3. Electronic Theses and Dissertations (ETDs) - All submissions
Permanent URI for this communityhttps://wiredspace.wits.ac.za/handle/10539/45
Browse
3 results
Search Results
Item Review of stokes flow past a sphere(2019) Banda, SiphoThe slow viscous incompressible flow past a stationary sphere is studied. We review Stokes and Oseen approximations. The stream function approach is used to derive the solutions of incompressible fluid flow that were obtained by Stokes and Oseen. We solve the Stokes expansion using Mathematica and the code is given in the algorithms. The explicit finite difference method (FDM) is used to solve the fourth order differential equation that was derived from the full Navier-Stokes equations. We also investigate numerical solutions to the Stokes expansion using standard (FDM) in Mathematica. Using FDM iteratively we can find approximate solutions to higher moments in the stream function and compare these solutions with those found from the numerical solutions to the full Navier-Stokes equations.Item Numerical investigation into sound synthesis by physical modeling(2018) Borole, LethaboA linear and a non-linear partial di erential equation is used as a phenomenological model to describe the synthesis of a vibrating string. The models are numerically simulated using nite di erence method and an exact solution of the linear partial di erential equation is derived using a functional transformation method. The functional transformation method is based on the transformation to the frequency domain in time and in space by applying the Laplace transformation and the Finite Sine transformation. The string is excited through the initial conditions, initial displacement and an initial velocity, of the system. Another excitation mode that is considered is the force density, where the initial conditions are set to zero. The force density is added as a Source term to the partial di erential equation and the initial excitation enters the system by the use of this term. To analyse the model di erent observation positions are considered, the observation points are the positions of the string where the vibrations are observed. The exact solution is used to verify the Finite di erence approximation and a spectrogram analysis of the di erent excitation points is used to asses the methods. The nite di erence method is then used to analysis the vibrations of the string. The nonlinear model include the e ects of tension modulation, which is de ned by the Kirchho -Carrier equation. The results are analysed using a quantitative analysis and a Fourier analysis.Item Lightning return stroke electromagnetics - time domain evaluation and application(2016) McAfee, Carson William IanThe work presented extends and contributes to the research of modelling lightning return stroke (RS) electromagnetic (EM) fields in the time domain. Although previous work in this area has focused on individual lightning electromagnetic pulse (LEMP) modelling techniques, there has not been an investigation into the strengths and weaknesses of different methods, as well as the implementation considerations of the models. This work critically compares three unique techniques (Finite Antenna, FDTD, and Single Cell FDTD) under the same ideal simulation parameters. The research presented will evaluate the EM fields in the range of 50m to 500m from the lightning channel. This range, often referred to as the near field distance, has a significant effect on lightning induced overvoltages on distribution lines, which are primarily created by the horizontal EM fields of the RS channel. These close distances have a significant effect on the model implementations, especially with the FDTD method. Each of these modelling methods is explained and tested through examples. The models are implemented in C++ and have been included in the Appendix to aid in future implementation. From the model simulations it is clear that the FDTD method is the most comprehensive model available. It allows for non-ideal ground planes, as well as complex simulation environments. However, FDTD has a number of numerical related errors that the Finite Antenna method does not suffer from. The Single Cell FDTD method is simple to implement and does not suffer from the same numerical errors as a full FDTD implementation, but is limited to simple simulation environments. This work contributes to the research field by comparing and evaluating three techniques and giving consideration to the implementation and the applicability to lightning EM simulations.