A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

A restrike waveform predictive model for shunt capacitor bank switching with point-on-wave recommendation

Circuit-breakers (CBs) are subject to electrical stresses with restrikes during capacitor bank operation. Stresses are caused by the overvoltages across CBs, the interrupting currents and the rate of rise of recovery voltage (RRRV). Such electrical stresses also depend on the types of system grounding and the types of dielectric strength curves. The aim of this study is to demonstrate a restrike waveform predictive model for a SF6 CB that considered the types of system grounding: grounded and non-grounded and the computation accuracy comparison on the application of the cold withstand dielectric strength and the hot recovery dielectric strength curve including the POW (point-on-wave) recommendations to make an assessment of increasing the CB remaining life. The simulation of SF6 CB stresses in a typical 400 kV system was undertaken and the results in the applications are presented. The simulated restrike waveforms produced with the identified features using wavelet transform can be used for restrike diagnostic algorithm development with wavelet transform to locate a substation with breaker restrikes. This study found that the hot withstand dielectric strength curve has less magnitude than the cold withstand dielectric strength curve for restrike simulation results. Computation accuracy improved with the hot withstand dielectric strength and POW controlled switching can increase the life for a SF6 CB.

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.