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

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Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling (Uncertainties 2020)

Part of the book series: Lecture Notes in Mechanical Engineering ((ABCMSMSE))

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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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Authors and Affiliations

  1. LMN, Normandy University, INSA Rouen, 76801, Saint-etienne du Rouvray Cedex, France

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

Authors
  1. Juan Manuel Rodriguez Sarita
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  2. Renata Troian
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  3. Beatriz Costa Bernardes
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  4. Eduardo Souza de Cursi
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Correspondence to Eduardo Souza de Cursi .

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Editors and Affiliations

  1. Department Mechanics/Civil Engineering, INSA Rouen Normandie, Saint-Etienne du Rouvray, France

    José Eduardo Souza De Cursi

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Rodriguez Sarita, J.M., Troian, R., Costa Bernardes, B., de Cursi, E.S. (2021). Uncertainty Quantification and Stochastic Modeling for the Determination of a Phase Change Boundary. In: De Cursi, J. (eds) Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling. Uncertainties 2020. Lecture Notes in Mechanical Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-030-53669-5_4

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  • DOI: https://doi.org/10.1007/978-3-030-53669-5_4

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