MULTIDOMAIN PSEUDOSPECTRAL TIME-DOMAIN (PSTD) METHOD FOR ACOUSTIC WAVES IN LOSSY MEDIA

2004 ◽  
Vol 12 (03) ◽  
pp. 277-299 ◽  
Author(s):  
YAN QING ZENG ◽  
QING HUO LIU ◽  
GANG ZHAO
Keyword(s):  
Acoustic Wave ◽  
Time Domain ◽  
Acoustic Waves ◽  
Numerical Solutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Computational Domain ◽  
Complex Objects ◽  
Lossy Media

A multidomain pseudospectral time-domain (PSTD) method is developed for acoustic wave equations in lossy media. The method is based on the spectral derivative operator approximated by Chebyshev Lagrange polynomials. In this multidomain scheme, the computational domain is decomposed into a set of subdomains conformal to the problem geometry. Each curved subdomain is then mapped onto a cube in the curvilinear coordinates so that a tensor-product Chebyshev grid can be utilized without the staircasing error. An unsplit-field, well-posed PML is developed as the absorbing boundary condition. The algorithm is validated by analytical solutions. The numerical solutions show that this algorithm is efficient for simulating acoustic wave phenomena in the presence of complex objects in inhomogeneous media. To our knowledge, the multidomain PSTD method for acoustics is a new development in three dimensions, although in two dimensions the method can be made equivalent to the two-dimensional method in electromagnetics.

Performance and stability of the double absorbing boundary method for acoustic-wave propagation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. T59-T72 ◽  
Author(s):  
Toby Potter ◽  
Jeffrey Shragge ◽  
David Lumley
Keyword(s):  
Boundary Layer ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Spectral Response ◽  
Domain Boundary ◽  
Grid Point ◽  
High Order ◽  
Computational Domain ◽  
Absorbing Boundary

The double absorbing boundary (DAB) is a novel extension to the family of high-order absorbing boundary condition operators. It uses auxiliary variables in a boundary layer to set up cancellation waves that suppress wavefield energy at the computational-domain boundary. In contrast to the perfectly matched layer (PML), the DAB makes no assumptions about the incoming wavefield and can be implemented with a boundary layer as thin as three computational grid-point cells. Our implementation incorporates the DAB into the boundary cell layer of high-order finite-difference (FD) techniques, thus avoiding the need to specify a padding region within the computational domain. We tested the DAB by propagating acoustic waves through homogeneous and heterogeneous 3D earth models. Measurements of the spectral response of energy reflected from the DAB indicate that it reflects approximately 10–15 dB less energy for heterogeneous models than a convolutional PML of the same computational memory complexity. The same measurements also indicate that a DAB boundary layer implemented with second-order FD operators couples well with higher-order FD operators in the computational domain. Long-term stability tests find that the DAB and CPML methods are stable for the acoustic-wave equation. The DAB has promise as a robust and memory-efficient absorbing boundary for 3D seismic imaging and inversion applications as well as other wave-equation applications in applied physics.

scholarly journals Periodic particle arrangements using standing acoustic waves

2019 ◽  
Vol 475 (2232) ◽  
pp. 20190574
Author(s):  
Fernando Guevara Vasquez ◽  
China Mauck
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Acoustic Radiation ◽  
Symmetric Matrix ◽  
Three Dimensions ◽  
Spherical Particles ◽  
Bravais Lattice ◽  
Global Minima ◽  
Small Particles ◽  
Spatially Periodic

We determine crystal-like materials that can be fabricated by using a standing acoustic wave to arrange small particles in a non-viscous liquid resin, which is cured afterwards to keep the particles in the desired locations. For identical spherical particles with the same physical properties and small compared to the wavelength, the locations where the particles are trapped correspond to the minima of an acoustic radiation potential which describes the net forces that a particle is subject to. We show that the global minima of spatially periodic acoustic radiation potentials can be predicted by the eigenspace of a small real symmetric matrix corresponding to its smallest eigenvalue. We relate symmetries of this eigenspace to particle arrangements composed of points, lines or planes. Since waves are used to generate the particle arrangements, the arrangement’s periodicity is limited to certain Bravais lattice classes that we enumerate in two and three dimensions.

The Mixed Virtual Element Method for Grids with Curved Interfaces in Single-Phase Flow Problems

2021 ◽  
Author(s):  
Franco Dassi ◽  
Alessio Fumagalli ◽  
Davide Losapio ◽  
Stefano Scialò ◽  
Anna Scotti ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Industrial Applications ◽  
Velocity Fields ◽  
Three Dimensions ◽  
Darcy Law ◽  
Computational Domain ◽  
Virtual Element Method ◽  
Virtual Element ◽  
Element Method

Abstract In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the physical boundary, are often met in real applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields are of paramount importance for the successful subsequent coupling with other physical phenomena such as transport. The virtual element method, as solution scheme, is known to be applicable in problems whose discretizations requires cells of general shape, and the mixed formulation is here preferred to obtain accurate velocity fields. To overcome the issues associated to the complex geometries and, at the same time, retaining the quality of the solutions, we present here the virtual element method to solve the Darcy problem, in mixed form, in presence of curved interfaces in two and three dimensions. The numerical scheme is presented in detail explaining the discrete setting with a focus on the treatment of curved interfaces. Examples, inspired from industrial applications, are presented showing the validity of the proposed approach.

scholarly journals A Numerical Method for Predicting Acoustical Wave Propagation in Open Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Johnny Papageorgakopoulos ◽  
Sokrates Tsangaris
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Near Field ◽  
Sound Field ◽  
Vortex Pair ◽  
Rectangular Domain ◽  
Two Dimensions ◽  
Curvilinear Coordinates ◽  
Benchmark Problems ◽  
Computational Domain

We present a numerical methodology for evaluating wave propagation phenomena in two dimensions in the time domain with focus on the linear acoustic second-order wave equation. An outline of the higher-order compact discretization schemes followed by the time discretization technique is first presented. The method is completed with the addition of spatial filtering based on the same compact schemes' principles. The important role of boundary conditions is subsequently addressed. Two popular ways to truncate the computational domain in the near field are presented and compared here: first the formulation of “absorbing conditions” in the form of partial differential equations especially for the origin and second the construction of an absorbing layer surrounding the domain, in which waves (after they have exited the domain) are attenuated and decayed exponentially. Subsequently, the method is assessed by recalling three benchmark problems. In the first where a Gaussian pulse is generated and propagated in a 2D rectangular domain, the accuracy and absorbability of the boundary conditions are compared. In the second, a similar situation is investigated but under curvilinear coordinates and under the presence of a solid body which scatters the pulse. Finally the sound field inducted by the flow of corotating vortex pair is calculated and compared with the corresponding analytical solution.

Analytical Solution for the Prediction of Temperature Distributions During Radio-Frequency Ablation of Cardiac Tissue

2003 ◽  
Author(s):  
Ryan T. Roper ◽  
Matthew R. Jones
Keyword(s):  
Analytical Solution ◽  
Radio Frequency ◽  
Numerical Solutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Tissue Temperature ◽  
Bench Mark ◽  
Bioheat Equation ◽  
Surface Integral ◽  
Temperature Distributions

One of the most effective methods of treatment for cardiac arrhythmias is radio-frequency (RF) ablation. Many studies have shown that the tissue temperature distribution is the key factor influencing lesion shape and size, and that accurate prediction of this distribution is essential to the further improvement of the procedure. Temperature distributions can be obtained by solving the bioheat equation, which has been done in several studies using numerical techniques. This paper describes the development of an analytical solution that can be used as a bench mark for subsequent numerical solutions. Using integral transforms, the bioheat equation is reduced to an ordinary differential equation with time as the independent variable. The solution has the form of a surface integral within another surface integral. An integration routine that extends the trapezoidal method of integration in two dimensions to an analogous method in three dimensions has been developed in order to evaluate the analytical solution. A C program was written to implement this method, and the program was validated using a surface integral with a known analytical solution. The program was then used to generate temperature profiles at various time values and for different convection coefficients.

Study on electromagnetic characteristics of plasma model-based on the symplectic multiresolution time-domain scheme

2020 ◽  
Vol 34 (06) ◽  
pp. 2050046
Author(s):  
Zhu Ma ◽  
Min Wei ◽  
Meng Li ◽  
Wenbin Xu
Keyword(s):  
Time Domain ◽  
Numerical Solutions ◽  
Numerical Dispersion ◽  
Computational Domain ◽  
Plasma Model ◽  
Perfectly Matched Layers ◽  
Factors Affecting ◽  
Transmission Coefficients ◽  
Plasma Slab ◽  
Dispersive Model

A novel numerical computation scheme, which is symplectic multiresolution time-domain (S-MRTD) scheme, for modeling plasma model is proposed. The loss plasma dispersive model is taken into account in S-MRTD scheme, and the detailed formulations of the proposed S-MRTD scheme are also provided. A one-dimensional perfectly matched layers (PML) are used to terminate the computational domain. The analyses of stability and numerical dispersion demonstrate that S-MRTD scheme is more efficient than traditional finite-different time-domain (FDTD) and MRTD methods. The energy conservation characteristics of S-MRTD scheme in electromagnetic simulation are proved by the propagation of pulse in free space for long-term simulation. In the end, the S-MRTD formulations are confirmed by computing the electric field intensity, reflection and the transmission coefficients for the pulse wave through an unmagnetized plasma slab. A favorable agreement between the numerical solutions is demonstrated, and the efficiency of the proposed scheme is verified. Meanwhile, numerical results show that plasma frequency, collision frequency and thickness are important factors affecting reflection and transmission coefficients.

Computation of Fan Noise Radiation through an Engine Exhaust Geometry with Flow

2007 ◽  
Vol 6 (3) ◽  
pp. 223-241 ◽  
Author(s):  
S.K. Richards ◽  
X.X. Chen ◽  
X. Huang ◽  
X. Zhang
Keyword(s):  
Acoustic Wave ◽  
Computational Model ◽  
Acoustic Waves ◽  
Near Field ◽  
Aircraft Engine ◽  
Computational Domain ◽  
Mean Flow ◽  
Engine Exhaust ◽  
Noise Radiation ◽  
Acoustic Treatment

This paper outlines a computational model of noise radiation from a realistic engine exhaust geometry with flow. The computational model described allows acoustic waves, propagating inside the bypass duct of a generic aircraft engine, to be admitted into a computational domain that includes the aft duct section, the exit plane of the duct, and the jet flow immediately downstream. The method has three parts: a matching process to admit acoustic waves into the induct propagation region; near field propagation inside the duct and diffraction at the lip of the exhaust duct; and an integral surface for far field directivity. In this model the near field propagation is determined by a numerical solution of a 2.5D form of the linearised Euler equations. The mean flow about which the equations are linearised is assumed to be axisymmetric. The proposed method is illustrated through a case study on the radiation of a typical fan assembly generated acoustic wave from a generic engine bypass duct. Inside the duct, an acoustic wave of circumferential order m = −13 and comprising five radial modes ( n = 1 – 5) is admitted into the model as inputs on the boundary of the computation domain. The radiation of the acoustic wave through the exhaust geometry and mean flow is determined, with the effect of acoustic treatment through the inclusion of lined duct sections also examined.

scholarly journals Time-to-depth conversion and seismic velocity estimation using time-migration velocity

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE205-VE210 ◽  
Author(s):  
Maria Cameron ◽  
Sergey Fomel ◽  
James Sethian
Keyword(s):  
Time Domain ◽  
Seismic Velocity ◽  
Migration Velocity ◽  
Two Dimensions ◽  
Velocity Estimation ◽  
Three Dimensions ◽  
Velocity Models ◽  
Time Migration ◽  
Geometric Spreading ◽  
Paraxial Ray

The objective was to build an efficient algorithm (1) to estimate seismic velocity from time-migration velocity, and (2) to convert time-migrated images to depth. We established theoretical relations between the time-migration velocity and seismic velocity in two and three dimensions using paraxial ray-tracing theory. The relation in two dimensions implies that the conventional Dix velocity is the ratio of the interval seismic velocity and the geometric spreading of image rays. We formulated an inverse problem of finding seismic velocity from the Dix velocity and developed a numerical procedure for solving it. The procedure consists of two steps: (1) computation of the geometric spreading of image rays and the true seismic velocity in time-domain coordinates from the Dix velocity; (2) conversion of the true seismic velocity from the time domain to the depth domain and computation of the transition matrices from time-domain coordinates todepth. For step 1, we derived a partial differential equation (PDE) in two and three dimensions relating the Dix velocity and the geometric spreading of image rays to be found. This is a nonlinear elliptic PDE. The physical setting allows us to pose a Cauchy problem for it. This problem is ill posed, but we can solve it numerically in two ways on the required interval of time, if it is sufficiently short. One way is a finite-difference scheme inspired by the Lax-Friedrichs method. The second way is a spectral Chebyshev method. For step 2, we developed an efficient Dijkstra-like solver motivated by Sethian’s fast marching method. We tested numerical procedures on a synthetic data example and applied them to a field data example. We demonstrated that the algorithms produce a significantly more accurate estimate of seismic velocity than the conventional Dix inversion. This velocity estimate can be used as a reasonable first guess in building velocity models for depth imaging.

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