TLM model of waves in moving media

Abstract

SUMMARYWaves in moving media arise in #uid mechanics and elastic mechanics and are especially signi"cant in acoustics. They are characterized by direction-dependent wave speeds. When compared with the wave equation, the governing di!erential equation, y RR # y VR # y VV "0 has an extra, cross derivative term. An original solution method based on transmission line matrix (TLM) modelling is presented. By means of supplementary link lines controlled by notional &diodes' the TLM mesh wave propagation characteristics are directionally biased. The algorithm is derived and performance assessed for the one-dimensional case. Numerical results agree closely with analytical solutions. The algorithm has interesting properties promising new application areas for TLM.

Wave speeds for a TLM model of moving media

“…In a companion paper [1], a new transmission line matrix (TLM) algorithm was presented for solving the equation…”

An alternative TLM method for steady‐state convection–diffusion

“…The two lines, referred to here as the "diffusion line" and the "convection line" are connected at each node as shown in Figure 2. Each section of the convection line has a notional diode, used previously in TLM to model waves in moving media [12,13], which allows pulses (either positive or negative) to travel in one direction only.…”

An investigation into time domain Doppler modelling using the TLM numerical method

“…2D TLM mesh and 2D scalar TLM node. TIME DOMAIN DOPPLER MODELLING (2), and a transmission coefficient (t) of 1 2 equally on the north, south and east lines. In the TLM iterative process this is usually termed as the scatter procedure, it is duplicated over the entire mesh of TLM nodes, this is most easily represented as a matrix equation of the form…”

“…Their work focuses on moving the medium as apposed to the source or receiver; this is an equivalent formulation that transposes the problems observed by moving sources in TLM (as will be illustrated in Section 3) to the boundaries of the mesh, which will be studied in Section 4. An alternative TLM approach was proposed by O'Connor [2], this suggests keeping the medium stationary while moving the source, using a modified approach to account for dispersive effects at the source, this will be analysed further in Section 3.…”