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2021 | OriginalPaper | Chapter

Uncertainty Quantification and Stochastic Modeling for the Determination of a Phase Change Boundary

Authors : Juan Manuel Rodriguez Sarita, Renata Troian, Beatriz Costa Bernardes, Eduardo Souza de Cursi

Published in: Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Publisher: Springer International Publishing

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Abstract

We consider the determination of solid/liquid interfaces by the solution of the Stefan problem, involving two heat equations in unknown domains (two-phase problem). We establish a regularized formulation of the Stefan problem, which is used to characterize approximated values of the field of temperatures as means of convenient stochastic processes, using Feynman-Kac representations. The results of the resulting stochastic method are compared to Finite Element Approximations and show to be comparable to T2 finite element approximations. We present an example of variability of the domains occupied by the phases. In future work, methods for the uncertainty quantification of infinite dimensional objects will be applied to characterize the variability of the regions.

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Title: Uncertainty Quantification and Stochastic Modeling for the Determination of a Phase Change Boundary
Authors: Juan Manuel Rodriguez Sarita
Renata Troian
Beatriz Costa Bernardes
Eduardo Souza de Cursi
Publisher: Springer International Publishing
Book: Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling
Print ISBN: 978-3-030-53668-8

Electronic ISBN: 978-3-030-53669-5

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-53669-5_4