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Numerical Simulations of Marble Sulfation

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Mathematical Modeling in Cultural Heritage

Part of the book series: Springer INdAM Series ((SINDAMS,volume 41))

Abstract

In this chapter we describe some computational techniques to approximate the evolution of gypsum crusts on marble monuments. Mathematical models of this phenomenon are typically based on partial differential equations and here we deliberately consider a quite simple one, so that we can focus on the numerical techniques that can be used to overcome the main difficulties of this kind of computations, namely the efficiency of the timestepping procedure and the complexity of the computational domains in real-world cases. First, the design of optimal preconditioners for Cartesian grid discretizations is reviewed. Then, we illustrate a technique to deal with non Cartesian domains by described via a level-set function. The chapter ends with a study of the influence of the surface curvature on the growth of the gypsum crust, that generalizes earlier analytical one-dimensional results.

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Acknowledgements

The work has been partly supported by INdAM GNCS.

Author information

Authors and Affiliations

  1. School of Engineering, Computing and Mathematics, Oxford Brookes University, Oxford, UK

    Armando Coco

  2. Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Como, Italy

    Marco Donatelli & Matteo Semplice

  3. Dipartimento di Scienze Umane e dell’Innovazione per il Territorio, Università dell’Insubria, Como, Italy

    Stefano Serra Capizzano

Authors
  1. Armando Coco
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  2. Marco Donatelli
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  3. Matteo Semplice
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  4. Stefano Serra Capizzano
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Corresponding author

Correspondence to Matteo Semplice .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Elena Bonetti

  2. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Cecilia Cavaterra

  3. Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Roma, Italy

    Roberto Natalini

  4. Dipartimento di Architettura, Università di Sassari, Alghero, Italy

    Margherita Solci

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Coco, A., Donatelli, M., Semplice, M., Serra Capizzano, S. (2021). Numerical Simulations of Marble Sulfation. In: Bonetti, E., Cavaterra, C., Natalini, R., Solci, M. (eds) Mathematical Modeling in Cultural Heritage. Springer INdAM Series, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-030-58077-3_7

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