scholarly journals Asymptotic analysis of the scattering problem for the Helmholtz equations with high wave numbers

2017 ◽  
Vol 37 (3) ◽  
pp. 1159-1181
Author(s):  
Daniel Bouche ◽  
◽  
Youngjoon Hong ◽  
Chang-Yeol Jung ◽  
◽  
...  
Keyword(s):  
Asymptotic Analysis ◽  
Scattering Problem ◽  
Helmholtz Equations ◽  
High Wave ◽  
Wave Numbers

scholarly journals A Hybrid Smoothed Finite Element Method for Predicting the Sound Field in the Enclosure with High Wave Numbers

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Haitao Wang ◽  
Xiangyang Zeng ◽  
Ye Lei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Field ◽  
Numerical Dispersion ◽  
Computational Accuracy ◽  
Dispersion Error ◽  
High Wave ◽  
Wave Numbers ◽  
Smoothed Finite Element Method ◽  
Element Method

Wave-based methods for acoustic simulations within enclosures suffer the numerical dispersion and then usually have evident dispersion error for problems with high wave numbers. To improve the upper limit of calculating frequency for 3D problems, a hybrid smoothed finite element method (hybrid SFEM) is proposed in this paper. This method employs the smoothing technique to realize the reduction of the numerical dispersion. By constructing a type of mixed smoothing domain, the traditional node-based and face-based smoothing techniques are mixed in the hybrid SFEM to give a more accurate stiffness matrix, which is widely believed to be the ultimate cause for the numerical dispersion error. The numerical examples demonstrate that the hybrid SFEM has better accuracy than the standard FEM and traditional smoothed FEMs under the condition of the same basic elements. Moreover, the hybrid SFEM also has good performance on the computational efficiency. A convergence experiment shows that it costs less time than other comparison methods to achieve the same computational accuracy.

New Finite Element Modeling Strategy for Large-Scale Industrial Problems in Structural Acoustics

2000 ◽  
Author(s):  
Saikat Dey ◽  
Luise S. Couchman
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Large Scale ◽  
Structural Acoustics ◽  
Simple Scheme ◽  
Numerical Examples ◽  
High Wave ◽  
Wave Numbers ◽  
Complex Structural ◽  
Modeling Strategy

Abstract A simple scheme to model and mesh stiffened shell-like structures is presented. Combined with a high-order finite/infinite element based infrastructure, it enables the solution of complex structural acoustics problems at high wave numbers. Numerical examples are presented to show the applicability of the method at high wave-numbers.

Numerical simulation of acoustic scattering from coaxial sound-penetrable spheres

2019 ◽  
Vol 14 (2) ◽  
pp. 115-124
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Radiation Source ◽  
Numerical Study ◽  
Numerical Technique ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Computer Time ◽  
Fixed Number ◽  
Helmholtz Equations ◽  
Spherical Waves ◽  
Penetrable Spheres

This paper presents a generalisation of the mathematical model and numerical study of the acoustic scattering problem from multiple spheres in the case of spheres through which the wave passes and whose centers are located on the same axis (the case of sound-penetrable and coaxial spheres) under the action of spherical waves from a monopoly radiation source arbitrarily located in space. When solving the Helmholtz equations, a numerical technique based on the fast multipole method has been adapted for this task, which allows one to achieve high accuracy of the results obtained with minimal computer time. Comparison of the different approaches to truncation infinite series in the expansion showed the following: the result with a good degree of accuracy by a single calculation gives approach based on the truncation of all the rows with a fixed number in each expansion, and the result with a certain degree of accuracy gives an approach based on comparing two consecutive values of the sum of the series. A numerical parametric analysis of the pressure distribution inside and outside the spheres is carried out for various values of their radii, physical characteristics of the external and internal media, the number of spheres, the distances between the centers of the spheres, the frequency of exposure and the location of the monopole radiation source. It is shown that at certain values of the parameters, the appearance of zones of decrease or increase in pressure behind sound-penetrable spheres is possible. The obtained results will further allow to carry out test calculations to verify the general numerical algorithm for the case of a multitude of spheres arbitrarily located in space.

Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

2012 ◽  
Vol 12 (4) ◽  
pp. 1275-1292 ◽  
Author(s):  
Qin Sheng ◽  
Hai-Wei Sun
Keyword(s):  
Helmholtz Equation ◽  
Numerical Stability ◽  
Splitting Method ◽  
Computational Procedure ◽  
Matrix Analysis ◽  
Wave Number ◽  
Large Wave ◽  
High Wave ◽  
Wave Numbers ◽  
Large Wave Number

AbstractThis paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number. Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense. Simulated examples are given to illustrate the conclusion.

The stability of pipe flow Part 1. Asymptotic analysis for small wave-numbers

1970 ◽  
Vol 43 (2) ◽  
pp. 279-290 ◽  
Author(s):  
W. P. Graebel
Keyword(s):  
Asymptotic Analysis ◽  
Poiseuille Flow ◽  
Reynolds Numbers ◽  
Transverse Component ◽  
Wave Number ◽  
Radial Velocity Component ◽  
Wave Numbers ◽  
Flow Part ◽  
The Stability ◽  
High Degree

The instability of Poiseuille flow in a pipe is considered for small disturbances. An asymptotic analysis is used which is similar to that found successful in plane Poiseuille flow. The disturbance is taken to travel in a spiral fashion, and comparison of the radial velocity component with the transverse component in the plane case shows a high degree of similarity, particularly near the critical point where the disturbance and primary flow travel with the same speed. Instability is found for azimuthal wave-numbers of 2 or greater, although the corresponding minimum Reynolds numbers are too small to compare favourably with either experiments or the initial restrictions on the magnitude of the wave-number.

Sign in / Sign up

Export Citation Format

Share Document