4,720 research outputs found
Modal element method for scattering of sound by absorbing bodies
The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder
Elastic Wave Eigenmode Solver for Acoustic Waveguides
A numerical solver for the elastic wave eigenmodes in acoustic waveguides of
inhomogeneous cross-section is presented. Operating under the assumptions of
linear, isotropic materials, it utilizes a finite-difference method on a
staggered grid to solve for the acoustic eigenmodes of the vector-field elastic
wave equation. Free, fixed, symmetry, and anti-symmetry boundary conditions are
implemented, enabling efficient simulation of acoustic structures with
geometrical symmetries and terminations. Perfectly matched layers are also
implemented, allowing for the simulation of radiative (leaky) modes. The method
is analogous to eigenmode solvers ubiquitously employed in electromagnetics to
find waveguide modes, and enables design of acoustic waveguides as well as
seamless integration with electromagnetic solvers for optomechanical device
design. The accuracy of the solver is demonstrated by calculating
eigenfrequencies and mode shapes for common acoustic modes in several simple
geometries and comparing the results to analytical solutions where available or
to numerical solvers based on more computationally expensive methods
Time-domain simulation of ultrasound propagation with fractional Laplacians for lossy-medium biological tissues with complicated geometries
Simulations of ultrasound wave propagation inside biological tissues have a wide range of practical
applications. In previous studies, wave propagation equations in lossy biological media are solved
either with convolutions, which consume a large amount of memory, or with pseudo-spectral methods, which cannot handle complicated geometries effectively. The approach described in the paper
employed a fractional central difference method (FCD), combined with the immersed boundary
(IB) method for the finite-difference, time-domain simulation. The FCD method can solve the fractional Laplace terms in Chen and Holm’s lossy-medium equations directly in the physical domain
without integral transforms. It also works naturally with the IB method, which enables a simple
Cartesian-type grid mesh to be used to solve problems with complicated geometries. The numerical
results agree very well with the analytical solutions for frequency power-law attenuation lossy
mediaThis research is partly supported by the U.S. Army under a cooperative Agreement No. W911NF-14-2-007
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