Dispersion analysis for a TLM mesh of symmetrical condensed nodes with stubs

Morente, Juan A.; Gimenez, G.; Portí, J.A.; Khalladi, Mohsine

doi:10.1109/22.348108

Cited by 20 publications

(14 citation statements)

References 6 publications

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“…One important point to be considered when using a discrete mesh, such as do TLM and FDTD, is that the mesh periodicity causes the solution to propagate at frequency‐dependent phase and group speed, even though the original medium is dispersionless. This numerical dispersion can be neglected as long as the mesh size dimension, Δ l , is chosen so that the minimum wavelength of interest is sampled at least 10 times, Δ l ≤0.1 λ min [ Morente et al , ]. It is important to note that this space sampling limit is more restrictive on the maximum valid frequency for the obtained results than the time sampling limit fixed by Shannon sampling theorem, f max =1/2Δ t .…”

Section: The Tlm Methodsmentioning

confidence: 99%

Full 3‐D TLM simulations of the Earth‐ionosphere cavity: Effect of conductivity on the Schumann resonances

et al. 2016

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Schumann resonances can be found in planetary atmospheres, inside the cavity formed by the conducting surface of the planet and the lower ionosphere. They are a powerful tool to investigate both the electric processes that occur in the atmosphere and the characteristics of the surface and the lower ionosphere. Results from a full 3‐D model of the Earth‐ionosphere electromagnetic cavity based on the Transmission‐Line Modeling (TLM) method are presented. A Cartesian scheme with homogeneous cell size of 10 km is used to minimize numerical dispersion present in spherical schemes. Time and frequency domain results have been obtained to study the resonance phenomenon. The effect of conductivity on the Schumann resonances in the cavity is investigated by means of numerical simulations, studying the transition from resonant to nonresonant response and setting the conductivity limit for the resonances to develop inside the cavity. It is found that the transition from resonant to nonresonant behavior occurs for conductivity values above roughly 10−9 S/m. For large losses in the cavity, the resonances are damped, but, in addition, the peak frequencies change according to the local distance to the source and with the particular electromagnetic field component. These spatial variations present steep variations around each mode's nodal position, covering distances around 1/4 of the mode wavelength, the higher modes being more sensitive to this effect than the lower ones. The dependence of the measured frequency on the distance to the source and particular component of the electric field offers information on the source generating these resonances.

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Section: The Tlm Methodsmentioning

confidence: 99%

Full 3‐D TLM simulations of the Earth‐ionosphere cavity: Effect of conductivity on the Schumann resonances

et al. 2016

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“…The literature presents two methods of deriving wave speeds in TLM systems: one based on circuit theory [2] and the other on evaluation of eigenvalues of a matrix representation of the problem using Floquet's theorem [3,4]. In this case, a new time-domain technique was developed to obtain a closed-form, analytical expression for the wave speed.…”

Section: Wave Speed In Analytical Formmentioning

confidence: 99%

TLM model of waves in moving media

O’Connor

2002

Int J Numerical Modelling

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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.

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“…Thus, a longitude Δ r = 5 km is given to the TLM nodes in the radial direction to allow modeling of the highest frequency dealt with in the numerical algorithm yet without requiring excessive computational resources. To reduce the numerical error associated with the mesh dispersion, the node should be as isotropic as possible so that stub values are as low as possible [ Morente et al , 1995]; consequently, Δ = Δ = Δ r / r 0 are the chosen arcs for the zenithal and azimuthal coordinates to establish the mesh structure, where Titan's radius is r 0 . The small dimensions of the TLM nodes compared with those of the system prevent us carrying out a simulation with the complete spherical shell cavity, so only a stretch with 80 × 200 × 200 nodes is considered.…”

Section: Tlm Numerical Model For Transverse Modes In Titan's Atmospherementioning

confidence: 99%

An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe

et al. 2009

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A numerical simulation of Titan's electromagnetic cavity in the VLF band is carried out using the Transmission Line Matrix (TLM) method, with the aim of assessing the VLF electric field spectra sent by the Huygens probe. In an Earth‐like model, successive peaks would be expected in the spectra, associated with multiple reflections of the electromagnetic wave on the external surfaces of Titan's electromagnetic cavity, formed by the ionosphere and a conductive ground or underground surface. However, owing to high losses conferred by the electrical conductivity to Titan's atmosphere, the direct numerical and experimental spectra are decreasing functions of the frequency without resonances or other special forms. The weak atmospheric resonances are extracted from the data measured by the Huygens's sensors after a procedure based on analysis of the late time response is applied to the experimental spectra. The new late time spectra present the appearance expected, with successive peaks and a mean between adjacent resonances of 0.67 kHz, in agreement with the late time TLM results when the Borucki et al. (2006) conductivity profile with aerosols is introduced in the numerical model. This gap in frequency between successive peaks gives an effective optical distance between the ground and the conductive ionosphere of approximately 220 km, considerably higher than the terrestrial one where this distance is around 75 km.

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Dispersion analysis for a TLM mesh of symmetrical condensed nodes with stubs

Cited by 20 publications

References 6 publications

Full 3‐D TLM simulations of the Earth‐ionosphere cavity: Effect of conductivity on the Schumann resonances

Full 3‐D TLM simulations of the Earth‐ionosphere cavity: Effect of conductivity on the Schumann resonances

TLM model of waves in moving media

An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe

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