A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates

Kampanis, Nikolaos A.; Delis, A. I.; Antonopoulou, Dimitra; Kozyrakis, Georgios V.

doi:10.1016/j.apnum.2011.05.005

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…( 6a), which corresponds to progressive waves in the +x direction. There are two different approaches for including irregular topography into the problem: (i) modelling the ground material as part of the propagation domain through seismo-acoustic models (Collins, 2012;Collins and Siegmann, 2015;Averbuch et al, 2020), or (ii) fitting the numerical grid to the boundary and using an impedance condition at the edge of the domain (Kampanis et al, 2013;Parakkal et al, 2012;Lin, 2019). While the former approach is more physically consistent, it involves coupling different physics at the ground surface, and is often too costly for the added benefit.…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Three-dimensional topographic effects on infrasound propagation across Ascension Island

Khodr

Green

Azarpeyvand

2022

Geophysical Journal International

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Summary Narrowband harmonic infrasound signals within the 1 to 8 Hz passband, generated by wind turbines on Ascension Island, have been recorded at four microbarometers located at distances of between 1.8 and 4.6 km from the source along different azimuths. Across one month of recordings in October 2010, amplitude ratios between the four recordings show temporal stability but deviate from the ratios expected for propagation across a flat plane. Using a recently developed three-dimensional parabolic equation method, that can incorporate realistic topography as a lower boundary, it is shown that these time-independent amplitude ratio deviations can be, in part, explained by acoustic interactions with topography that has scale lengths on the order of a few hundreds of metres. These interactions comprise both two-dimensional barrier effects that reduce sound levels behind high topography, and three-dimensional diffractive effects that increase sound levels behind topographic obstacles. For the Ascension Island case study, amplitudes along two of the four paths can be successfully modelled using a two-dimensional model, indicating that barrier effects dominate for these path geometries. Amplitude ratios along a third path, and the frequency-dependence of these ratios, are better simulated using a three-dimensional model that captures the out-of-plane diffractive effects around a prominent hill. The fourth path is poorly modelled using the three-dimensional model, which overpredicts acoustic amplitudes in this case. We hypothesise that this mismatch is likely to be due to a simplified description of the wind turbine source term. This study provides further observational confirmation that topographic interactions need to be considered when interpreting locally propagating infrasound, and shows that for harmonic narrowband sources a parabolic equation solver incorporating realistic boundary conditions provides an efficient method for simulating topographic interactions.

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Section: Mathematical Backgroundmentioning

confidence: 99%

Three-dimensional topographic effects on infrasound propagation across Ascension Island

Khodr

Green

Azarpeyvand

2022

Geophysical Journal International

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“…Such techniques have been extensively used in 2D: notable contributions include the Generalized Terrain PE (GTPE) (Sack and West, 1995) and the Beilis-Tappert PE (BTPE) (Parakkal et al, 2012), which both rely on the Beilis and Tappert (1979) mapping. A similar approach has been used in conjunction with finiteelements by Kampanis et al (2013) to model propagation over irregular terrain in a refractive atmosphere.…”

Section: Introductionmentioning

confidence: 99%

An iterative three-dimensional parabolic equation solver for propagation above irregular boundaries

Khodr

Azarpeyvand

Green

2020

The Journal of the Acoustical Society of America

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This paper describes the development of an iterative three-dimensional parabolic equation solver that takes into account the effects of irregular boundaries and refraction from a layered atmosphere. A terrain-following coordinate transformation, based on the well-known Beilis-Tappert mapping, is applied to the narrow-angle parabolic equation in an inhomogeneous media. The main advantage of this approach, which has been used in two dimensions in the past, is the simplification of the impedance boundary condition at the earth's surface. The transformed initialboundary value problem is discretized using the Crank-Nicholson marching scheme in the propagating direction and second-order finite-differences in the transversal plane. The proposed method relies on an efficient iterative fixedpoint solver, which involves the inversion of tridiagonal matrices only. The accuracy of the method is evaluated through a comparison with boundary element simulations in a homogeneous atmosphere above a Gaussian hill. Results show that transversal scattering occurs in the shadow zone of the obstacle where the two-dimensional parabolic equation underestimates the pressure amplitude. The model is particularly suited for the simulation of infrasound in a three-dimensional environment with realistic topographies. V

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A finite difference solver for incompressible Navier–Stokes flows in complex domains

Kozyrakis

Delis

Kampanis

2017

Applied Numerical Mathematics

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A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates

Cited by 5 publications

References 24 publications

Three-dimensional topographic effects on infrasound propagation across Ascension Island

Three-dimensional topographic effects on infrasound propagation across Ascension Island

An iterative three-dimensional parabolic equation solver for propagation above irregular boundaries

A finite difference solver for incompressible Navier–Stokes flows in complex domains

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