The Transition Regime

Cercignani, Carlo

doi:10.1007/978-1-4612-1039-9_7

The Boltzmann Equation and Its Applications

1988

DOI: 10.1007/978-1-4612-1039-9_7

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The Transition Regime

Carlo Cercignani

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Cited by 2 publications

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“…It can be noted here that the second moment of the distribution function f (x, ξ, t) (eq. ( 5)) is not to be typically used to calculate the temperature field, since it yields a fixed Prandtl number [14]. As a result, eq.…”

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confidence: 99%

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An enthalpy-based thermal lattice Boltzmann model for non-isothermal systems

Chatterjee

2009

Europhys. Lett.

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An enthalpy-based thermal lattice Boltzmann model is introduced for simulating a class of strongly coupled thermo-hydrodynamic problems. The novelty of the model lies in the formulation of an enthalpy density distribution function to simulate the temperature field, in place of the existing internal energy density distribution function. The proposed model has a clear advantage over the earlier internal energy density distribution function based thermal lattice Boltzmann model, in a sense that it can simulate certain classes of thermofluidic transport problems without facing mathematical difficulties in handling with additional energy source terms.

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“…It is well known that following the Chapman-Enskog multiscale expansion [14], it is possible to arrive at the macroscopic Navier-Stokes equation from the Boltzmann transport equation. Let us investigate the behavior of the presently introduced Boltzmann energy transport equation in the long-wavelength and low-frequency limit, in this respect.…”

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An enthalpy-based thermal lattice Boltzmann model for non-isothermal systems

Chatterjee

2009

Europhys. Lett.

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Methods of modelling dispersive sound speed profiles of Martian atmosphere and their effects on sound propagation paths

Sun¹,

Cui²,

Li³

et al. 2022

Acta Phys. Sin.

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At present, Mars acoustic detection is gradually becoming an important new tool for the knowledge and exploration of Mars. To explore the sources of Mars sound, it is necessary to study the sound speed and the sound attenuation in the thin and low-temperature Martian atmosphere, and to model the sound propagation in the stratified atmosphere. Based on the extremely low pressure of Mars and the large variation of gas composition with altitude, we proposed a simulation method based on the Navier-Stokes (NS) equation and the mixed-gas model to calculate the vertical profiles of sound speed and attenuation in the Martian atmosphere at 0~250 km altitude in this paper. By comparing sound-speed profiles at different frequencies, there is notably sound dispersion in the Martian atmosphere, especially at high altitudes and in the high frequency range. It is also verified through sound speed measurement experiments verify that significant sound dispersion does exist in low-pressure carbon dioxide, illustrating the need to consider sound dispersion in the modelling of Martian sound speed profiles. The scope of application of the NS equation in modelling the sound speed of the Martian atmosphere is also discussed, as the NS equation may fail in a too rarefied gas. Next, the non-dispersive ideal-gas sound speed profiles and the dispersive NS sound speed at different frequencies (0.01 Hz, 0.1 Hz, 1 Hz) were applied to simulate the sound propagation paths in the multilayered Martian atmosphere. And both cases of the Martian ground-based and high-altitude sources were compared respectively. It is found that the dispersive sound speed has a significant effect on the sound propagation path on Mars. The main impact is that the first fold back height and the first return distance of the sound ray to the surface are shortened, which directly changes the area and location of the acoustic quiet zone. The effect of dispersion on the sound propagation path becomes more notable with both the increasing frequency and the elevation of the acoustic source, confirming that consideration of dispersion has a significant effect on the calculation of the sound propagation path.

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The Transition Regime

Cited by 2 publications

References 88 publications

An enthalpy-based thermal lattice Boltzmann model for non-isothermal systems

An enthalpy-based thermal lattice Boltzmann model for non-isothermal systems

Methods of modelling dispersive sound speed profiles of Martian atmosphere and their effects on sound propagation paths

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