Numerical Factorization of Propagation Operator for Hyperbolic Equations and Application to One-way, True Amplitude One-way Equations and Bremmer Series

被引:0
作者
Clément Rudel
Sébastien Pernet
Jean-Philippe Brazier
机构
[1] ONERA,
[2] Université de Toulouse,undefined
来源
Journal of Scientific Computing | 2022年 / 93卷
关键词
One-way equations; Hyperbolic; Euler equations; True amplitude; Bremmer series; Backscattering;
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摘要
This paper presents a purely numerical factorization of the propagation operator for a generic hyperbolic equation, based on the work of Towne & Colonius in 2015, that does not require heavy analytical development. This method is applied to form one-way equations with the objective of computing the propagation of waves inside a medium. The main advantage of this formulation is that pseudo eigenvectors and eigenvalues matrices are built, leading to the possibility to use the one-way equations into a true amplitude formalism and/or inside a Bremmer series. These two methods allow an extension of the domain of application of the one-way equations when the medium of propagation presents variations along the privileged direction. In particular, these formulations allow to take into account the phenomena of reflection and refraction of the incident wave. Finally numerical results are presented on different 2D situations based on the linearized Euler equations and compared to the results obtained with a full wave resolution. The issues of both the accuracy and the requirements in computational resources of the one-way resolution are also addressed.
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  • [1] Andersson P(1998)On a Stabilization Procedure for the Parabolic Stability Equations J. Eng. Math. 33 311-332
  • [2] Henningson D(2014)The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena Surv. Geophys. 35 359-393
  • [3] Hanifi A(2001)Microlocal Diagonalization of Strictly Hyperbolic Pseudodifferential Systems and Application to the Design of Radiation Conditions in Electromagnetism SIAM J. Appl. Math. 61 1877-1905
  • [4] Angus DA(1951)Approximation as the First Term of a Geometric-Optical Series Commun. Pure Appl. Math. 4 105-115
  • [5] Antoine X(2019)Modelling of Jet Noise: A Perspective from Large-Eddy Simulations Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377 20190081-481
  • [6] Barucq H(1971)Toward a Unified Theory of Reflector Mapping Geophysics 36 467-3282
  • [7] Bremmer H(1996)Generalization of the Bremmer Coupling Series J. Math. Phys. 37 3246-2532
  • [8] The WKB(2013)Coarse-Grid Computation of the One-Way Propagation of Coupled Modes in a Varying Cross-Section Waveguide The Journal of the Acoustical Society of America 133 2528-191
  • [9] Brès GA(1999)Compact Finite Difference Schemes on Non-Uniform Meshes. Application to Direct Numerical Simulations of Compressible Flows Int. J. Numer. Meth. Fluids 29 159-46
  • [10] Lele SK(2003)High-Order Non-Reflecting Boundary Scheme for Time-Dependent Waves J. Comput. Phys. 186 24-1932