An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller tha...An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.展开更多
Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wav...Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wave equation with damping,a difference(ASC-N,alternating segment Crank-Nicolson)scheme with intrinsic parallelism is proposed.Based on alternating technology,the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson(C-N)scheme.The unconditional stability and convergence are rigorously analyzed.The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.展开更多
The speed of sound waves in a fluidized bed is investigated using CFD-DEM numerical simulations, Appro- priate initial and boundary conditions are applied to reproduce bed phenomena. The effect of varying the height o...The speed of sound waves in a fluidized bed is investigated using CFD-DEM numerical simulations, Appro- priate initial and boundary conditions are applied to reproduce bed phenomena. The effect of varying the height of the bed is also studied. The results of the simulations matched those from the literature. The pressure and particle velocity profiles obtained feature oscillatory behavior to which functions （based on a damped standing wave） were fitted, enabling an explicit dependence on time and space variables to be established. These fitted functions were substituted into the linearized governing equations for the two-phase flow. These solutions enabled a new relationship to be derived for the speed of sound and damping in the system. The conclusion drawn is tbat the damping in the system is governed by the effective bulk viscosity of the solid phase, which arises from the particle viscosity.展开更多
基金supported by the National Natural Science Foundation of China (11172028,10772014)
文摘An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.
基金by the Subproject of Major Science and Technology Program of China(No.2017ZX07101001-01)the Fundamental Research Funds for the Central Universities(Nos.2018MS168 and 2020MS043).
文摘Anomalous diffusion is a widespread physical phenomenon,and numerical methods of fractional diffusion models are of important scientific significance and engineering application value.For time fractional diffusion-wave equation with damping,a difference(ASC-N,alternating segment Crank-Nicolson)scheme with intrinsic parallelism is proposed.Based on alternating technology,the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson(C-N)scheme.The unconditional stability and convergence are rigorously analyzed.The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.
文摘The speed of sound waves in a fluidized bed is investigated using CFD-DEM numerical simulations, Appro- priate initial and boundary conditions are applied to reproduce bed phenomena. The effect of varying the height of the bed is also studied. The results of the simulations matched those from the literature. The pressure and particle velocity profiles obtained feature oscillatory behavior to which functions （based on a damped standing wave） were fitted, enabling an explicit dependence on time and space variables to be established. These fitted functions were substituted into the linearized governing equations for the two-phase flow. These solutions enabled a new relationship to be derived for the speed of sound and damping in the system. The conclusion drawn is tbat the damping in the system is governed by the effective bulk viscosity of the solid phase, which arises from the particle viscosity.
