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2021 | OriginalPaper | Chapter

Numerical Simulations of Marble Sulfation

Authors : Armando Coco, Marco Donatelli, Matteo Semplice, Stefano Serra Capizzano

Published in: Mathematical Modeling in Cultural Heritage

Publisher: Springer International Publishing

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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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previous chapter Mathematical Models for Infrared Analysis Applied to Cultural Heritage

next chapter The Damage Induced by Atmospheric Pollution on Stone Surfaces: The Chemical Characterization of Black Crusts

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Title: Numerical Simulations of Marble Sulfation
Authors: Armando Coco
Marco Donatelli
Matteo Semplice
Stefano Serra Capizzano
Publisher: Springer International Publishing
Book: Mathematical Modeling in Cultural Heritage
Print ISBN: 978-3-030-58076-6

Electronic ISBN: 978-3-030-58077-3

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-58077-3_7

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