Acoustic simulation using a novel approach for reducing dispersion error. (20th October 2016)

• Record Type: Journal Article
• Authors: Wang, G.; Cui, X.Y.; Li, G.Y.
• Is Part Of: International journal for numerical methods in fluids. Volume 84:Number 3(2017)
• Page Start: 109
• Page End: 134
• Publication Date: 2016-10-20
• Subjects: Helmholtz equation -- numerical methods -- Shepard interpolation -- linear shape function -- dispersion error; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4339
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: It is well‐known that the traditional finite element method (FEM) fails to provide accurate results to the Helmholtz equation with the increase of wave number because of the 'pollution error' caused by numerical dispersion. In order to overcome this deficiency, a gradient‐weighted finite element method (GW‐FEM) that combines Shepard interpolation and linear shape functions is proposed in this work. Three‐node triangular and four‐node tetrahedral elements that can be generated automatically are first used to discretize the problem domain in 2D and 3D spaces, respectively. For each independent element, a compacted support domain is then formed based on the element itself and its adjacent elements sharing common edges (or faces). With the aid of Shepard interpolation, a weighted acoustic gradient field is then formulated, which will be further used to construct the discretized system equations through the generalized Galerkin weak form. Numerical examples demonstrate that the present algorithm can significantly reduces the dispersion error in computational acoustics. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : A novel approach that combines Shepard interpolation and linear shape functions is proposed for reducing the dispersion error in acoustic analysis. For each independent element, the gradient field is formed based on the element itself and its adjacent elements sharing common edges (or faces). Theoretic analysis and numerical results illustrate that the present algorithm performs well in simulating high wavenumber problems.