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Temporal-spatial discretization and fractional latency techniques for wave propagation in heterogeneous media De Rybel, Tom


This thesis presents the development of a novel, transient wave propagation simulator using time-decoupled transmission line models. The models are based on the electro-magnetic transient program (EMTP) power system transient analysis tools, extended to two dimensions. The new tool is targeted at acoustic wave propagation phenomena. The method, called TINA for transient insular nodal analysis, uses temporal interpolation and fractional latency to maintain synchronicity in heterogeneous media. The fractional latency method allows the model cells to operate at a local simulation time step which can be a non-integer ratio of the global simulation time step. This simplifies synchronicity and saves computation time and memory. Thévenin equivalents are used to interface the mesh cells and provide an abstraction of the cell content. Numerically, the method is of the transmission-line matrix (TLM) family. In the thesis, loss-less and distortion-less models are considered. The loss-less transmission line models are studied for their stability and numerical error, for which analytical expressions are derived based on the simulation parameters. A number of new relations were discovered and discussed. The TINA method is evaluated in 2D using acoustic experiments, and also a new method is proposed for obtaining impulse responses in time-domain simulation, based on a periodic, band-limited impulse signals.

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