Electrification is one of the key factors to be considered in the design of power transformers utilizing dielectric liquid as a coolant. Compared with enormous quantity of experimental and analytical studies on electrification, numerical simulations are very few. This paper describes essential elements of numerical solution methods for the charge transport equations in a space between concentric cylinders. It is found that maintaining the conservation property of the convective terms in the governing equations is of the uttermost importance for numerical accuracy, in particular at low reaction rates. Parametric study on the charge transport on the axial plane of the annular space with a predetermined velocity shows that when the convection effect is weak the solutions tend to a one-dimensional nature, where diffusion is simply balanced by conduction. As the convection effect is increased the contours of charge distribution approach the fluid streamlines. Thus, when the conduction effect is weak, charge distribution tends to be uniform and the role of the convection effect becomes insignificant. At an increased conduction effect, on the other hand, the fluid motion transports the charge within the electric double layers toward the top and bottom boundaries leading to an increased amount of total charge in the domain.

A computational code adopting immersed boundary methods for compressible gas-particle multiphase turbulent flows is developed and validated through two-dimensional numerical experiments. The turbulent flow region is modeled by a second-order pseudo skew-symmetric form with minimum dissipation, while the monotone upstream-centered scheme for conservation laws (MUSCL) scheme is employed in the shock region. The present scheme is applied to the flow around a two-dimensional cylinder under various freestream Mach numbers. Compared with the original MUSCL scheme, the minimum dissipation enabled by the pseudo skew-symmetric form significantly improves the resolution of the vortex generated in the wake while retaining the shock capturing ability. In addition, the resulting aerodynamic force is significantly improved. Also, the present scheme is successfully applied to moving two-cylinder problems.

Two mathematical models are used to simulate water quality in a nonuniform flow stream. The first model is the hydrodynamic model that provides the velocity field and the elevation of water. The second model is the dispersion model that provides the pollutant concentration field. Both models are formulated in one-dimensional equations. The traditional Crank-Nicolson method is also used in the hydrodynamic model. At each step, the flow velocity fields calculated from the first model are the input into the second model as the field data. A modified MacCormack method is subsequently employed in the second model. This paper proposes a simply remarkable alteration to the MacCormack method so as to make it more accurate without any significant loss of computational efficiency. The results obtained indicate that the proposed modified MacCormack scheme does improve the prediction accuracy compared to that of the traditional MacCormack method.

A finite Fourier transform is used to perform both linear and nonlinear stability analyses of a Darcy-Lapwood system of convective rolls. The method shows how many modes are unstable, the wave number instability band within each mode, the maximum growth rate (most critical) wave numbers on each mode, and the nonlinear growth rates for each amplitude as a function of the porous Rayleigh number. Single amplitude controls the nonlinear growth rates and thereby the physical flow rate and fluid velocity, on each mode. They are called the flak amplitudes. A discrete Fourier transform is used for numerical simulations and here frequency combinations appear that the traditional cut-off infinite transforms do not have. The discrete show a stationary solution in the weak instability phase, but when carried past 2 unstable modes they show fluctuating motion where all amplitudes except the flak may be zero on the average. This leads to a flak amplitude scaling process of the heat conduction, producing an eddy heat conduction coefficient where a Nu-R_aL relationship is found. It fits better to experiments than previously found solutions but is lower than experiments.

Wave propagation problems can be solved using a variety of methods. However, in many cases, the joint use of different numerical procedures to model different parts of the problem may be advisable and strategies to perform the coupling between them must be developed. Many works have been published on this subject, addressing the case of electromagnetic, acoustic, or elastic waves and making use of different strategies to perform this coupling. Both direct and iterative approaches can be used, and they may exhibit specific advantages and disadvantages. This work focuses on the use of iterative coupling schemes for the analysis of wave propagation problems, presenting an overview of the application of iterative procedures to perform the coupling between different methods. Both frequency- and time-domain analyses are addressed, and problems involving acoustic, mechanical, and electromagnetic wave propagation problems are illustrated.