Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmos...Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.展开更多
In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical...In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme.展开更多
In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from th...In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying.展开更多
In order to improve the accuracy of forecasts of atmospheric and oceanic phenomena which possess a wide range of space and time scales, it is crucial to design the high-order and stable schemes. On the basis of the ex...In order to improve the accuracy of forecasts of atmospheric and oceanic phenomena which possess a wide range of space and time scales, it is crucial to design the high-order and stable schemes. On the basis of the explicit square-conservative scheme, a high-order compact explicit square-conservative scheme is proposed in this paper. This scheme not only keeps the square-conservative characteristics, but also is of high accuracy. The numerical example shows that this scheme has less computing errors and better computational stability, and it could be considered to be tested and used in many atmospheric and oceanic problems.展开更多
In this paper, a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations, whose coefficients are determined according to accuracy constraints, necessary conditions of squa...In this paper, a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations, whose coefficients are determined according to accuracy constraints, necessary conditions of square conservation, and historical observation information under the linear supposition. As in the linear case, the schemes also have obvious superiority in overall performance in the nonlinear case compared with traditional finite difference schemes, e.g., the leapfrog(LF) scheme and the complete square conservation difference(CSCD) scheme that do not use historical observations in determining their coefficients, and the retrospective time integration(RTI) scheme that does not consider compatibility and square conservation. Ideal numerical experiments using the one-dimensional nonlinear advection equation with an exact solution show that this three-step scheme minimizes its root mean square error(RMSE) during the first 2500 integration steps when no shock waves occur in the exact solution, while the RTI scheme outperforms the LF scheme and CSCD scheme only in the first 1000 steps and then becomes the worst in terms of RMSE up to the 2500th step. It is concluded that reasonable consideration of accuracy, square conservation, and historical observations is also critical for good performance of a finite difference scheme for solving nonlinear equations.展开更多
Quantitative studies of scientific problems require solving correspondent mathematical models. Although a great deal of mathematical models of evolutional problems are set up under continuous space-time meaning, they ...Quantitative studies of scientific problems require solving correspondent mathematical models. Although a great deal of mathematical models of evolutional problems are set up under continuous space-time meaning, they usually had to be solved numerically after space-time discretization because nonlinear mathematical models except some展开更多
One important way to overcome nonlinear computational instability is to construct the complete square conservative finite-differential schemes, which have been widely used in the numerical simulations of atmospheric a...One important way to overcome nonlinear computational instability is to construct the complete square conservative finite-differential schemes, which have been widely used in the numerical simulations of atmospheric and oceanic problems. The schemes ever con-展开更多
In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the...In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.展开更多
The time distances of the completely square-conservative difference schemes in an explicit way are still limited by the stability criteria, though the schemes keep the advantages of traditional square-conservative sch...The time distances of the completely square-conservative difference schemes in an explicit way are still limited by the stability criteria, though the schemes keep the advantages of traditional square-conservative schemes systhetically. How to lengthen the time distances is the central problem in this note. To solve this problem, the aforesaid explicit schemes are improved to be unconditionally stable in theory, according to the thought of upstream differ-展开更多
The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian ...The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian system in the linear situation, thus laying a theoretical basis for the application and extension of symplectic schemes to square conservations systems, and of those schemes with quadratic conservation properties to Hamiltonian systems.展开更多
Two main problems in the numerical weather prediction are how to improve the computational precision of schemes and how to save the CPU time for integrations. In this note, the splitting method, which is applied to th...Two main problems in the numerical weather prediction are how to improve the computational precision of schemes and how to save the CPU time for integrations. In this note, the splitting method, which is applied to the difference schemes of explicit and complete square conservation, is described according to the separability of the adjustment stage (the fast process) and the advection stage (the slow process) in atmospheric motion.展开更多
基金the Outstanding State Key Laboratory Project of National Science Foundation of China (Grant No. 40023001 )the Key Innovatio
文摘Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.
基金the Ministry of Science and Technology of China for funding the National Basic Research Program of China (973 Program,Grant No.2011CB309704)
文摘In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme.
文摘In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying.
文摘In order to improve the accuracy of forecasts of atmospheric and oceanic phenomena which possess a wide range of space and time scales, it is crucial to design the high-order and stable schemes. On the basis of the explicit square-conservative scheme, a high-order compact explicit square-conservative scheme is proposed in this paper. This scheme not only keeps the square-conservative characteristics, but also is of high accuracy. The numerical example shows that this scheme has less computing errors and better computational stability, and it could be considered to be tested and used in many atmospheric and oceanic problems.
基金the Ministry of Science and Technology of China for the National Basic Research Program of China(973 Program,Grant No.2011CB309704)
文摘In this paper, a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations, whose coefficients are determined according to accuracy constraints, necessary conditions of square conservation, and historical observation information under the linear supposition. As in the linear case, the schemes also have obvious superiority in overall performance in the nonlinear case compared with traditional finite difference schemes, e.g., the leapfrog(LF) scheme and the complete square conservation difference(CSCD) scheme that do not use historical observations in determining their coefficients, and the retrospective time integration(RTI) scheme that does not consider compatibility and square conservation. Ideal numerical experiments using the one-dimensional nonlinear advection equation with an exact solution show that this three-step scheme minimizes its root mean square error(RMSE) during the first 2500 integration steps when no shock waves occur in the exact solution, while the RTI scheme outperforms the LF scheme and CSCD scheme only in the first 1000 steps and then becomes the worst in terms of RMSE up to the 2500th step. It is concluded that reasonable consideration of accuracy, square conservation, and historical observations is also critical for good performance of a finite difference scheme for solving nonlinear equations.
文摘Quantitative studies of scientific problems require solving correspondent mathematical models. Although a great deal of mathematical models of evolutional problems are set up under continuous space-time meaning, they usually had to be solved numerically after space-time discretization because nonlinear mathematical models except some
基金Project supported by the National Item 75-09-01-15.
文摘One important way to overcome nonlinear computational instability is to construct the complete square conservative finite-differential schemes, which have been widely used in the numerical simulations of atmospheric and oceanic problems. The schemes ever con-
基金Partly supported by the State Major Key Project for Basic Researches
文摘In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.
基金Project partly supported by the State Major Key Project for Basic Researches.
文摘The time distances of the completely square-conservative difference schemes in an explicit way are still limited by the stability criteria, though the schemes keep the advantages of traditional square-conservative schemes systhetically. How to lengthen the time distances is the central problem in this note. To solve this problem, the aforesaid explicit schemes are improved to be unconditionally stable in theory, according to the thought of upstream differ-
基金the State Major Key Project for Basic Researches
文摘The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian system in the linear situation, thus laying a theoretical basis for the application and extension of symplectic schemes to square conservations systems, and of those schemes with quadratic conservation properties to Hamiltonian systems.
文摘Two main problems in the numerical weather prediction are how to improve the computational precision of schemes and how to save the CPU time for integrations. In this note, the splitting method, which is applied to the difference schemes of explicit and complete square conservation, is described according to the separability of the adjustment stage (the fast process) and the advection stage (the slow process) in atmospheric motion.
