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.

Boundary conditions on a finite grid: Applications with pseudospectral wave propagation

Geophysics ◽  
1997 ◽  
Vol 62 (5) ◽  
pp. 1544-1557 ◽  
Author(s):  
Huatao Wu ◽  
Jonathan M. Lees
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Optimal Parameter ◽  
Two Dimensions ◽  
New Method ◽  
Head Waves ◽  
Vertical Fault ◽  
Reduction Function ◽  
Grid Nodes

A new method for calculating boundary conditions at the free surface and along absorbing boundaries of a finite grid is presented. A finite, twice differentiable reduction function that achieves a 99% reduction over three wavelengths is proposed and tested. In the context of pseudospectral wave propagation, this implies a boundary layer of at least six grid nodes. The method is analyzed in one and two dimensions and the problems of waves impinging on corners are addressed. The reduction function recommended is [Formula: see text] where α is a parameter to be determined by optimization. Tests of the performance of the new method versus other common schemes are presented and analyzed. We provide a strategy for determining the optimal parameter in the reduction function. Synthetic Rayleigh waves are observed at the free surface of the simulation. Experiments with a vertical fault plane show the presence of direct, reflected, transmitted, and head waves. The presence of head waves may be used to analyze velocity contrasts across fault zones.

AN ALGORITHM FOR DIRECT SIMULATION OF LINEAR WAVE PROPAGATION IN IRREGULAR REGIONS

2009 ◽  
Vol 17 (04) ◽  
pp. 331-356
Author(s):  
XUEMEI CHEN ◽  
JOEL C. W. ROGERS ◽  
STEVEN L. MEANS ◽  
WILLIAM G. SZYMCZAK
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Linear Wave ◽  
Computational Domain ◽  
Direct Simulation ◽  
Fluid Medium ◽  
Linear Wave Propagation ◽  
Multiple Bubbles

A numerical algorithm has been developed to simulate linear wave propagation in media containing irregular inhomogeneities, especially irregular voids in fluids. The computational domain is extended to include the regions occupied by the inhomogeneities through replacing the boundaries with properly chosen sources. The solution corresponding to Dirichlet boundary conditions on the inhomogeneities is presented. This algorithm can be used to calculate linear wave propagation in a fluid medium with multiple bubbles.

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.

scholarly journals Efficient Near-Field Analysis of the Electromagnetic Scattering Based on the Dirichlet-to-Neumann Map

2019 ◽  
Vol 9 (19) ◽  
pp. 4179
Author(s):  
Perrotta ◽  
Maffucci ◽  
Ventre ◽  
Tamburrino
Keyword(s):  
Boundary Conditions ◽  
Electromagnetic Scattering ◽  
Near Field ◽  
Scattering Problem ◽  
Computational Cost ◽  
Field Analysis ◽  
Classical Solutions ◽  
Computational Domain ◽  
Solution Domain ◽  
Differential Formulation

This paper proposes an efficient technique to solve the electromagnetic scattering problem, in the near zone of scatterers illuminated by external fields. The technique is based on a differential formulation of the Helmholtz equation discretized in terms of a finite element method (FEM). In order to numerically solve the problem, it is necessary to truncate the unbounded solution domain to obtain a bounded computational domain. This is usually done by defining fictitious boundaries where absorbing conditions are imposed, for example by applying the perfect matching layer (PML) approach. In this paper, these boundary conditions are expressed in an analytical form by using the Dirichlet-to-Neumann (DtN) operator. Compared to classical solutions such as PML, the proposed approach based on the DtN: (i) avoids the errors related to approximated boundary conditions; (ii) allows placing the boundary in close proximity to the scatterers, thus, reducing the solution domain to be meshed and the related computational cost; (iii) allows dealing with objects of arbitrary shapes and materials, since the shape of the boundary independent from those of the scatterers. Case-studies on problems related to the scattering from cable bundles demonstrate the accuracy and the computational advantage of the proposed technique, compared to existing ones.

HIGH-ORDER RADIATION BOUNDARY CONDITIONS FOR STRATIFIED MEDIA AND CURVILINEAR COORDINATES

2012 ◽  
Vol 20 (02) ◽  
pp. 1240002 ◽  
Author(s):  
THOMAS HAGSTROM
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Curvilinear Coordinates ◽  
Stratified Media ◽  
Computational Domain ◽  
Progressive Wave ◽  
Radiation Boundary Conditions ◽  
Local Radiation ◽  
Radiation Boundary ◽  
Homogeneous Media

Optimized local radiation boundary conditions to truncate the computational domain by a rectangular boundary have been constructed for acoustic waves propagating into a homogeneous, isotropic far field. Here we try to achieve comparable efficiencies in stratified media and cylindrical coordinates. We find that conditions constructed for homogeneous media are highly effective in the stratified case. On the circle we derive boundary conditions by optimizing a semidiscretized perfectly matched layer. Though we are unsuccessful in matching the accuracies of the Cartesian case, our experiments show that older sequences based on the progressive wave expansion are surprisingly efficient.

Coupling of Potential Flow and CFD Model for Fluid and Structure Interactions

2021 ◽  
Author(s):  
Haihua Xu ◽  
Yali Zhang ◽  
Harrif Santo ◽  
Kie Hian Chua ◽  
Yun Zhi Law ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Potential Flow ◽  
Near Field ◽  
Wave Structure ◽  
Numerical Dissipation ◽  
Far Field ◽  
Computational Domain ◽  
Field Region ◽  
Regular Wave ◽  
Cfd Model

Abstract Computational Fluid Dynamics (CFD) tools are widely used to simulate wave and structure interactions in marine & offshore industry. However, conventional CFD tools require significant computational resources. This is largely due to the requirement of large computational domain to ensure adequate development of nonlinear wave evolutions as well as to avoid boundary effects resulting from wave interacting with any fixed or floating structures in the domain. Furthermore, very fine mesh elements are required to avoid excessive numerical dissipation during wave propagation. All of these factors will significantly increase the computational costs, resulting in the conventional CFD approaches being impractical for simulations of wave-structure interactions over a long duration. In this paper, a coupled potential flow and CFD model is developed to reduce the simulation cost. The model decomposes the simulation domain into far-field and near-field region. Wave propagation in the far-field region is simulated by a potential flow solver (High-Order Spectral or HOS method), while the wave-structure interactions in the near-field region are simulated by a fully nonlinear, viscous, and two-phase CFD solver (Star-CCM+). A forcing zone is distributed between the two regions to blend the computational outputs from the potential flow into the CFD solvers. The coupling algorithm has been developed to improve the accuracy and efficiency. The coupled solver is applied to simulate two cases, namely regular wave propagation, and regular wave interaction with a vertical cylinder. Finally, a simulation of a 3D wave encountering an FPSO (Floating Production Storage and Offloading) is presented.

On Boundary Conditions for Acoustic Computations in Non-Uniform Mean Flows

1997 ◽  
Vol 05 (03) ◽  
pp. 297-315 ◽  
Author(s):  
Thomas Z. Dong
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Near Field ◽  
Wave Radiation ◽  
Computational Domain ◽  
Mean Flow ◽  
Exterior Field ◽  
Artificial Boundary ◽  
Artificial Boundaries ◽  
The Mean

Many acoustic problems involve acoustic wave radiation to the exterior field. A common approach in numerical simulations is to restrict the computational domain to a finite region with artificial boundaries. The so-called radiation or non-reflecting boundary conditions must be imposed at those artificial boundaries. Most existing non-reflecting boundary conditions are derived for computing disturbances propagating in a known uniform mean flow near the boundaries. In many applications such as the computation of jet noise or turbofan noise, the mean flow at an artificial boundary is non-uniform and unknown. The mean flow also needs to be computed in these cases. Incorrect computation of this mean flow at the boundary could directly affect the near field physics as well as the far field acoustics. In the present paper, a set of boundary conditions is proposed which focuses on computing the correct mean solution at an artificial boundary, while still maintaining the non-reflecting feature for the outgoing transient and acoustic waves.

OPTIMAL LOCAL NONREFLECTING BOUNDARY CONDITIONS FOR TIME-DEPENDENT WAVES

2000 ◽  
Vol 08 (01) ◽  
pp. 157-170 ◽  
Author(s):  
IGOR PATLASHENKO ◽  
DAN GIVOLI
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Two Dimensions ◽  
Time Dependent ◽  
Computational Domain ◽  
Element Discretization ◽  
Nonreflecting Boundary Conditions ◽  
Time Harmonic ◽  
Starting Point ◽  
Artificial Boundaries

Nonreflecting Boundary Conditions (NRBCs) are often used on artificial boundaries as a method for the numerical solution of wave problems in unbounded domains. Recently, a two-parameter hierarchy of optimal local NRBCs of increasing order has been developed for elliptic problems, including the problem of time-harmonic acoustic waves. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary condition in the L2 norm for functions which can be Fourier-decomposed. The optimal NRBCs are combined with finite element discretization in the computational domain. Here this approach is extended to time-dependent acoustic waves. In doing this, the Semi-Discrete DtN approach is used as the starting point. Numerical examples involving propagating disturbances in two dimensions are given.

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