12,081 research outputs found
On-surface radiation condition for multiple scattering of waves
The formulation of the on-surface radiation condition (OSRC) is extended to
handle wave scattering problems in the presence of multiple obstacles. The new
multiple-OSRC simultaneously accounts for the outgoing behavior of the wave
fields, as well as, the multiple wave reflections between the obstacles. Like
boundary integral equations (BIE), this method leads to a reduction in
dimensionality (from volume to surface) of the discretization region. However,
as opposed to BIE, the proposed technique leads to boundary integral equations
with smooth kernels. Hence, these Fredholm integral equations can be handled
accurately and robustly with standard numerical approaches without the need to
remove singularities. Moreover, under weak scattering conditions, this approach
renders a convergent iterative method which bypasses the need to solve single
scattering problems at each iteration.
Inherited from the original OSRC, the proposed multiple-OSRC is generally a
crude approximate method. If accuracy is not satisfactory, this approach may
serve as a good initial guess or as an inexpensive pre-conditioner for Krylov
iterative solutions of BIE
An integral formulation for wave propagation on weakly non-uniform potential flows
An integral formulation for acoustic radiation in moving flows is presented.
It is based on a potential formulation for acoustic radiation on weakly
non-uniform subsonic mean flows. This work is motivated by the absence of
suitable kernels for wave propagation on non-uniform flow. The integral
solution is formulated using a Green's function obtained by combining the
Taylor and Lorentz transformations. Although most conventional approaches based
on either transform solve the Helmholtz problem in a transformed domain, the
current Green's function and associated integral equation are derived in the
physical space. A dimensional error analysis is developed to identify the
limitations of the current formulation. Numerical applications are performed to
assess the accuracy of the integral solution. It is tested as a means of
extrapolating a numerical solution available on the outer boundary of a domain
to the far field, and as a means of solving scattering problems by rigid
surfaces in non-uniform flows. The results show that the error associated with
the physical model deteriorates with increasing frequency and mean flow Mach
number. However, the error is generated only in the domain where mean flow
non-uniformities are significant and is constant in regions where the flow is
uniform
An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions
This paper presents a high-order accelerated algorithm for the solution of the integral-equation formulation of volumetric scattering problems. The scheme is particularly well suited to the analysis of “thin” structures as they arise in certain applications (e.g., material coatings); in addition, it is also designed to be used in conjunction with existing low-order FFT-based codes to upgrade their order of accuracy through a suitable treatment of material interfaces. The high-order convergence of the new procedure is attained through a combination of changes of parametric variables (to resolve the singularities of the Green function) and “partitions of unity” (to allow for a simple implementation of spectrally accurate quadratures away from singular points). Accelerated evaluations of the interaction between degrees of freedom, on the other hand, are accomplished by incorporating (two-face) equivalent source approximations on Cartesian grids. A detailed account of the main algorithmic components of the scheme are presented, together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results
- …