Dispersion analysis of two-dimensional unstructured transmission line modelling (UTLM)

• Main Author: Khashan, Lamia M. A.
• Published: University of Nottingham 2015
• Subjects: 537; QC501 Electricity and magnetism
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.666918

Numerical simulation techniques play an important role due to their flexibility in dealing with a broad range of complex geometries and material responses. This flexibility requires substantial computational time and memory. Most numerical methods use structured grid for graphical discretization, although this approach is straightforward it is not ideal for smoothly curved boundaries. In this thesis the two-dimensional Transmission Line Modelling (TLM) method based on unstructured meshes is adopted. TLM is an established numerical simulation technique that has been employed in a variety of applications area. Using unstructured meshes to discretize the problem domain permits smooth boundary presentation which provides significant enhancement in the flexibility and accuracy of the TLM simulations. An algorithm is developed to implement Unstructured Transmission Line Modelling (UTLM) which is carefully designed for simplicity and scalability of model size. Several examples are employed to test the accuracy and efficiency of the UTLM simulations. Delaunay meshes, as a type of unstructured meshes, provide good quality triangles but have the disadvantage of providing close to zero transmission line length which has impact on the maximum permissible time step for stable operation. In this thesis, a simple perturbation method for relaxing the minimum link length and clustering triangles in pairs is presented, which permits substantial increase in time step and hence computational runtime to be made without compromising the simulation stability or accuracy. Also, a new model for relaxing the short link lines that fall on the boundaries is presented. UTLM method is based on temporal and spatial sampling of electromagnetic fields which results in dispersion. In this thesis, dispersion characteristics of the unstructured TLM mesh are investigated and compared against structured TLM results for different mesh sizes and shapes. Unlike the structured TLM mesh, the unstructured mesh gives rise to spatial mode coupling. Intermodal coupling behaviour is investigated in a statistical manner upon the change of the mesh local characteristics.