Application of Smoothed Finite Element Method to Two-Dimensional Exterior Problems of Acoustic Radiation

Abstract

In this work, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems. The SFEM-Q4 can be regarded as a combination of the standard finite element method (FEM) and the gradient smoothing technique (GST) from the meshfree methods. In the SFEM-Q4, only the values of shape functions (not the derivatives) at the quadrature points are needed and the traditional requirement of coordinate transformation procedure is not necessary to implement the numerical integration. Consequently, no additional degrees of freedom are required as compared with the original FEM. In addition, the original “overly-stiff” FEM model for acoustic problems (governed by the Helmholtz equation) is properly softened due to the gradient smoothing operations implemented over the smoothing domains and the present SFEM-Q4 possesses a relatively appropriate stiffness of the continuous system. Therefore, the well-known numerical dispersion error for Helmholtz equation is decreased significantly and very accurate numerical solutions can be obtained by using relatively coarse meshes. In order to truncate the unbounded domains and employ the domain-based numerical method to tackle the acoustic radiation in unbounded domains, the Dirichlet-to-Neumann (DtN) map is used to ensure that there are no spurious reflections from the far field. The numerical results from several numerical examples demonstrate that the present SFEM-Q4 is quite effective to handle acoustic radiation problems and can produce more accurate numerical results than the standard FEM.

Axisymmetric scattering of a fluid spheroid illuminated by an acoustical Bessel beam

“…In addition, Edmundo Lavia et al derived a computational method to calculate the exact solution for liquid spheroid which agrees with reported predicted results obtained through approximated solution for far-field and near-field regimes [8]. Based on the discussions of the scattering of the fluid spheroid, the acoustical radiation force of a fluid spheroid or a liquid-filled spherical shell could be obtained, which could benefit the application of the biomedical, drug deliver, biochemistry and other areas [9].…”

Analysis acoustic target strength of anechoic coatings in low frequency based on equivalent parameter inversion

“…According to the periodicity of cavity, the model of anechoic coatings can be simplified to the unit cell to analyze the acoustic scattered properties by the Bloch theorem [6]. Therefore, the following periodic boundary conditions should be satisfied [1]:…”

“…Anechoic coatings can reduce the reflection of sound waves, so it is necessary for researchers to study the acoustic scattering properties of the shell structures covered by anechoic coatings. The Finite Element Method (FEM) is most popular numerical techniques for handling acoustic computation [1,2]. Kim established a numerical methodology based on Kirchhoff approximation to simulate the acoustic target strength (TS) of a submarine attached with anechoic coatings, and the finite element method is applied to calculate the acoustic pressure reflection coefficient [3].…”

A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media

“…Therefore, it is necessary to obtain their approximate solutions by using some efficient numerical methods. The finite difference method (FDM) and the finite element (FEM) techniques [8] are classical tools for the numerical modeling of the ADR problem. A detailed review of the classic methods involving FEMs and FDMs can be found in [9].…”