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CONSTRUCTION OF PERFECT CONSERVATIVE AND explicit FINITE-DIFFERENCE scheme OF GLOBAL TWO-DIMENSIONAL QUASIGEOSTROPHIC MODEL

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Progress in Natural Science:Materials International 1992年第3期 258-264页

作者：顾恒垣 Academia Sinica Beijing 100080 Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG) Institute of Atmospheric Physics(IAP) PRC

To avoid computational instability,some gross conservative properties are *** on[1],in which these quantities were conserved in the case of space-difference,the unique scheme——perfectconservative and explicit finite... 详细信息

关键词： quasi-geostrophic motion perfect conservation explicit scheme

Simulation of open channel flows by an explicit incompressible mesh-free method

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Journal of Hydrodynamics 2023年第2期35卷 287-298页

作者： Zhi-jian Huang Ti-bing Xu David Z.Zhu Song-da Zhang School of Civil and Environmental Engineering and Geography Science Ningbo UniversityNingbo315211China Department of Civil and Environmental Engineering University of AlbertaAlbertaCanada Ningbo River Management Center Ningbo315303China

In this study,to simulate open channel flows,an explicit incompressible mesh-free method is employed in which the pressure field is obtained by explicitly solving the pressure Poisson *** capture the velocity information in open channel flows,the source term in the pressure Poisson equation is modified while the spatial discretization of gradient and Laplacian models is based on the moving particle semi-implicit(MPS)*** inflow boundary condition is treated by injecting fluid particles into the domain according to the inlet discharge,and the outflow condition is handled by prescribing the pressure distribution and removing the fluid particles beyond the *** explicit incompressible mesh-free method is then used to simulate open channel flows,including weir flow,hydraulic jump,and flow over an *** the simulations,velocity distribution and flow pattern are *** simulated results are compared to available experimental measurements and other numerical *** is a good agreement between the simulated results and the experimental *** shows that the explicit incompressible mesh-free method can reproduce the flow characteristics in the open channel flows.

关键词： Mesh-free method explicit scheme weir flow hydraulic jump velocity distribution

A CLASS OF explicit FORWARD TIME-DIFFERENCE SQUARE CONSERVATIVE schemeS

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Acta Mechanica Sinica 1995年第1期11卷 8-14页

作者：王斌季仲贞 LASG Institute of Atmospheric PhysicsChinese Academy of Sciences

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications.

关键词： GEOMETRIC PRINCIPLE SQUARE CONSERVATION CONSISTENT DISSIPATION explicit scheme

explicit and Weakly Implicit schemes for a Class of Generalized KdV Equation

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 187-189页

作者： Shaohong ZHU(Dept. of Mathematics, Tianjin Normal University, Tianjin 300074, China) Department of Mathematics Tianjin Normal University Tianjin 300074 China

In this paper, the convergence and stability of the explicit scheme and theweakly implicit scheme for a class of generallied KdV equation are proved. The sharpstability condition is obtained.

关键词： generalized KdV equation explicit scheme weakly implicit scheme convergence stability

Efficient and Stable Exponential Runge-Kutta Methods for Parabolic Equations

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Advances in Applied Mathematics and Mechanics 2017年第1期9卷 157-172页

作者： Liyong Zhu School of Mathematics and Systems Science Beihang UniversityXueyuan Road No.37Haidian DistrictBeijing 100191China

In this paper we develop explicit fast exponential Runge-Kutta methods for the numerical solutions of a class of parabolic *** incorporating the linear splitting technique into the explicit exponential Runge-Kutta schemes,we are able to greatly improve the numerical *** proposed numerical methods could be fast implemented through use of decompositions of compact spatial difference operators on a regular mesh together with discrete fast Fourier transform *** exponential Runge-Kutta schemes are easy to be adopted in adaptive temporal approximations with variable time step sizes,as well as applied to stiff nonlinearity and boundary conditions of different *** stabilities of the proposed schemes and their comparison with other schemes are *** also numerically demonstrate accuracy,stability and robustness of the proposed method through some typical model problems.

关键词： Exponential Runge-Kutta method explicit scheme linear splitting discrete fast Fourier transforms Allen-Cahn equation

A New explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrodinger Equation

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Advances in Applied Mathematics and Mechanics 2018年第1期10卷 242-260页

作者： Yanhong Yang Yongzhong Song Haochen Li Yushun Wang Jiangsu Key Laboratory for NSLSCS Institute of MathematicsSchool of Mathematical SciencesNanjing Normal UniversityNanjing 210023China Department of Mathematics College of TaizhouNanjing Normal UniversityTaizhou 225300China LMAM CAPT and School of Mathematical SciencesPekingUniversityBeijing 100871China

In this paper,we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schr odinger *** key idea is to rewrite the equation as an infinite-dimensional Hamiltonian system and discrete the system by using Fourier pseudospectral method in space and symplectic Euler method in *** composing two different symplectic Euler methods for the ODEs resulted from semi-discretization in space,we get a new explicit scheme for the target equation which is of second order in space and spectral accuracy in *** canonical Hamiltonian form of the resulted ODEs is presented and the new derived scheme is proved strictly to be *** new scheme is totally explicitwhereas symplectic scheme are generally implicit or *** stability analysis is carried and a necessary Courant-Friedrichs-Lewy condition is *** numerical results are reported to test the accuracy and efficiency of the proposed method in long-term computing.

关键词： Klein-Gordon-Schr odinger equation Fourier pseudospectral method symplectic scheme explicit scheme

REDUCED AUGMENTED LAGRANGIAN BI-CONJUGATE GRADIENT METHOD FOR IMPACT-CONTACT PROBLEMS

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Acta Mechanica Solida Sinica 1998年第3期11卷 241-252页

作者： Li Nansheng Sha Desong Sun Huanchun Dalian Univ Technol Dept Engn Mech Dalian 116023 Peoples R China

To avoid the numerical oscillation of the penalty method andnon-compatibility with ex- plicit operators of conventional Lagrangemultiplier methods used in transient contact problems to en- forcesurface contact conditions, a new approach to enforcing surfacecontact constraints for the tran- sient nonlinear finite elementproblems, referred to as 'the reduced augmented Lagrangianbi-conjugate gradient method (ALCG)', is developed in this *** on the nonlinear constrained optimization theory and iscompatible with the explicit time integration scheme, this approachcan also be used in implicit scheme naturally.

关键词： impact-contact problems contact constraints explicit scheme

Constructions and Applied Examinations of a Kind of Square-Conservative schemes in High Precision in the Time Direction

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Advances in Atmospheric Sciences 1993年第3期10卷 315-324页

作者：季仲贞王斌 LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100080

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.

关键词： Completely square-conservative explicit scheme High precision in the time direction Harmonious dissipative operator

Numerical Methods for Solving Logarithmic Nonlinear Schrödinger’s Equation

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Journal of Applied Mathematics and Physics 2022年第12期10卷 3635-3648页

作者： Anees Al-Harbi Waleed Al-Hamdan Luwai Wazzan Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia

In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method. These schemes will be subjected to accuracy and stability tests before being used. Efficacy and robustness of the techniques under consideration will be demonstrated using an exact solution, one-Gausson, as well as conserved quantities. Interaction of two-soliton will be conducted. The numerical findings revealed, the interplay behavior is flexible.

关键词： explicit scheme Implicit scheme Exact Solutions Bounded Domain Stability One Soliton Soliton Interaction Gaussons