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Algorithms 2009, 2(1), 1-18; doi:10.3390/a2010001

A Finite Element Flux-Corrected Transport Method for Wave Propagation in Heterogeneous Solids

* ,
Politecnico di Milano, Dipartimento di Ingegneria Strutturale, Piazza L. da Vinci 32, 20133 Milano, Italy
* Author to whom correspondence should be addressed.
Received: 29 October 2008 / Revised: 31 December 2008 / Accepted: 9 January 2009 / Published: 13 January 2009
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When moving discontinuities in solids need to be simulated, standard finite element (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 heterogeneous 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 interphases 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 propagating along homogeneous and composite rods.
Keywords: flux-corrected transport algorithm; composite dynamics; shock waves flux-corrected transport algorithm; composite dynamics; shock waves
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Mariani, S.; Martini, R.; Ghisi, A. A Finite Element Flux-Corrected Transport Method for Wave Propagation in Heterogeneous Solids. Algorithms 2009, 2, 1-18.

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