scholarly journals ANALYSIS OF DISPERSION ERRORS IN ACOUSTIC WAVE SIMULATIONS

2006 ◽  
Vol 5 (1) ◽  
pp. 62
Author(s):  
R. A. C. Germanos ◽  
L. F. De Souza
Keyword(s):  
Acoustic Wave ◽  
Fourth Order ◽  
Finite Differences ◽  
Acoustic Waves ◽  
Time Integration ◽  
Compact Scheme ◽  
High Order Accuracy ◽  
Discretization Schemes ◽  
Analysis Of Dispersion ◽  
The Waves

The governing equations of the acoustic problem are the compressible Euler equations. The discretization of these equations has to ensure that the acoustic waves are transported with non-dispersive and non-dissipative characteristics. In the present study numerical simulations of a standing acoustic wave are performed. Four different space discretization schemes are tested, namely, a second order finite-differences, a fourth order finitedifferences, a fourth order finite-differences compact scheme and a sixth order finite-differences compact scheme. The time integration is done with a fourth order Runge-Kutta scheme. The results obtained are compared with linearized analytical solutions. The influence of the dispersion on the simulation of a standing wave is analyzed. The results confirm that high order accuracy schemes can be more efficient for simulation of acoustic waves, especially the waves with high frequency.

Research on the Method to Decompose Propagation Sound Wave in Annular Duct

2012 ◽  
Vol 472-475 ◽  
pp. 1074-1077
Author(s):  
Zhan Xin Liu
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Decomposition Methods ◽  
Benchmark Problems ◽  
Fourier Mode ◽  
Governing Equations ◽  
Experiment Data ◽  
Annular Duct ◽  
Energy Relations ◽  
The Waves

There are many benchmark problems which have exact solutions or experiment data to gauge the simulation of aeroacoustic problems. Annular duct acoustic modes are good benchmark problems of this kind. The waves propagated along the duct can be considered as the summation of infinite Fourier modes. The energy relations of a single Fourier mode are deduced from governing equations in this paper. To investigate the properties of acoustic wave propagating along the duct, it’s necessary to decompose acoustic waves in the duct into multiple Fourier modes; the decomposition methods are presented.

scholarly journals Acoustic Wave Properties in Footpoints of Coronal Loops in 3D MHD Simulations

2021 ◽  
Vol 922 (2) ◽  
pp. 225
Author(s):  
Julia M. Riedl ◽  
Tom Van Doorsselaere ◽  
Fabio Reale ◽  
Marcel Goossens ◽  
Antonino Petralia ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Standing Waves ◽  
Initial Energy ◽  
Solar Chromosphere ◽  
Coronal Loops ◽  
Mhd Simulations ◽  
Wave Flux ◽  
The Waves ◽  
Wave Properties

Abstract Acoustic waves excited in the photosphere and below might play an integral part in the heating of the solar chromosphere and corona. However, it is yet not fully clear how much of the initially acoustic wave flux reaches the corona and in what form. We investigate the wave propagation, damping, transmission, and conversion in the lower layers of the solar atmosphere using 3D numerical MHD simulations. A model of a gravitationally stratified expanding straight coronal loop, stretching from photosphere to photosphere, is perturbed at one footpoint by an acoustic driver with a period of 370 s. For this period, acoustic cutoff regions are present below the transition region (TR). About 2% of the initial energy from the driver reaches the corona. The shape of the cutoff regions and the height of the TR show a highly dynamic behavior. Taking only the driven waves into account, the waves have a propagating nature below and above the cutoff region, but are standing and evanescent within the cutoff region. Studying the driven waves together with the background motions in the model reveals standing waves between the cutoff region and the TR. These standing waves cause an oscillation of the TR height. In addition, fast or leaky sausage body-like waves might have been excited close to the base of the loop. These waves then possibly convert to fast or leaky sausage surface-like waves at the top of the main cutoff region, followed by a conversion to slow sausage body-like waves around the TR.

scholarly journals Formation of a Complex Topologies of SAW-Based Inertial Sensors by Laser Thin Film Local Evaporation

Micromachines ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 10
Author(s):  
Alexander Kukaev ◽  
Dmitry Lukyanov ◽  
Denis Mikhailenko ◽  
Daniil Safronov ◽  
Sergey Shevchenko ◽  
...  
Keyword(s):  
Thin Film ◽  
Acoustic Wave ◽  
Surface Acoustic Wave ◽  
Acoustic Waves ◽  
Inertial Sensors ◽  
Surface Acoustic Waves ◽  
Sensing Element ◽  
Small Series ◽  
Evaporation Technique ◽  
Photolithography Process

Originally, sensors based on surface acoustic waves are fabricated using photolithography, which becomes extremely expensive when a small series or even single elements are needed for the research. A laser thin film local evaporation technique is proposed to substitute the photolithography process in the production of surface acoustic wave based inertial sensors prototypes. To estimate its potential a prototype of a surface acoustic wave gyroscope sensing element was fabricated and tested. Its was shown that the frequency mismatch is no more than 1%, but dispersion of the wave on small inertial masses leads to a spurious parasitic signal on receiving electrodes. Possible ways of its neglecting is discussed.

Parametric excitation of magnetoacoustic waves by a pump magnetic field in a high-β plasma

1977 ◽  
Vol 17 (1) ◽  
pp. 93-103 ◽  
Author(s):  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Parametric Excitation ◽  
Acoustic Waves ◽  
Magnetic Pressure ◽  
Gas Pressure ◽  
Alfven Wave ◽  
Fast Wave ◽  
Magnetoacoustic Waves ◽  
Background Magnetic Field ◽  
The Waves

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).

Linear and Nonlinear Analysis of Additively Manufactured Material With Different Porosity Induced by Varying Material Printing Speed Using Guided Acoustic Waves

2021 ◽  
Author(s):  
SeHyuk Park ◽  
Hamad Alnuaimi ◽  
Anna Hayes ◽  
Madison Sitkiewicz ◽  
Umar Amjad ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Nonlinear Analysis ◽  
Lead Zirconate Titanate ◽  
Acoustic Waves ◽  
Scanning Speed ◽  
Lead Zirconate ◽  
Nonlinear Ultrasonic ◽  
Scan Speed ◽  
Linear And Nonlinear ◽  
Characterization Of Materials

Abstract Guided acoustic wave based techniques have been found to be very effective for damage detection, and both quantitative and qualitative characterization of materials. In this research, guided acoustic wave techniques are used for porosity evaluation of additively manufactured materials. A metal 3D printer, Concept Laser Mlab 200 R Cusing™, is used to manufacture 316L additively manufactured (AM) stainless steel specimens. Two levels of porosity are investigated in this study, which was controlled by a suitable combination of scan speed and laser power. The sample with lower level of porosity is obtained with a low scanning speed. Lead Zirconate Titanate (PZT) transducers are used to generate guided acoustic waves. The signal is excited and propagated through the specimens in a single sided transmission mode setup. Signal processing of the recorded signals for damage analysis involves both linear and nonlinear analyses. Linear ultrasonic parameters such as the time-of-flight and magnitude of the propagating waves are recorded. The nonlinear ultrasonic parameter, the Sideband Peak Count Index (SPC-I) is obtained by a newly developed nonlinear analysis technique. Results obtained for both specimens are analyzed and compared using both linear and nonlinear ultrasonic techniques. Finally, the effectiveness of SPC-I technique in monitoring porosity levels in AM specimens is discussed.

FOURTH-ORDER COMPACT SCHEME FOR OPTION PRICING UNDER THE MERTON’S AND KOU’S JUMP-DIFFUSION MODELS

2018 ◽  
Vol 21 (04) ◽  
pp. 1850027 ◽  
Author(s):  
KULDIP SINGH PATEL ◽  
MANI MEHRA
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Linear Equations ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Compact Scheme ◽  
Discrete Problem ◽  
Option Prices ◽  
Fully Discrete ◽  
Fourth Order Compact Scheme

In this paper, a compact scheme with three time levels is proposed to solve the partial integro-differential equation that governs the option prices in jump-diffusion models. In the proposed compact scheme, the second derivative approximation of the unknowns is approximated using the value of these unknowns and their first derivative approximations, thereby allowing us to obtain a tridiagonal system of linear equations for a fully discrete problem. Moreover, the consistency and stability of the proposed compact scheme are proved. Owing to the low regularity of typical initial conditions, a smoothing operator is employed to ensure the fourth-order convergence rate. Numerical illustrations concerning the pricing of European options under the Merton’s and Kou’s jump-diffusion models are presented to validate the theoretical results.

scholarly journals Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160798 ◽  
Author(s):  
Wenjun Cai ◽  
Huai Zhang ◽  
Yushun Wang
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Conservation Law ◽  
Heterogeneous Media ◽  
Numerical Dispersion ◽  
Discrete Version ◽  
Symplectic Method ◽  
Ode System ◽  
Strang Splitting

We propose a novel stable and efficient dissipation-preserving method for acoustic wave propagations in attenuating media with both correct phase and amplitude. Through introducing the conformal multi-symplectic structure, the intrinsic dissipation law and the conformal symplectic conservation law are revealed for the damped acoustic wave equation. The proposed algorithm is exactly designed to preserve a discrete version of the conformal symplectic conservation law. More specifically, two subsystems in conjunction with the original damped wave equation are derived. One is actually the conservative Hamiltonian wave equation and the other is a dissipative linear ordinary differential equation (ODE) system. Standard symplectic method is devoted to the conservative system, whereas the analytical solution is obtained for the ODE system. An explicit conformal symplectic scheme is constructed by concatenating these two parts of solutions by the Strang splitting technique. Stability analysis and convergence tests are given thereafter. A benchmark model in homogeneous media is presented to demonstrate the effectiveness and advantage of our method in suppressing numerical dispersion and preserving the energy dissipation. Further numerical tests show that our proposed method can efficiently capture the dissipation in heterogeneous media.

scholarly journals Analysis of Propagation and Distribution Characteristics of Leakage Acoustic Waves in Water Supply Pipelines

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5450
Author(s):  
Yunfei Li ◽  
Yang Zhou ◽  
Ming Fu ◽  
Fan Zhou ◽  
Zhaozhao Chi ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Water Supply ◽  
Acoustic Waves ◽  
Simulation Analysis ◽  
Acoustic Signals ◽  
Detection Methods ◽  
Acoustic Analogy ◽  
Acoustic Wave Propagation ◽  
Source Characteristics ◽  
Water Supply Pipeline

Leakage detection methods based on the analysis of leakage acoustic signals provide an effective technical approach for detecting small leaks in water supply pipelines. From a technical perspective, the study of the propagation characteristics of acoustic waves generated by the leakage in the water supply pipeline is necessary for detecting the leak location on the basis of acoustic signals. In this study, a 3D transient leakage acoustic wave propagation equation was derived by combining the principles of fluid dynamics and Lighthill acoustic analogy theory. The propagation of the leakage-induced noise in water supply pipeline was modelled theoretically. We simulated the propagation of a leakage acoustic wave under different conditions for different target scenarios encountered in actual pipeline inspections. Specifically, we analysed the effect of different factors, such as the pipe size and acoustic source characteristics, on acoustic propagation. Finally, the simulated experiments were practically performed using a self-designed simulated water supply pipeline and self-developed spherical water supply pipeline detector to validate the simulation analysis. The results of this study provide a theoretical guidance and basis for the analysis of characteristics of leakage acoustic wave signals and the recognition of leakage conditions in water supply pipelines.

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