A survey of weakly-nonlinear acoustic models: 1910–2009

Jordan, P.M.

doi:10.1016/j.mechrescom.2016.02.014

Cited by 39 publications

(36 citation statements)

References 46 publications

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“…There are many nonlinear acoustic models in the literature that serve as approximations of the compressible Navier-Stokes system; we refer the interested reader to the survey [23]. One of the most popular models is the Kuznetsov equation…”

Section: Problem Settingmentioning

confidence: 99%

Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics

Fritz

Nikolić

Wohlmuth

2018

Math. Models Methods Appl. Sci.

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We study the Blackstock equation which models the propagation of nonlinear sound waves through dissipative fluids. Global well-posedness of the model with homogeneous Dirichlet boundary conditions is shown for small initial data. To this end, we employ a fixed-point technique coupled with well-posedness results for a linearized model and appropriate energy estimates. Furthermore, we obtain exponential decay for the energy of the solution. We present additionally a finite element-based method for solving the Blackstock equation and illustrate the behavior of solutions through several numerical experiments.

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Section: Problem Settingmentioning

confidence: 99%

Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics

Fritz

Nikolić

Wohlmuth

2018

Math. Models Methods Appl. Sci.

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“…34is the dusty gas shock analog of the critical acceleration wave amplitude value exhibited by the "Darcy-Jordan model" 12 of poroacoustics; see, e.g., Ref. [20,Eq. (96)], wherein the dimensionless Darcy coefficient divided by two, i.e., δ/2 (not to be confused with the diffusivity of sound divided by two), corresponds to κ here.…”

Section: Observations and Final Remarksmentioning

confidence: 99%

Finite-amplitude acoustics under the classical theory of particle-laden flows

Jordan¹

2019

Evolution Equations &Amp; Control Theory

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We consider acoustic propagation in a particle-laden fluid, specifically, a perfect gas, under a model system based on the theories of Marble (1970) and Thompson (1972). Our primary aim is to understand, via analytical methods, the impact of the particle phase on the acoustic velocity field. Working under the finite-amplitude approximation, we investigate singular surface and traveling wave phenomena, as admitted by both phases of the flow. We show, among other things, that the particle velocity field admits a singular surface one order higher than that of the gas phase, that the particleto-gas density ratio plays a number of critical roles, and that traveling wave solutions are only possible for sufficiently small values of the Mach number. i.e., the particle specific heat (at constant pressure) is negligibly small; see Thompson [34, pp. 553-556]. The immediate (practical) consequence of this assumption is τ T = 0 (⇒ the absence of thermal inertia), where τ T ∝ c pp is the thermal relaxation time.

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“…We suppose the wave is moving into a region in which u X , p and θ are constants, so that u + X , p + and θ + are constants, where the jump notation [ü] =ü − −ü + is used. The idea is to differentiate equation (19), and take the jumps, and then employ the one-dimensional equivalents of equations (14), (15) and (16) together with the Hadamard relation and the equation for the jump of a product. Since the calculations are now well known we simply state the final result.…”

Section: Amplitude Calculationmentioning

confidence: 99%

“…The topic of wave propagation in porous and acoustic media is one of great interest in the current research literature, see e.g. Biot [1], Brunnhuber and Jordan [2], Christov [3], Christov and Jordan [4], Christov et al [5], Ciarletta and Straughan [6][7][8], Jordan [9][10][11][12][13][14], Jordan and Puri [15], Jordan and Saccomandi [16], Jordan et al [17,18], Paoletti [19], Rossmanith and Puri [20,21], Wei and Jordan [22].…”

Section: Introductionmentioning

confidence: 99%