A tutorial on the Nonlinear Progressive wave Equation (NPE)—Part 1

McDonald, B. Edward; Caine, P.; West, M.

doi:10.1016/0003-682x(94)90059-0

Cited by 14 publications

(16 citation statements)

References 1 publication

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“…It was originally developed to describe long-range underwater acoustic propagation from high intensity sources (such as explosions) due to its efficient moving grid formulation. The NPE is derived in terms of a single variable from Euler's conservation of mass and momentum equations with the assumptions that associated shocks are weak and that propagation is strongest in the preferred direction of propagation (range direction) (McDonald et al, 1994). The assumption that propagation is strongest in range will be referred to as the small angle approximation.…”

Section: List Of Figures and Tablesmentioning

confidence: 99%

“…Further, the NPE is capable of describing several different physical effects of propagation such as diffraction, refraction, and nonlinear steepening. The approach used in the derivation presented here is taken from a previously published paper (McDonald et al, 1994). One assumes that the background medium velocity is zero and that the pulse is at sufficiently far distance from the source (a distance where pressures may be assumed to have "acoustic" values).…”

Section: Derivation Of the Npementioning

confidence: 99%

“…This chapter will give a detailed derivation of the nonlinear progressive wave equation (NPE), following largely from the earlier work of (McDonald et al, 1994). After deriving the equation, the FCT algorithm (McDonald & Ambrosiano, 1984) will be described, and FD methods used will be explained.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear acoustic pulse propagation in range-dependent underwater environments

Maestas

Collis

2012

The Journal of the Acoustical Society of America

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The nonlinear progressive wave equation (NPE) is a time-domain formulation of Eulers fluid equations designed to model low angle wave propagation using a wave-following computational domain. The standard formulation consists of four separate mathematical quantities that physically represent refraction, nonlinear steepening, radial spreading, and diffraction. The latter two of these effects are linear whereas the steepening and refraction are nonlinear. This formulation recasts pressure, density, and velocity into a single variable a dimensionless pressure perturbation which allows for greater efficiency in calculations.The wave-following frame of reference permits the simulation of long-range propagation that is useful in modeling the effects of blast waves in the ocean waveguide. Nonlinear effects such as weak shock formation are accurately captured with the NPE. The numerical implementation is a combination of two numerical schemes: a finite-difference Crank-Nicholson algorithm for the linear terms of the NPE and a flux-corrected transport algorithm for the nonlinear terms. In this work, an existing implementation is extended to allow for a penetrable fluid bottom. Range-dependent environments, characterized by sloping bathymetry, are investigated and benchmarked using a rotated coordinate system approach.

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Section: List Of Figures and Tablesmentioning

confidence: 99%

Section: Derivation Of the Npementioning

confidence: 99%

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Nonlinear acoustic pulse propagation in range-dependent underwater environments

Maestas

Collis

2012

The Journal of the Acoustical Society of America

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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%

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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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

West

1995

Applied Acoustics

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A tutorial on the Nonlinear Progressive wave Equation (NPE)—Part 1

Cited by 14 publications

References 1 publication

Nonlinear acoustic pulse propagation in range-dependent underwater environments

Nonlinear acoustic pulse propagation in range-dependent underwater environments

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

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

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