A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx...A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).展开更多
A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By usi...A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By using a kind of special interpolation, the high resolution Boltzmann type difference scheme is constructed. Finally, numerical tests show that the schemes are effective and useful.展开更多
Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under...Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under three different greening schemes in typical areas of the Guangzhou University campus.The results indicate that the outdoor thermal environment is significantly influenced by the underlying surface materials and vegetation.The temperature of brick-paved surface is 0.9℃higher than that of natural soil surfaces under tree shade.Numerical simulations further confirm that increasing vegetation coverage effectively reduces outdoor air temperature.When the greening rate increases to 40%,the outdoor average temperature decreases by 0.7℃and relative humidity increases by approximately 4%,while wind speed remains minimal change.The cooling effect of vegetation is found to extend vertically to an altitude of 13 m.As the greening rate increases from 15%to 40%,the Mean Radiant Temperature(MRT)decreases from 50.6℃to 28.9℃,which is lower than the average ambient temperature,indicating improved thermal conditions.The Physiological Equivalent Temperature(PET)decreases from 40.2℃to 30.0℃,with the proportion of the areas classified as″very hot″reducing by 36.8%,significantly improving thermal comfort across most areas.Therefore,changing the ground material and greening landscape design can effectively alter the outdoor wind and thermal environment of the campus,thereby enhancing the thermal comfort for the campus community.展开更多
In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes...In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes with intrinsic parallelism are justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problem, without assuming the existence of the smooth solutions for the origillal problem.展开更多
A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can e...A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.展开更多
To improve the spectral characteristics of the high-order weighted compact nonlinear scheme(WCNS),optimized flux difference schemes are proposed.The disadvantages in previous optimization routines,i.e.,reducing formal...To improve the spectral characteristics of the high-order weighted compact nonlinear scheme(WCNS),optimized flux difference schemes are proposed.The disadvantages in previous optimization routines,i.e.,reducing formal orders,or extending stencil widths,are avoided in the new optimized schemes by utilizing fluxes from both cell-edges and cell-nodes.Optimizations are implemented with Fourier analysis for linear schemes and the approximate dispersion relation(ADR)for nonlinear schemes.Classical difference schemes are restored near discontinuities to suppress numerical oscillations with use of a shock sensor based on smoothness indicators.The results of several benchmark numerical tests indicate that the new optimized difference schemes outperform the classical schemes,in terms of accuracy and resolution for smooth wave and vortex,especially for long-time simulations.Using optimized schemes increases the total CPU time by less than 4%.展开更多
The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the ...The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001).展开更多
A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh rat...A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh ratio r = Deltat/(Deltax)(2) = Deltat/(Deltay)(2) = Deltat/(Deltaz)(2) less than or equal to 1/2, which is better than that of all the other explicit difference schemes. And when the order of truncation error is 0((Deltat)(2) + (Deltax)(4)), the stability condition is r less than or equal to 1/6, which contains the known results.展开更多
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 new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbol...In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.展开更多
In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability c...In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.展开更多
In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial deriv...In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.展开更多
The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, wher...The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.展开更多
This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some nume...This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.展开更多
The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical vi...The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.展开更多
A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and t...A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).展开更多
This paper improves and generalizes the two difference schemes presented in paper [1] and gives a new difference scheme for second order linear elliptic partial differential equations, its difference matrix is a matri...This paper improves and generalizes the two difference schemes presented in paper [1] and gives a new difference scheme for second order linear elliptic partial differential equations, its difference matrix is a matrix and because of the stability of the M-matrix, it is convergent by the asynchronous iterative method on multiprocessors. Then this paper gives a class of differeifce schemes for linear elliptic PDEs so that their difference matrixes are all M-matrixes and their asynchronous parallel computation are convergent.展开更多
Construction of high-order difference schemes based on Taylor series expansion has long been a hot topic in computational mathematics, while its application in comprehensive weather models is still very rare. Here, th...Construction of high-order difference schemes based on Taylor series expansion has long been a hot topic in computational mathematics, while its application in comprehensive weather models is still very rare. Here, the properties of high-order finite difference schemes are studied based on idealized numerical testing, for the purpose of their application in the Global/Regional Assimilation and Prediction System(GRAPES) model. It is found that the pros and cons due to grid staggering choices diminish with higher-order schemes based on linearized analysis of the one-dimensional gravity wave equation. The improvement of higher-order difference schemes is still obvious for the mesh with smooth varied grid distance. The results of discontinuous square wave testing also exhibits the superiority of high-order schemes. For a model grid with severe non-uniformity and non-orthogonality, the advantage of high-order difference schemes is inapparent, as shown by the results of two-dimensional idealized advection tests under a terrain-following coordinate. In addition, the increase in computational expense caused by high-order schemes can be avoided by the precondition technique used in the GRAPES model. In general, a high-order finite difference scheme is a preferable choice for the tropical regional GRAPES model with a quasi-uniform and quasi-orthogonal grid mesh.展开更多
In the present paper two contents are enclosed .First ,the Fourier analysis approach of the dispersion relation and group velocity effect of finite difference schemes is discussed.the defects of the approach is pointe...In the present paper two contents are enclosed .First ,the Fourier analysis approach of the dispersion relation and group velocity effect of finite difference schemes is discussed.the defects of the approach is pointed out and the correction is made;Second,a new systematic analysis method -remaider -effect analysis (abbr.REAM)is proposed by means of the modified partial differential equations (abbr MPDE)of finite difference schemes.The analysis is based on the synthetical study of the rational dispersion-and dissipation relations of finite difference schemes.And the method clearly possesses constructivity展开更多
文摘A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).
文摘A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By using a kind of special interpolation, the high resolution Boltzmann type difference scheme is constructed. Finally, numerical tests show that the schemes are effective and useful.
基金Science and Technology Research Project of Guang-dong Meteorological Bureau(GRMC2022M21)Guangdong Basic and Applied Basic Research Foundation(2023A1515012240)Research Project of Guangzhou Meteor-ological Bureau(M202218)。
文摘Reasonable greening design can effectively alleviate campus heat environment issues.This study uses the ENVI-met numerical model,along with in-situ observations and simulations,to analyze the thermal environment under three different greening schemes in typical areas of the Guangzhou University campus.The results indicate that the outdoor thermal environment is significantly influenced by the underlying surface materials and vegetation.The temperature of brick-paved surface is 0.9℃higher than that of natural soil surfaces under tree shade.Numerical simulations further confirm that increasing vegetation coverage effectively reduces outdoor air temperature.When the greening rate increases to 40%,the outdoor average temperature decreases by 0.7℃and relative humidity increases by approximately 4%,while wind speed remains minimal change.The cooling effect of vegetation is found to extend vertically to an altitude of 13 m.As the greening rate increases from 15%to 40%,the Mean Radiant Temperature(MRT)decreases from 50.6℃to 28.9℃,which is lower than the average ambient temperature,indicating improved thermal conditions.The Physiological Equivalent Temperature(PET)decreases from 40.2℃to 30.0℃,with the proportion of the areas classified as″very hot″reducing by 36.8%,significantly improving thermal comfort across most areas.Therefore,changing the ground material and greening landscape design can effectively alter the outdoor wind and thermal environment of the campus,thereby enhancing the thermal comfort for the campus community.
文摘In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes with intrinsic parallelism are justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problem, without assuming the existence of the smooth solutions for the origillal problem.
基金Project supported by the National Natural Science Foundation of China (Nos. 10172015 and 90205010)
文摘A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.
基金Project supported by the National Key Project(No.GJXM92579)the Defense Industrial Technology Development Program(No.C1520110002)the State Administration of Science,Technology and Industry for National Defence,China。
文摘To improve the spectral characteristics of the high-order weighted compact nonlinear scheme(WCNS),optimized flux difference schemes are proposed.The disadvantages in previous optimization routines,i.e.,reducing formal orders,or extending stencil widths,are avoided in the new optimized schemes by utilizing fluxes from both cell-edges and cell-nodes.Optimizations are implemented with Fourier analysis for linear schemes and the approximate dispersion relation(ADR)for nonlinear schemes.Classical difference schemes are restored near discontinuities to suppress numerical oscillations with use of a shock sensor based on smoothness indicators.The results of several benchmark numerical tests indicate that the new optimized difference schemes outperform the classical schemes,in terms of accuracy and resolution for smooth wave and vortex,especially for long-time simulations.Using optimized schemes increases the total CPU time by less than 4%.
基金the National Outstanding Youth Scientist Foundation of China (GrantNo. 49825109), the Key Innovation Project of Chinese Academ
文摘The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001).
文摘A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh ratio r = Deltat/(Deltax)(2) = Deltat/(Deltay)(2) = Deltat/(Deltaz)(2) less than or equal to 1/2, which is better than that of all the other explicit difference schemes. And when the order of truncation error is 0((Deltat)(2) + (Deltax)(4)), the stability condition is r less than or equal to 1/6, which contains the known results.
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 NSFC grant 11872210 and the Science Challenge Project,No.TZ2016002the NSFC Grant 11926103 when he visited Tianyuan Mathematical Center in Southeast China,Xiamen 361005,Fujian,Chinathe NSFC Grant 12071392 and the Science Challenge Project,No.TZ2016002.
文摘In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.
基金Supported by NSF of the Education Department of Henan Province(20031100010)
文摘In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.
文摘In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.
基金Project supported by the National Natural Science Foundation of China(Grant No.11471262)Henan University of Technology High-level Talents Fund,China(Grant No.2018BS039)
文摘The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.
文摘This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.
基金Acknowledgments. This work was supported by the China National Key Development Planning Project for Ba-sic Research (Abbreviation: 973 Project Grant No. G1999032801), the Chinese Academy of Sciences Key Innovation Direction Project (Grant No. KZCX2208)
文摘The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.
文摘A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).
文摘This paper improves and generalizes the two difference schemes presented in paper [1] and gives a new difference scheme for second order linear elliptic partial differential equations, its difference matrix is a matrix and because of the stability of the M-matrix, it is convergent by the asynchronous iterative method on multiprocessors. Then this paper gives a class of differeifce schemes for linear elliptic PDEs so that their difference matrixes are all M-matrixes and their asynchronous parallel computation are convergent.
基金supported by the National Natural Science Foundation of China (Grant No. U1811464)。
文摘Construction of high-order difference schemes based on Taylor series expansion has long been a hot topic in computational mathematics, while its application in comprehensive weather models is still very rare. Here, the properties of high-order finite difference schemes are studied based on idealized numerical testing, for the purpose of their application in the Global/Regional Assimilation and Prediction System(GRAPES) model. It is found that the pros and cons due to grid staggering choices diminish with higher-order schemes based on linearized analysis of the one-dimensional gravity wave equation. The improvement of higher-order difference schemes is still obvious for the mesh with smooth varied grid distance. The results of discontinuous square wave testing also exhibits the superiority of high-order schemes. For a model grid with severe non-uniformity and non-orthogonality, the advantage of high-order difference schemes is inapparent, as shown by the results of two-dimensional idealized advection tests under a terrain-following coordinate. In addition, the increase in computational expense caused by high-order schemes can be avoided by the precondition technique used in the GRAPES model. In general, a high-order finite difference scheme is a preferable choice for the tropical regional GRAPES model with a quasi-uniform and quasi-orthogonal grid mesh.
文摘In the present paper two contents are enclosed .First ,the Fourier analysis approach of the dispersion relation and group velocity effect of finite difference schemes is discussed.the defects of the approach is pointed out and the correction is made;Second,a new systematic analysis method -remaider -effect analysis (abbr.REAM)is proposed by means of the modified partial differential equations (abbr MPDE)of finite difference schemes.The analysis is based on the synthetical study of the rational dispersion-and dissipation relations of finite difference schemes.And the method clearly possesses constructivity
