{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:41:04Z","timestamp":1760222464074,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2009,1,13]],"date-time":"2009-01-13T00:00:00Z","timestamp":1231804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a2010001","type":"journal-article","created":{"date-parts":[[2009,1,13]],"date-time":"2009-01-13T12:25:36Z","timestamp":1231849536000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Finite Element Flux-Corrected Transport Method for Wave Propagation in Heterogeneous Solids"],"prefix":"10.3390","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5111-9800","authenticated-orcid":false,"given":"Stefano","family":"Mariani","sequence":"first","affiliation":[{"name":"Politecnico di Milano, Dipartimento di Ingegneria Strutturale, Piazza L. da Vinci 32, 20133 Milano, Italy"}]},{"given":"Roberto","family":"Martini","sequence":"additional","affiliation":[{"name":"Politecnico di Milano, Dipartimento di Ingegneria Strutturale, Piazza L. da Vinci 32, 20133 Milano, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2280-0490","authenticated-orcid":false,"given":"Aldo","family":"Ghisi","sequence":"additional","affiliation":[{"name":"Politecnico di Milano, Dipartimento di Ingegneria Strutturale, Piazza L. da Vinci 32, 20133 Milano, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2009,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1002\/eqe.4290050306","article-title":"Improved numerical dissipation for time integration algorithms in structural dynamics","volume":"5","author":"Hilber","year":"1977","journal-title":"Earthquake Engineering and Structural Dynamics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0045-7825(96)01036-5","article-title":"Explicit time integration algorithms for structural dynamics with optimal numerical dissipation","volume":"137","author":"Hulbert","year":"1996","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/0021-9991(73)90147-2","article-title":"Flux-corrected transport. 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II: generalization of the method","volume":"18","author":"Book","year":"1975","journal-title":"Journal of Computational Physics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1006\/jcph.2001.6955","article-title":"Flux correction tools for finite elements","volume":"175","author":"Kuzmin","year":"2002","journal-title":"Journal of Computational Physics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1002\/fld.493","article-title":"Multidimensional FEM-FCT schemes for arbitrary time stepping","volume":"42","author":"Kuzmin","year":"2003","journal-title":"International Journal for Numerical Methods in Fluids"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1830","DOI":"10.1190\/1.1443915","article-title":"Elimination of numerical dispersion in finite-difference modeling and migration by flux-corrected transport","volume":"60","author":"Fei","year":"1995","journal-title":"Geophysics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.wavemoti.2004.04.002","article-title":"An FE-FCT method with implicit functions for the study of shock wave propagation in solids","volume":"40","author":"Xiao","year":"2004","journal-title":"Wave Motion"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1002\/cnm.883","article-title":"A lattice Boltzmann method for shock wave propagation in solids","volume":"23","author":"Xiao","year":"2007","journal-title":"Communications in Numerical Methods in Engineering"},{"key":"ref_10","unstructured":"Zienkiewicz, O. 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