In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved dire...In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.展开更多
为了提升采煤机运行安全性与稳定性,以MG300-700-AWD型采煤机为研究对象,通过有限元法对采煤机平滑靴与中部槽接触碰撞特性进行了研究。研究发现,中部槽安装间隙量与高度差是影响平滑靴接触碰撞特性的重要因素,随着安装间隙量与高度差...为了提升采煤机运行安全性与稳定性,以MG300-700-AWD型采煤机为研究对象,通过有限元法对采煤机平滑靴与中部槽接触碰撞特性进行了研究。研究发现,中部槽安装间隙量与高度差是影响平滑靴接触碰撞特性的重要因素,随着安装间隙量与高度差的提高,平滑靴碰撞特性应力升高,当安装间隙量超过30 mm,平滑靴产生的接触力会超过ZG25CrMn Ni Mo许用应力的222.67 MPa,增加平滑靴碰撞损伤的危险。采煤机运行过程中应注重安装间隙量与高度差的控制,通过实践应用验证了模拟分析结果的合理性,将安装间隙量与高度差控制在较低水平范围内,可保证整个采煤机稳定运行,有利于煤矿开采工作更好地开展。展开更多
In the practical problems such as nuclear waste pollution and seawater intrusion etc., many problems are reduced to solving the convection-diffusion equation, so the research of convection-diffusion equation is of gre...In the practical problems such as nuclear waste pollution and seawater intrusion etc., many problems are reduced to solving the convection-diffusion equation, so the research of convection-diffusion equation is of great value. In this work, a spectral method is presented for solving one and two dimensional convection-diffusion equation with source term. The finite difference method is also used to solve the convection diffusion equation. The numerical experiments show that the spectral method is more efficient than other methods for solving the convection-diffusion equation.展开更多
In this paper,we present a linearized compact difference scheme for onedimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions.The initial singularity of the solutio...In this paper,we present a linearized compact difference scheme for onedimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions.The initial singularity of the solution is considered,which often generates a singular source and increases the difficulty of numerically solving the equation.The Crank-Nicolson technique,combined with the midpoint formula and the second-order convolution quadrature formula,is used for the time discretization.To increase the spatial accuracy,a fourth-order compact difference approximation,which is constructed by two compact difference operators,is adopted for spatial discretization.Then,the unconditional stability and convergence of the proposed scheme are strictly established with superlinear convergence accuracy in time and fourth-order accuracy in space.Finally,numerical experiments are given to support our theoretical results.展开更多
The standard finite difference scheme(forward difference approximation for time derivative and central difference approximations for spatial derivatives)for fourth-order nonlinear diffusion filter allows very small ti...The standard finite difference scheme(forward difference approximation for time derivative and central difference approximations for spatial derivatives)for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results.The alternating directional implicit(ADI)splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size.In this paper,we develop 3×3 stencils for the approximation of second-order spatial derivatives based on the finite pointset method.We then make use of these stencils for approximating the fourth-order partial differential equation.We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme,without compromising on the quality of the filtered image.Further,we demonstrate through numerical simulations that the proposed scheme is more efficient,in obtaining quality filtered image,than an ADI splitting scheme.展开更多
文摘In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.
文摘为了提升采煤机运行安全性与稳定性,以MG300-700-AWD型采煤机为研究对象,通过有限元法对采煤机平滑靴与中部槽接触碰撞特性进行了研究。研究发现,中部槽安装间隙量与高度差是影响平滑靴接触碰撞特性的重要因素,随着安装间隙量与高度差的提高,平滑靴碰撞特性应力升高,当安装间隙量超过30 mm,平滑靴产生的接触力会超过ZG25CrMn Ni Mo许用应力的222.67 MPa,增加平滑靴碰撞损伤的危险。采煤机运行过程中应注重安装间隙量与高度差的控制,通过实践应用验证了模拟分析结果的合理性,将安装间隙量与高度差控制在较低水平范围内,可保证整个采煤机稳定运行,有利于煤矿开采工作更好地开展。
文摘In the practical problems such as nuclear waste pollution and seawater intrusion etc., many problems are reduced to solving the convection-diffusion equation, so the research of convection-diffusion equation is of great value. In this work, a spectral method is presented for solving one and two dimensional convection-diffusion equation with source term. The finite difference method is also used to solve the convection diffusion equation. The numerical experiments show that the spectral method is more efficient than other methods for solving the convection-diffusion equation.
基金supported by Natural Science Foundation of Jiangsu Province of China(Grant No.BK20201427)National Natural Science Foundation of China(Grant Nos.11701502 and 11871065)。
文摘In this paper,we present a linearized compact difference scheme for onedimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions.The initial singularity of the solution is considered,which often generates a singular source and increases the difficulty of numerically solving the equation.The Crank-Nicolson technique,combined with the midpoint formula and the second-order convolution quadrature formula,is used for the time discretization.To increase the spatial accuracy,a fourth-order compact difference approximation,which is constructed by two compact difference operators,is adopted for spatial discretization.Then,the unconditional stability and convergence of the proposed scheme are strictly established with superlinear convergence accuracy in time and fourth-order accuracy in space.Finally,numerical experiments are given to support our theoretical results.
文摘The standard finite difference scheme(forward difference approximation for time derivative and central difference approximations for spatial derivatives)for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results.The alternating directional implicit(ADI)splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size.In this paper,we develop 3×3 stencils for the approximation of second-order spatial derivatives based on the finite pointset method.We then make use of these stencils for approximating the fourth-order partial differential equation.We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme,without compromising on the quality of the filtered image.Further,we demonstrate through numerical simulations that the proposed scheme is more efficient,in obtaining quality filtered image,than an ADI splitting scheme.
