scholarly journals Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation

2013 ◽  
Vol 13 (3) ◽  
pp. 671-684 ◽  
Author(s):  
Erlend Magnus Viggen
Keyword(s):  
Boltzmann Equation ◽  
Sound Propagation ◽  
Navier Stokes ◽  
Sound Waves ◽  
Discrete Velocity ◽  
Numerical Resolution ◽  
Discretisation Error ◽  
Order Of Magnitude ◽  
Plane Sound ◽  
Propagation Properties

AbstractAs the numerical resolution is increased and the discretisation error decreases, the lattice Boltzmann method tends towards the discrete-velocity Boltzmann equation (DVBE). An expression for the propagation properties of plane sound waves is found for this equation. This expression is compared to similar ones from the Navier-Stokes and Burnett models, and is found to be closest to the latter. The anisotropy of sound propagation with the DVBE is examined using a two-dimensional velocity set. It is found that both the anisotropy and the deviation between the models is negligible if the Knudsen number is less than 1 by at least an order of magnitude.

scholarly journals Is there enough star formation in simulated protoclusters?

2020 ◽  
Vol 501 (2) ◽  
pp. 1803-1822
Author(s):  
Seunghwan Lim ◽  
Douglas Scott ◽  
Arif Babul ◽  
David J Barnes ◽  
Scott T Kay ◽  
...  
Keyword(s):  
Star Formation ◽  
Galaxy Formation ◽  
Star Formation History ◽  
Test Case ◽  
Numerical Resolution ◽  
Formation History ◽  
Order Of Magnitude ◽  
History Of ◽  
Hydrodynamical Simulations ◽  
Formation Efficiency

ABSTRACT As progenitors of the most massive objects, protoclusters are key to tracing the evolution and star formation history of the Universe, and are responsible for ${\gtrsim }\, 20$ per cent of the cosmic star formation at $z\, {\gt }\, 2$. Using a combination of state-of-the-art hydrodynamical simulations and empirical models, we show that current galaxy formation models do not produce enough star formation in protoclusters to match observations. We find that the star formation rates (SFRs) predicted from the models are an order of magnitude lower than what is seen in observations, despite the relatively good agreement found for their mass-accretion histories, specifically that they lie on an evolutionary path to become Coma-like clusters at $z\, {\simeq }\, 0$. Using a well-studied protocluster core at $z\, {=}\, 4.3$ as a test case, we find that star formation efficiency of protocluster galaxies is higher than predicted by the models. We show that a large part of the discrepancy can be attributed to a dependence of SFR on the numerical resolution of the simulations, with a roughly factor of 3 drop in SFR when the spatial resolution decreases by a factor of 4. We also present predictions up to $z\, {\simeq }\, 7$. Compared to lower redshifts, we find that centrals (the most massive member galaxies) are more distinct from the other galaxies, while protocluster galaxies are less distinct from field galaxies. All these results suggest that, as a rare and extreme population at high z, protoclusters can help constrain galaxy formation models tuned to match the average population at $z\, {\simeq }\, 0$.

scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

Scheduling Algorithms With Application to Parallel Computing of Aeroacoustics

2000 ◽  
Author(s):  
Alex Povitsky
Keyword(s):  
Energy Transfer ◽  
Sound Propagation ◽  
Scheduling Algorithm ◽  
Multiprocessor Systems ◽  
Scheduling Problem ◽  
Sound Waves ◽  
Mean Flow ◽  
Shop Scheduling ◽  
Special Case ◽  
Efficient Parallelization

Abstract In this study we consider one method of parallelization of implicit numerical schemes on multiprocessor systems. Then, the parallel high-order compact numerical algorithm is applied to physics of amplification of sound waves in a non-uniform mean flow. Due to the pipelined nature of this algorithm, its efficient parallelization is based on scheduling of processors for other computational tasks while otherwise the processors stay idle. In turn, the proposed scheduling algorithm is taken as a special case of the general shop scheduling problem and possible extentions and generalizations of the proposed scheduling methodology are discussed. Numerical results are discussed in terms of baroclinic generation of wave-associated vorticity that appear to be a key process in energy transfer between a non-uniform mean flow and a propagating disturbance. The discovered phenomenon leads to significant amplification of sound waves and controls the direction of sound propagation.

scholarly journals Reliable Acoustic Path and Direct-Arrival Zone Spatial Gain Analysis for a Vertical Line Array

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3462 ◽  
Author(s):  
Chunyu Qiu ◽  
Shuqing Ma ◽  
Yu Chen ◽  
Zhou Meng ◽  
Jianfei Wang
Keyword(s):  
Sound Propagation ◽  
Correlation Coefficients ◽  
Deep Ocean ◽  
Vertical Line ◽  
Horizontal Line ◽  
Acoustic Path ◽  
Vertical Arrays ◽  
Peak Structure ◽  
Line Array ◽  
Propagation Properties

A method is developed in this paper to calculate the spatial gain of a vertical line array when the plane-wave assumption is not applicable and when the oceanic ambient noise is correlated. The proposed optimal array gain (OAG), which can evaluate the array’s performance and effectively guide its deployment, can be given by an equation in which the noise gain (NG) is subtracted from the signal gain (SG); hence, a high SG and a negative NG can enhance the performance of the array. OAGs and SGs with different array locations are simulated and analyzed based on the sound propagation properties of the direct-arrival zone (DAZ) and the reliable acoustic path (RAP) using ray theory. SG and NG are related to the correlation coefficients of the signals and noise, respectively, and the vertical correlation is determined by the structures of the multipath arrivals. The SG in the DAZ is always high because there is little difference between the multipath waves, while the SG in the RAP changes with the source-receiver range because of the variety of structure in the multiple arrivals. The SG under different conditions is simulated in this work. The “dual peak” structure can often be observed in the vertical directionality pattern of the noise because of the presence of bottom reflection and deep sound channel. When the directions of the signal and noise are close, the conventional beamformer will enhance the correlation of not only the signals but also the noise; thus, the directivity of the signals and noise are analyzed. Under the condition of having a typical sound speed profile, the OAG in some areas of the DAZ and RAP can achieve high values and even exceed the ideal gain of horizontal line array 10 logN dB, while, in some other areas, it will be lowered because of the influence of the NG. The proposed method of gain analysis can provide analysis methods for vertical arrays in the deep ocean under many conditions with references. The theory and simulation are tested by experimental data.

Plane Sound Waves

2020 ◽  
pp. 43-57
Author(s):  
Anatoly Kistovich ◽  
Konstantin Pokazeev ◽  
Tatiana Chaplina
Keyword(s):  
Sound Waves ◽  
Plane Sound
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