In this paper, the proper generalized decomposition (PGD) is presented for the solution of the parametric heat equation for an actual geothermal application. The physical domain is composed by ten geothermal probes inserted in the ground. The temperature profile along the probes is imposed as a parametric Dirichlet condition. The soil properties are parameters difficult to estimate in real life applications, and a parametric analysis is often required. In order to analyse their influence on the geothermal system. Moreover, another problem in modelling geothermal systems is the construction of the 3D mesh near probes. By employing PGD techniques, it is possible to overcome the large computational costs, because PGD is an a priori model reduction method that allow reducing the numerical complexity of the problem through separation of variables and parameters. In addition, the standard PGD strategy fails to converge for the case analysed in this paper, therefore an alternative strategy based on residual minimization idea has been used. In the present work, the authors analyse the effects of the probes presence on the soil temperature, by means of the developed PGD model.

### Proper generalized decomposition for geothermal applications

#### Abstract

In this paper, the proper generalized decomposition (PGD) is presented for the solution of the parametric heat equation for an actual geothermal application. The physical domain is composed by ten geothermal probes inserted in the ground. The temperature profile along the probes is imposed as a parametric Dirichlet condition. The soil properties are parameters difficult to estimate in real life applications, and a parametric analysis is often required. In order to analyse their influence on the geothermal system. Moreover, another problem in modelling geothermal systems is the construction of the 3D mesh near probes. By employing PGD techniques, it is possible to overcome the large computational costs, because PGD is an a priori model reduction method that allow reducing the numerical complexity of the problem through separation of variables and parameters. In addition, the standard PGD strategy fails to converge for the case analysed in this paper, therefore an alternative strategy based on residual minimization idea has been used. In the present work, the authors analyse the effects of the probes presence on the soil temperature, by means of the developed PGD model.
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2021
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11591/517760`
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