Geodesic
A streamline derivative POD-ROM for advection-diffusion-reaction equations
Samuele Rubino1
1 Departmento EDAN & IMUS, Universidad of Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain; e-mail: samuele@us.es
ESAIM. Proceedings, Tome 64 (2018), pp. 121-136.

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We introduce a new streamline derivative projection-based closure modeling strategy for the numerical stabilization of Proper Orthogonal Decomposition-Reduced Order Models (POD-ROM). As a first preliminary step, the proposed model is analyzed and tested for advection-dominated advection-diffusion-reaction equations. In this framework, the numerical analysis for the Finite Element (FE) discretization of the proposed new POD-ROM is presented, by mainly deriving the corresponding error estimates. Numerical tests for advection-dominated regime show the effciency of the proposed method, as well the increased accuracy over the standard POD-ROM that discovers its well-known limitations very soon in the numerical settings considered, i.e. for low diffusion coeffcients.
DOI : 10.1051/proc/201864121

Samuele Rubino 1

1 Departmento EDAN & IMUS, Universidad of Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain; e-mail: samuele@us.es 
@article{EP_2018_64_a9,
     author = {Samuele Rubino},
     title = {A streamline derivative {POD-ROM} for advection-diffusion-reaction equations},
     journal = {ESAIM. Proceedings},
     pages = {121--136},
     publisher = {mathdoc},
     volume = {64},
     year = {2018},
     doi = {10.1051/proc/201864121},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201864121/}
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Samuele Rubino. A streamline derivative POD-ROM for advection-diffusion-reaction equations. ESAIM. Proceedings, Tome 64 (2018), pp. 121-136. doi : 10.1051/proc/201864121. http://geodesic.mathdoc.fr/articles/10.1051/proc/201864121/

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