The Auxiliary Differential Equations Perfectly Matched Layers Based on the Hybrid SETD and PSTD Algorithms for Acoustic Waves

2018 ◽  
Vol 26 (01) ◽  
pp. 1750031 ◽  
Author(s):  
Chunhua Deng ◽  
Ma Luo ◽  
Mengqing Yuan ◽  
Bo Zhao ◽  
Mingwei Zhuang ◽  
...  
Keyword(s):  
Differential Equations ◽  
Time Domain ◽  
Acoustic Waves ◽  
Wave Equations ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Spectral Element ◽  
Body Waves ◽  
Perfectly Matched Layers ◽  
Absorbing Boundary

The perfectly matched layer (PML) absorbing boundary condition has been proven to absorb body waves and surface waves very efficiently at non-grazing incidence. However, the traditional PML would generate large spurious reflections at grazing incidence, for example, when the sources are located near the truncating boundary and the receivers are at a large offset. In this paper, a new PML implementation is presented for the boundary truncation in three-dimensional spectral element time domain (SETD) for solving acoustic wave equations. This method utilizes pseudospectral time-domain (PSTD) method to solve first-order auxiliary differential equations (ADEs), which is more straightforward than that in the classical FEM framework.

Spectral-Element Simulations of Acoustic Waves Induced by a Moving Underwater Source

2019 ◽  
Vol 27 (03) ◽  
pp. 1850040 ◽  
Author(s):  
S. F. Lloyd ◽  
C. Jeong ◽  
H. N. Gharti ◽  
J. Vignola ◽  
J. Tromp
Keyword(s):  
Acoustic Waves ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Coupled System ◽  
Spectral Element ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Side Scan Sonar ◽  
Absorbing Boundaries ◽  
Acoustic Sources

In this study, we model acoustic waves induced by moving acoustic sources in three-dimensional (3D) underwater settings based on a spectral-element method (SEM). Numerical experiments are conducted using the SEM software package SPECFEM3D_Cartesian, which facilitates fluid–solid coupling and absorbing boundary conditions. Examples presented in this paper include an unbounded fluid truncated by using absorbing boundaries, and a shallow-water waveguide modeled as a fluid–solid coupled system based on domain decomposition. In the numerical experiments, the SEM-computed pressures match their analytical counterparts. SEM solutions of pressures at points behind and ahead of modeled moving acoustic sources show a frequency shift, i.e., a Doppler effect, which matches the analytical solution. This paper contributes to the field of passive sonar-based detection of moving acoustic sources, and addresses the challenge of computing wave responses generated by side-scan sonar by using moving sources of continuous signals.

scholarly journals New Explicit Solutions to the Fractional-Order Burgers’ Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. Hafiz Uddin ◽  
Mohammad Asif Arefin ◽  
M. Ali Akbar ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Rational Function ◽  
Acoustic Waves ◽  
Burgers Equation ◽  
Three Dimensional ◽  
Wall Friction ◽  
Weakly Nonlinear ◽  
Bubbly Liquids ◽  
Fractional Differential ◽  
Accuracy Of Results

The closed-form wave solutions to the time-fractional Burgers’ equation have been investigated by the use of the two variables G ′ / G , 1 / G -expansion, the extended tanh function, and the exp-function methods translating the nonlinear fractional differential equations (NLFDEs) into ordinary differential equations. In this article, we ascertain the solutions in terms of tanh , sech , sinh , rational function, hyperbolic rational function, exponential function, and their integration with parameters. Advanced and standard solutions can be found by setting definite values of the parameters in the general solutions. Mathematical analysis of the solutions confirms the existence of different soliton forms, namely, kink, single soliton, periodic soliton, singular kink soliton, and some other types of solitons which are shown in three-dimensional plots. The attained solutions may be functional to examine unidirectional propagation of weakly nonlinear acoustic waves, the memory effect of the wall friction through the boundary layer, bubbly liquids, etc. The methods suggested are direct, compatible, and speedy to simulate using algebraic computation schemes, such as Maple, and can be used to verify the accuracy of results.

scholarly journals Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling

Solid Earth ◽  
2017 ◽  
Vol 8 (5) ◽  
pp. 969-986 ◽  
Author(s):  
Shaolin Liu ◽  
Dinghui Yang ◽  
Xingpeng Dong ◽  
Qiancheng Liu ◽  
Yongchang Zheng
Keyword(s):  
Boundary Condition ◽  
Wave Field ◽  
Scattered Wave ◽  
Spectral Element ◽  
Perfectly Matched Layers ◽  
Time Step ◽  
Absorbing Boundary ◽  
Field Modeling ◽  
Adjoint Tomography ◽  
Gradient Calculation

Abstract. The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency–wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM155-SM167 ◽  
Author(s):  
Dimitri Komatitsch ◽  
Roland Martin
Keyword(s):  
Wave Equation ◽  
Seismic Wave ◽  
Isotropic Material ◽  
Grazing Incidence ◽  
Perfectly Matched Layer ◽  
Point Of View ◽  
Body Waves ◽  
Memory Storage ◽  
Elastic Wave Equation ◽  
Absorbing Boundary

The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from a numerical point of view for the elastic wave equation to absorb both body waves with nongrazing incidence and surface waves. However, at grazing incidence the classical discrete PML method suffers from large spurious reflections that make it less efficient for instance in the case of very thin mesh slices, in the case of sources located close to the edge of the mesh, and/or in the case of receivers located at very large offset. We demonstrate how to improve the PML at grazing incidence for the differential seismic wave equation based on an unsplit convolution technique. The improved PML has a cost that is similar in terms of memory storage to that of the classical PML. We illustrate the efficiency of this improved convolutional PML based on numerical benchmarks using a finite-difference method on a thin mesh slice for an isotropic material and show that results are significantly improved compared with the classical PML technique. We also show that, as the classical PML, the convolutional technique is intrinsically unstable in the case of some anisotropic materials.

Numerical Approach to Far Field Acoustic Wave Propagation from a Prolate Spheroidal Surface

1993 ◽  
Vol 115 (4) ◽  
pp. 448-451 ◽  
Author(s):  
J. P. Wright
Keyword(s):  
Acoustic Waves ◽  
Wave Equations ◽  
Pressure Field ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Weighted Sums ◽  
Far Field ◽  
Prolate Spheroidal ◽  
Orthogonal Functions ◽  
Spheroidal Surface

A method is described for calculating the far field, transient, three-dimensional pressure field generated by acoustic waves emanating from a prolate spheroidal surface. The pressure field is expanded in a series of spherical harmonics, which leads to a system of linear, tridiagonal, one dimensional wave equations that can be integrated efficiently by numerical techniques based on the method of characteristics. Integrals involving orthogonal functions are approximated by a numerically robust scheme where exact orthogonality is obtained (in the absence of round-off errors) in terms of weighted sums over a discrete variable.

Sign in / Sign up

Export Citation Format

Share Document