蛙跳(leapfrog)时间差分格式采用Asselin-Robert时间滤波方案去除计算解能够降低原始方程组的时间差分格式的计算精度,采用二阶Adams-Bashforth格式构造的欧拉前差方案可弥补蛙跳格式的不足,即:在不存在计算解的条件下去除滤波的影响,...蛙跳(leapfrog)时间差分格式采用Asselin-Robert时间滤波方案去除计算解能够降低原始方程组的时间差分格式的计算精度,采用二阶Adams-Bashforth格式构造的欧拉前差方案可弥补蛙跳格式的不足,即:在不存在计算解的条件下去除滤波的影响,更大程度的保持方程组的计算准确性。本文基于NCAR CAM3.0(Community Atmosphere Model 3.0)完善的软件平台,将原模式的三时间层蛙跳时间差分方案修改为两时间层二阶Adams-Bashforth时间差分格式,对与重力波有关项使用中央差隐式处理,以此构建半隐式大气环流谱模式。利用动力检验的方法探讨模式对垂直分辨率的敏感性,从而寻找模式在较小计算代价下提高计算效果的可能。通过斜压波实验发现,提高垂直分辨率使模式具有更强的斜压波模拟能力,其模拟效果甚至已经与提高水平分辨率的效果相当,可以作为一种弥补模式运算效率不足的可行方案。展开更多
The Asselin-Robert time As an attractive alternative filter used in the leaptYog scheme does degrade the accuracy of calculations. to leapfrog time differencing, the second-order Adams-Bashforth method is not subject ...The Asselin-Robert time As an attractive alternative filter used in the leaptYog scheme does degrade the accuracy of calculations. to leapfrog time differencing, the second-order Adams-Bashforth method is not subject to time splitting instability and keeps excellent calculation accuracy. A second-order Adams- Bashforth model has been developed, which represents better stability, excellent convergence and improved simulation of prognostic variables. Based on these results, the higher-order Adams-Bashforth methods are developed on the basis of NCAR （National Center for Atmospheric Research） CAM 3.1 （Community Atmosphere Model 3.1） and the characteristics of dynamical cores are analyzed in this paper. By using Lorenz nonlinear convective equations, the filtered leapfrog scheme shows an excellent pattern for eliminating 2At wave solutions after 20 steps but represents less computational solution accuracy. The fourth-order Adams- Bashforth method is closely converged to the exact solution and provides a reference against which other methods may be compared. Thus, the Adams-Bashforth methods produce more accurate and convergent solution with differencing order increasing. The Held-Suarez idealized test is carried out to demonstrate that all methods have similar climate states to the results of many other global models for long-term integration. Besides, higher-order methods perform better in mass conservation and exhibit improvement in simulating tropospheric westerly jets, which is likely equivalent to the advantages of increasing horizontal resolutions. Based on the idealized baroclinic wave test, a better capability of the higher-order method in maintaining simulation stability is convinced. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the higher-order method has a better ability in the simulation of baroclinic wave perturbation.展开更多
The Asselin-Robert time filter used in the leapfrog scheme can degrade the accuracy of calculations.The second-order Adams-Bashforth method with the same accuracy as the leapfrog scheme is not subject to time splittin...The Asselin-Robert time filter used in the leapfrog scheme can degrade the accuracy of calculations.The second-order Adams-Bashforth method with the same accuracy as the leapfrog scheme is not subject to time splitting instability.A new semi-implicit atmospheric general circulation spectral model is developed on the basis of NCAR（National Center for Atmospheric Research）CAM3.0（Community Atmosphere Model 3.0）.In this new model,the second-order Adams-Bashforth method is used as an alternative to the leapfrog scheme,and a Crank-Nicholson scheme is incorporated for the treatment of fast gravity modes.In this paper,the new model is tested by the Held-Suarez test and an idealized baroclinic wave test.Results of the Held-Suarez test show that the second-order Adams-Bashforth model has similar climate states to those of many other global models and it converges with resolutions.Based on the idealized baroclinic wave test,the capability of different time differencing methods for keeping the initial steady-state are compared. This convinces a better ability of the second-order Adams-Bashforth method in maintaining the stability of the initial state.Furthermore,after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation,the second-order Adams-Bashforth method has an excellent property of convergence,and can represent the process of the baroclinic wave development much better than the original scheme in CAM3.0.A long-term integration of the new model during the period of 1980–1999 is also carried out and compared with that of CAM3.0.It is found that due to the reduction of simulation errors of prognostic variables,the second-order Adams-Bashforth method also has a better simulation ability for the diagnostic variables,such as precipitation.展开更多
This study aims to structure and evaluate a newCOVID-19modelwhich predicts vaccination effect in theKingdom of Saudi Arabia(KSA)under Atangana-Baleanu-Caputo(ABC)fractional derivatives.On the statistical aspect,we ana...This study aims to structure and evaluate a newCOVID-19modelwhich predicts vaccination effect in theKingdom of Saudi Arabia(KSA)under Atangana-Baleanu-Caputo(ABC)fractional derivatives.On the statistical aspect,we analyze the collected statistical data of fully vaccinated people from June 01,2021,to February 15,2022.Then we apply the Eviews program to find the best model for predicting the vaccination against this pandemic,based on daily series data from February 16,2022,to April 15,2022.The results of data analysis show that the appropriate model is autoregressive integratedmoving average ARIMA(1,1,2),and hence,a forecast about the evolution of the COVID-19 vaccination in 60 days is presented.The theoretical aspect provides equilibrium points,reproduction number R0,and biologically feasible region of the proposed model.Also,we obtain the existence and uniqueness results by using the Picard-Lindel method and the iterative scheme with the Laplace transform.On the numerical aspect,we apply the generalized scheme of the Adams-Bashforth technique in order to simulate the fractional model.Moreover,numerical simulations are performed dependent on real data of COVID-19 in KSA to show the plots of the effects of the fractional-order operator with the anticipation that the suggested model approximation will be better than that of the established traditional model.Finally,the concerned numerical simulations are compared with the exact real available date given in the statistical aspect.展开更多
In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered....In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered.Using Lyapunov theory,we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model,and the fractional models,whenever the basic reproduction number R0 is greater than one.By using fixed point theory,we prove existence,and conditions of the uniqueness of solutions,as well as the stability and convergence of numerical schemes.Numerical simulations for both models,using fractional Euler method and Adams–Bashforth method,respectively,are provided to confirm the effectiveness of used approximation methods for different values of the fractional-orderγ.展开更多
文摘蛙跳(leapfrog)时间差分格式采用Asselin-Robert时间滤波方案去除计算解能够降低原始方程组的时间差分格式的计算精度,采用二阶Adams-Bashforth格式构造的欧拉前差方案可弥补蛙跳格式的不足,即:在不存在计算解的条件下去除滤波的影响,更大程度的保持方程组的计算准确性。本文基于NCAR CAM3.0(Community Atmosphere Model 3.0)完善的软件平台,将原模式的三时间层蛙跳时间差分方案修改为两时间层二阶Adams-Bashforth时间差分格式,对与重力波有关项使用中央差隐式处理,以此构建半隐式大气环流谱模式。利用动力检验的方法探讨模式对垂直分辨率的敏感性,从而寻找模式在较小计算代价下提高计算效果的可能。通过斜压波实验发现,提高垂直分辨率使模式具有更强的斜压波模拟能力,其模拟效果甚至已经与提高水平分辨率的效果相当,可以作为一种弥补模式运算效率不足的可行方案。
基金Supported by the China Meteorological Administration Special Fund for Numerical Prediction of GRAPES(2200504)
文摘The Asselin-Robert time As an attractive alternative filter used in the leaptYog scheme does degrade the accuracy of calculations. to leapfrog time differencing, the second-order Adams-Bashforth method is not subject to time splitting instability and keeps excellent calculation accuracy. A second-order Adams- Bashforth model has been developed, which represents better stability, excellent convergence and improved simulation of prognostic variables. Based on these results, the higher-order Adams-Bashforth methods are developed on the basis of NCAR （National Center for Atmospheric Research） CAM 3.1 （Community Atmosphere Model 3.1） and the characteristics of dynamical cores are analyzed in this paper. By using Lorenz nonlinear convective equations, the filtered leapfrog scheme shows an excellent pattern for eliminating 2At wave solutions after 20 steps but represents less computational solution accuracy. The fourth-order Adams- Bashforth method is closely converged to the exact solution and provides a reference against which other methods may be compared. Thus, the Adams-Bashforth methods produce more accurate and convergent solution with differencing order increasing. The Held-Suarez idealized test is carried out to demonstrate that all methods have similar climate states to the results of many other global models for long-term integration. Besides, higher-order methods perform better in mass conservation and exhibit improvement in simulating tropospheric westerly jets, which is likely equivalent to the advantages of increasing horizontal resolutions. Based on the idealized baroclinic wave test, a better capability of the higher-order method in maintaining simulation stability is convinced. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the higher-order method has a better ability in the simulation of baroclinic wave perturbation.
基金the China Meteorological Administration Special Fund for GRAPES System Numerical Prediction
文摘The Asselin-Robert time filter used in the leapfrog scheme can degrade the accuracy of calculations.The second-order Adams-Bashforth method with the same accuracy as the leapfrog scheme is not subject to time splitting instability.A new semi-implicit atmospheric general circulation spectral model is developed on the basis of NCAR（National Center for Atmospheric Research）CAM3.0（Community Atmosphere Model 3.0）.In this new model,the second-order Adams-Bashforth method is used as an alternative to the leapfrog scheme,and a Crank-Nicholson scheme is incorporated for the treatment of fast gravity modes.In this paper,the new model is tested by the Held-Suarez test and an idealized baroclinic wave test.Results of the Held-Suarez test show that the second-order Adams-Bashforth model has similar climate states to those of many other global models and it converges with resolutions.Based on the idealized baroclinic wave test,the capability of different time differencing methods for keeping the initial steady-state are compared. This convinces a better ability of the second-order Adams-Bashforth method in maintaining the stability of the initial state.Furthermore,after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation,the second-order Adams-Bashforth method has an excellent property of convergence,and can represent the process of the baroclinic wave development much better than the original scheme in CAM3.0.A long-term integration of the new model during the period of 1980–1999 is also carried out and compared with that of CAM3.0.It is found that due to the reduction of simulation errors of prognostic variables,the second-order Adams-Bashforth method also has a better simulation ability for the diagnostic variables,such as precipitation.
基金supported by the Deanship of Scientific Research,Imam Mohammad Ibn Saud Islamic University (IMSIU),Saudi Arabia,Grant No. (21-13-18-069).
文摘This study aims to structure and evaluate a newCOVID-19modelwhich predicts vaccination effect in theKingdom of Saudi Arabia(KSA)under Atangana-Baleanu-Caputo(ABC)fractional derivatives.On the statistical aspect,we analyze the collected statistical data of fully vaccinated people from June 01,2021,to February 15,2022.Then we apply the Eviews program to find the best model for predicting the vaccination against this pandemic,based on daily series data from February 16,2022,to April 15,2022.The results of data analysis show that the appropriate model is autoregressive integratedmoving average ARIMA(1,1,2),and hence,a forecast about the evolution of the COVID-19 vaccination in 60 days is presented.The theoretical aspect provides equilibrium points,reproduction number R0,and biologically feasible region of the proposed model.Also,we obtain the existence and uniqueness results by using the Picard-Lindel method and the iterative scheme with the Laplace transform.On the numerical aspect,we apply the generalized scheme of the Adams-Bashforth technique in order to simulate the fractional model.Moreover,numerical simulations are performed dependent on real data of COVID-19 in KSA to show the plots of the effects of the fractional-order operator with the anticipation that the suggested model approximation will be better than that of the established traditional model.Finally,the concerned numerical simulations are compared with the exact real available date given in the statistical aspect.
文摘In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered.Using Lyapunov theory,we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model,and the fractional models,whenever the basic reproduction number R0 is greater than one.By using fixed point theory,we prove existence,and conditions of the uniqueness of solutions,as well as the stability and convergence of numerical schemes.Numerical simulations for both models,using fractional Euler method and Adams–Bashforth method,respectively,are provided to confirm the effectiveness of used approximation methods for different values of the fractional-orderγ.
