A tutorial on the non-linear progressive wave equation (NPE). Part 2. Derivation of the three-dimensional Cartesian version without use of perturbation expansions

Caine, P.; West, M.

doi:10.1016/0003-682x(94)00043-u

Cited by 8 publications

(6 citation statements)

References 3 publications

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“…The NPE model is well adapted for long-range sound propagation applications and it can account for most features of weakly non-linear sound propagation outdoors: geometrical spreading, weak non-linearities, refraction effects (see for example [27,6]), site topography [24], ground impedance [23] and thermoviscous effects [39]. Different models, such as the Fast Field Program (FFP, see [14,31]) or the (linear, frequency-domain) Parabolic Equation (PE, see [15]) could as well be used.…”

Section: Scope and Range Of Applicabilitymentioning

confidence: 99%

“…The non-linear parabolic equation (NPE) has first been developed by McDonald and Kuperman in 1987 [28] (see also [27,6]) and has been successfully used for underwater acoustics simulations 9 [1,7] and blast wave propagation in air [40,2,21]. The NPE model for a 2D domain with Cartesian coordinates (x, z) filed with air is:…”

Section: General Overview Of Npe Modelsmentioning

confidence: 99%

“…Parameter w belongs to the admissible set 6 . The stochastic model for non-linear sound propagation over urban cities is defined by…”

Section: Stochastic Non-linear Propagation Over Urban Citiesmentioning

confidence: 99%

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Computational Model for Long-Range Non-Linear Propagation over Urban Cities

Leissing¹,

Soize²,

Jean³

et al. 2010

Acta Acustica united with Acustica

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A computational model for long-range non-linear sound propagation over urban environments is described. First the probability model of the geometrical parameters of an urban environment are determined using Information Theory and the Maximum Entropy Principle. The propagation model is then presented: it is based on the non-linear parabolic equation (NPE) and its extension to propagation in porous media, in which the urban layer of the real system is represented by a porous ground layer. The uncertainties introduced by the use of this simplified model and the presence of the variability of the real system are taken into account with a probabilistic model. Reference solutions are obtained thanks to the boundary element method (BEM); these experimental observations are then used to identify the parameters of the probability model. This inverse stochastic problem is solved using an evolutionary algorithm which involves both the mean-square method and the maximum likelihood method. Applications and model validation are then presented for two different urban environment morphologies. It is shown that the identification method provides an accurate and robust way for identifying the stochastic model parameters, independently of the variability of the real system. Constructed confidence regions are in good agreement with the numerical observations.

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Section: Scope and Range Of Applicabilitymentioning

confidence: 99%

Section: General Overview Of Npe Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Computational Model for Long-Range Non-Linear Propagation over Urban Cities

Leissing¹,

Soize²,

Jean³

et al. 2010

Acta Acustica united with Acustica

View full text Add to dashboard Cite

show abstract

“…The NPE equation is usually used to describe short-time pulses and a long-range propagation, for instance, in an ocean wave-guide, where the refraction phenomena are important [7,31], while the KZK equation typically models the ultrasonic propagation with strong diffraction phenomena, combining with finite amplitude effects (see Ref. [36] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Models of nonlinear acoustics viewed as an approximation of the Navier–Stokes and Euler compressible isentropic systems

Dekkers

Rozanova-Pierrat

2020

Communications in Mathematical Sciences

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“…The physical context and the physical usage of the KZK and the NPE equations are different: the NPE equation is helpful to describe short-time pulses and a long-range propagation, for instance, in an ocean wave-guide, where the refraction phenomena are important [7,38], while the KZK equation typically models the ultrasonic propagation with strong diffraction phenomena, combining with finite amplitude effects (see [42] and the references therein). But in the same time [12], there is a bijection between the variables of these two models and they can be presented by the same type differential operator with constant positive coefficients:…”

mentioning

confidence: 99%

Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

Dekkers¹,

Rozanova-Pierrat²,

Khodygo³

2020

Discrete &Amp; Continuous Dynamical Systems - A

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We relate together different models of non linear acoustic in thermoelastic media as the Kuznetsov equation, the Westervelt equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressive wave Equation (NPE) and estimate the time during which the solutions of these models keep closed in the L 2 norm. The KZK and NPE equations are considered as paraxial approximations of the Kuznetsov equation. The Westervelt equation is obtained as a nonlinear approximation of the Kuznetsov equation. Aiming to compare the solutions of the exact and approximated systems in found approximation domains the well-posedness results (for the Kuznetsov equation in a half-space with periodic in time initial and boundary data) are obtained.

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A tutorial on the non-linear progressive wave equation (NPE). Part 2. Derivation of the three-dimensional Cartesian version without use of perturbation expansions

Cited by 8 publications

References 3 publications

Computational Model for Long-Range Non-Linear Propagation over Urban Cities

Computational Model for Long-Range Non-Linear Propagation over Urban Cities

Models of nonlinear acoustics viewed as an approximation of the Navier–Stokes and Euler compressible isentropic systems

Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation

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