, the model covered area is extended to the whole globe from its original case with the grid pointof North Pole considered as an isolated island and the results of experiment are shown to be acceptable.展开更多
Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of p...Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.展开更多
When simulating the propagation of seismic waves in some special structures,such as tunnels and boreholes,finite difference forward modeling in the polar system has higher accuracy than the traditional Cartesian syste...When simulating the propagation of seismic waves in some special structures,such as tunnels and boreholes,finite difference forward modeling in the polar system has higher accuracy than the traditional Cartesian system.In actual situations,the polar space is the most irregular.To solve this problem,a forward modeling method for an irregular polar coordinate system is proposed to improve the simulation accuracy.First,an irregular surface of the polar space was meshed into an irregular polar system.After the transformation,the undulating surface was mapped into a plane one,and the wavefield was then computed in an irregular polar system.The Lebedev staggered grid was used to solve the wave equations in the irregular polar system.In addition,the artificial absorption boundary,cylindrical free boundary,and circumferential boundary conditions were used to absorb the boundary reflection.We selected three polar space models to demonstrate the new method in this study.The results show that the proposed elastic simulation method in an irregular polar coordinate system can produce more accurate and stable simulation results when modeling seismic wave propagation in an irregular polar space.Elastic full waveform inversion further shows that the irregular polar system elastic simulation method can accurately simulate the wavefield in an undulating polar space.展开更多
For an exponentially position-dependent mass, we obtain the exact solutionsof the three-dimensional Schrodinger equation by using coordinate transformation method for thereference problems with Coulomb potential, Krat...For an exponentially position-dependent mass, we obtain the exact solutionsof the three-dimensional Schrodinger equation by using coordinate transformation method for thereference problems with Coulomb potential, Kratzer potential, and spherically square potential wellof infinite depth, respectively. The explicit expressions for the energy eigenvalues and thecorresponding eigenfunctions of the three systems are presented.展开更多
This paper deals with the numerical simulation of incompressible turbulent boundary flow of a flat plate with the pseudo-spectral matrix method. In order to appear more than 10 nodes in the turbulent base-stratum and ...This paper deals with the numerical simulation of incompressible turbulent boundary flow of a flat plate with the pseudo-spectral matrix method. In order to appear more than 10 nodes in the turbulent base-stratum and transition of 43×43 computational grids,a coordinate transformation is put up from physical panel to computational panel. Several zero turbulent models are computed comparatively. The results are credible when comparing with the previous methods.展开更多
基金National Natural Science Foundation of China (40233031)
文摘Due to the decrease in grid size associated with the convergence of meridians toward the poles inspherical coordinates, the time steps in many global climate models with finite-difference method are restrictedto be unpleasantly small. To overcome the problem, a reduced grid is introduced to LASG/IAP world oceangeneral circulation models. The reduced grid is implemented successfully in the coarser resolutions versionmodel L30T63 at first. Then, it is carried out in the improved version model LICOM with finer resolutions. Inthe experiment with model L30T63, under time step unchanged though, execution time per single model run isshortened significantly owing to the decrease of grid number and filtering execution in high latitudes. Resultsfrom additional experiments with L30T63 show that the time step of integration can be quadrupled at most inreduced grid with refinement ratio 3. In the experiment with model LICOM and with the model’s original timestep unchanged, the model covered area is extended to the whole globe from its original case with the grid pointof North Pole considered as an isolated island and the results of experiment are shown to be acceptable.
文摘Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.
基金funded by the Science and Technology Project of CNPC Southwest Oil and Gas Field Branch (202,20301-01-03)。
文摘When simulating the propagation of seismic waves in some special structures,such as tunnels and boreholes,finite difference forward modeling in the polar system has higher accuracy than the traditional Cartesian system.In actual situations,the polar space is the most irregular.To solve this problem,a forward modeling method for an irregular polar coordinate system is proposed to improve the simulation accuracy.First,an irregular surface of the polar space was meshed into an irregular polar system.After the transformation,the undulating surface was mapped into a plane one,and the wavefield was then computed in an irregular polar system.The Lebedev staggered grid was used to solve the wave equations in the irregular polar system.In addition,the artificial absorption boundary,cylindrical free boundary,and circumferential boundary conditions were used to absorb the boundary reflection.We selected three polar space models to demonstrate the new method in this study.The results show that the proposed elastic simulation method in an irregular polar coordinate system can produce more accurate and stable simulation results when modeling seismic wave propagation in an irregular polar space.Elastic full waveform inversion further shows that the irregular polar system elastic simulation method can accurately simulate the wavefield in an undulating polar space.
基金The project supported by National Natural Science Foundation for Outstanding Young Scientists of China under Grant No. 10125521Fund of the Education Ministry of China under Grant No. 20010284036, the State Key Research Program of China under Grant N
文摘For an exponentially position-dependent mass, we obtain the exact solutionsof the three-dimensional Schrodinger equation by using coordinate transformation method for thereference problems with Coulomb potential, Kratzer potential, and spherically square potential wellof infinite depth, respectively. The explicit expressions for the energy eigenvalues and thecorresponding eigenfunctions of the three systems are presented.
文摘This paper deals with the numerical simulation of incompressible turbulent boundary flow of a flat plate with the pseudo-spectral matrix method. In order to appear more than 10 nodes in the turbulent base-stratum and transition of 43×43 computational grids,a coordinate transformation is put up from physical panel to computational panel. Several zero turbulent models are computed comparatively. The results are credible when comparing with the previous methods.
