A Novel Triangular Element with Continuous Nodal Acoustic Pressure Gradient for Acoustic Scattering Problems

Yingbin Chai,T.y Li ,Yongou Zhang

doi:10.1155/2019/7436472

Abstract

To improve the performance of the standard finite element (FE) method in acoustic simulation, a novel triangular element with continuous nodal acoustic pressure gradient (FEM-T3-CNG) is presented to solve two-dimensional underwater acoustic scattering problems. In this FEM-T3-CNG model, the local approximation (LA) is represented by using the least-squares (LS) scheme, and the standard FE shape functions are employed to satisfy the partition of unity (PU) concept. In order to possess the important delta Kronecker property, the constrained orthonormalized LS (CO-LS) is utilized to construct the hybrid nodal shape functions. Incorporating the present FEM-T3-CNG element with the proper nonreflecting boundary condition, the two-dimensional underwater acoustic scattering problems in the infinite domain could be solved ultimately. The numerical results show that the present FEM-T3-CNG element behaves much better than the standard FEM-T3 element in terms of computation accuracy and can be regarded as a good alternative approach in exterior acoustic computation.

Highlights

To improve the performance of the standard finite element (FE) method in acoustic simulation, a novel triangular element with continuous nodal acoustic pressure gradient (FEM-T3-CNG) is presented to solve two-dimensional underwater acoustic scattering problems
Incorporating the present finite element method (FEM)-T3-CNG element with the proper nonreflecting boundary condition, the two-dimensional underwater acoustic scattering problems in the infinite domain could be solved . e numerical results show that the present FEM-T3-CNG element behaves much better than the standard FEM-T3 element in terms of computation accuracy and can be regarded as a good alternative approach in exterior acoustic computation
Introduction e acoustic scattering by underwater objects is a very important physical phenomenon in acoustics and its main concern is how the acoustic wave is affected by the objects standing in its propagation path. e underwater acoustic scattering has a very strong background in many practical engineering application fields, such as ocean resource exploration, sound navigation and ranging, and underwater collision prevention and rescue to name a few. erefore, how to precisely calculate and predict the acoustic scattered field is of great importance to improve the acoustical properties of the ocean engineering structures

Summary

Research Article

A Novel Triangular Element with Continuous Nodal Acoustic Pressure Gradient for Acoustic Scattering Problems. To improve the performance of the standard finite element (FE) method in acoustic simulation, a novel triangular element with continuous nodal acoustic pressure gradient (FEM-T3-CNG) is presented to solve two-dimensional underwater acoustic scattering problems. In this FEM-T3-CNG model, the local approximation (LA) is represented by using the least-squares (LS) scheme, and the standard FE shape functions are employed to satisfy the partition of unity (PU) concept. The SBM has been successfully applied in many engineering problems, such as the seismic wave problems [15] and electromagnetic wave problems [16] Another alternative numerical approach for acoustic scattering computation is the classical finite element method (FEM). Using the standard weighted residual techniques, the exterior acoustic wave equation can be formulated in the following matrix form [18]:

Computational domain Ω

Numerical Results

Percentage amplitude decay