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Based on the finite element method (FEM), the parametric variational principle (PVP) is combined with a numerical time-domain integral method to simulate the dynamic behavior of the pantograph-catenary system. Based on PVP, formulations for the nonlinear droppers in the catenary and for the contact between the pantograph and the contact wire are proposed. The formulations can accurately determine the tension state or compression state of the nonlinear droppers and the contact state between the pantograph and the contact wire. Based on the periodicity of the catenary and the precise integration method (PIM), a numerical time-integration method is developed for the dynamic responses of the catenary. For this method, the matrix exponential of only one unit cell of the catenary is computed, which greatly improves the computational efficiency. Moreover, the validation shows that the formulations can compute the contact force accurately and represent the nonlinearity of the droppers, which demonstrates the accuracy and reliability of the proposed method. Finally, the dynamic behaviors of the pantograph-catenary system with different types of catenaries are simulated. [ABSTRACT FROM AUTHOR]

The simple low-dissipation advection upwind splitting method (SLAU) scheme is a parameter-free, low-dissipation upwind scheme that has been applied in a wide range of aerodynamic numerical simulations. In spite of its successful applications, the SLAU scheme could be showing shock instabilities on unstructured grids, as many other contact resolved upwind schemes. Therefore, a hybrid upwind flux scheme is devised for improving the shock stability of SLAU scheme, without compromising on accuracy and low Mach number performance. Numerical flux function of the hybrid scheme is written in a general form, in which only the scalar dissipation term is different from that of the SLAU scheme. The hybrid dissipation term is defined by using a differentiable multidimensional-shock-detection pressure weight function, and the dissipation term of SLAU scheme is combined with that of the Van Leer scheme. Furthermore, the hybrid dissipation term is only applied for the solution of momentum fluxes in numerical flux function. Based on the numerical test results, the hybrid scheme is deemed to be a successful improvement on the shock stability of SLAU scheme, without compromising on the efficiency and accuracy. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the shallow water problem is discussed. By treating the incompressible condition as the constraint, a constrained Hamilton variational principle is presented for the shallow water problem. Based on the constrained Hamilton variational principle, a shallow water equation based on displacement and pressure (SWE-DP) is developed. A hybrid numerical method combining the finite element method for spatial discretization and the Zu-class method for time integration is created for the SWEDP. The correctness of the proposed SWE-DP is verified by numerical comparisons with two existing shallow water equations (SWEs). The effectiveness of the hybrid numerical method proposed for the SWE-DP is also verified by numerical experiments. Moreover, the numerical experiments demonstrate that the Zu-class method shows excellent performance with respect to simulating the long time evolution of the shallow water. [ABSTRACT FROM AUTHOR]

A symplectic algorithm with nonuniform grids is proposed for solving the hypersensitive optimal control problem using the density function. The proposed method satisfies the first-order necessary conditions for the optimal control problem that can preserve the structure of the original Hamiltonian systems. Furthermore, the explicit Jacobi matrix with sparse symmetric character is derived to speed up the convergence rate of the resulting nonlinear equations. Numerical simulations highlight the features of the proposed method and show that the symplectic algorithm with nonuniform grids is more computationally efficient and accuracy compared with uniform grid implementations. Besides, the symplectic algorithm has obvious advantages on optimality and convergence accuracy compared with the direct collocation methods using the same density function for mesh refinement. [ABSTRACT FROM AUTHOR]

A semianalytical spectral element method (SEM) is proposed for electromagnetic simulations of 3-D layered structures. 2-D spectral elements are employed to discretize the cross section of a layered structure, and the Legendre transformation is then used to cast the semidiscretized problem from the Lagrangian system into the Hamiltonian system. A Riccati equation-based high precision integration method is utilized to perform integration along the longitudinal direction, which is the undiscretized direction, to generate the stiffness matrix of the whole layered structure. The final system of equations by the semianalytical SEM will take the form of a set of linear equations with a block tri-diagonal matrix, which can be solved efficiently by the block Thomas algorithm. Numerical examples demonstrate the high efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

• The mechanical friction force during the control rod drop is treated as a time-variant uncertainty for uncertainty analysis; • The interval process model is used to describe the time-variant uncertain mechanical friction during the CR drop; • The uncertainty analysis of CR drop considering various uncertain parameters is conducted; • A novel and general computational framework for uncertainty analysis of CR drop, UA-CRD, is proposed. Due to the influence of multiple factors, the control rod drop involves some uncertain parameters. The mechanical friction on the control rod is a time-variant uncertain parameter and is related to the position of the control rod. For the first time, this paper adopts the interval process model, which accurately describes the uncertainty parameters by using small-scale samples, to describe the uncertain mechanical friction on the control rod. The numerical experimental results demonstrate that the interval process model can describe the mechanical friction with high accuracy, even when employing small-scale samples. Furthermore, it is found that the uncertainty analysis can be considered as solving the extremal problem of a black-box model. Based on it, we propose a novel and general calculation framework for uncertainty analysis of control rod drop, UA-CRD. Through the analysis of numerical examples, it is verified that UA-CRD can accurately and efficiently conduct the uncertainty analysis of control rod drop. [ABSTRACT FROM AUTHOR]