Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly im...Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.展开更多
The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special r...The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.展开更多
A novel numerical method for fiber Raman amplifier (FRA) from standard propagation equations is presented and derived based on the one-step method for ordinary differential equation (ODE). The proposed algorithm is ef...A novel numerical method for fiber Raman amplifier (FRA) from standard propagation equations is presented and derived based on the one-step method for ordinary differential equation (ODE). The proposed algorithm is effective in solving FRA equations including all the interactions among pumps, signals, and noises. Applications of the numerical analysis to practical FRA-based systems show a great reduction in computation time in comparison with the average power method and the fourth-order Runge-Kutta (RK) method, under the same condition. Also the proposed method can decrease the computing time over three orders of magnitude with excellent accuracy promises in comparison with the direct integration method.展开更多
文摘Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.
文摘The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.
文摘A novel numerical method for fiber Raman amplifier (FRA) from standard propagation equations is presented and derived based on the one-step method for ordinary differential equation (ODE). The proposed algorithm is effective in solving FRA equations including all the interactions among pumps, signals, and noises. Applications of the numerical analysis to practical FRA-based systems show a great reduction in computation time in comparison with the average power method and the fourth-order Runge-Kutta (RK) method, under the same condition. Also the proposed method can decrease the computing time over three orders of magnitude with excellent accuracy promises in comparison with the direct integration method.
