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a finite element flux-corrected transport method for wave propagation in heterogeneous solids波传播的有限元flux-corrected运输方法异构固体
Algorithms 2009, 2, 1-18; doi:10.3390/a2010001
OPEN ACCESS
algorithms
ISSN 1999-4893
/journal/algorithms
Article
A Finite Element Flux-Corrected Transport Method for Wave
Propagation in Heterogeneous Solids
Stefano Mariani 1,⋆, Roberto Martini 1 and Aldo Ghisi 1
Politecnico di Milano, Dipartimento di Ingegneria Strutturale, Piazza L. da Vinci 32, 20133 Milano,
Italy
E-mails: stefano.mariani@polimi.it; roberto.martini@mail.polimi.it; aldo.ghisi@polimi.it
⋆ Author to whom correspondence should be addressed.
Received: 29 October 2008; in revised form: 31 December 2008 / Accepted: 9 January 2009 /
Published: 13 January 2009
Abstract: When moving discontinuities in solids need to be simulated, standard finite ele-
ment (FE) procedures usually attain low accuracy because of spurious oscillations appearing
behind the discontinuity fronts. To assure an accurate tracking of traveling stress waves in het-
erogeneous media, we propose here a flux-corrected transport (FCT) technique for structured
as well as unstructured space discretizations. The FCT technique consists of post-processing
the FE velocity field via diffusive/antidiffusive fluxes, which rely upon an algorithmic length-
scale parameter. To study the behavior of heterogeneous bodies featuring compliant inter-
phases of any shape, a general scheme for computing diffusive/antidiffusive fluxes close to
phase boundaries is proposed too. The performance of the new FE-FCT method is assessed
through one-dimensional and two-dimensional simulations of dilatational stress waves prop-
agating a
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