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Verification of the Domains Tracking Algorithm for Solving the System of Allen-Cahn and Cahn-Hilliard Equations

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Computational Science and Its Applications – ICCSA 2023 Workshops (ICCSA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14104))

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Abstract

The sintering process is widely used in modern industry because it allows for obtaining materials with predefined properties. Chemical or physical techniques can measure these properties. Besides the cost of such methods, it is worth noting that some techniques destroy samples, which causes difficulties in measuring the parameters’ evolution. Computer simulation of the sintering process allows for overcoming these difficulties. The sintering models based on the system of Cahn-Hilliard and Allen-Cahn equations require optimization if the number of grains is large. However, optimizations affect the solution; thus, a detailed quality assessment is required. The article presents such a study for our optimization: the Allen-Cahn equations are solved in small subdomains of the whole computational domain, which change over time. We provide comparative tests between solutions obtained by our algorithm and solutions obtained by solving the system in the whole domain. Besides common approaches, we use powerful tools of topology: Hausdorff distance and Betti numbers. The choice of the algorithm parameters is justified by obtained accuracy and efficiency.

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Acknowledgements

Dmitry Prokhorov implemented the pahse-field method and developed algorithms for computing the characteristics of the grains packing digital representation under the support of the basic research program of the Russian Academy of Sciences contract no. FWZZ-2022-0022. Yaroslav Bazaikin analyzed the results under the institutional support of the Faculty of Science, Jan Evangelista Purkyně University in Ústí nad Labem, Czech Republic. Vadim Lisitsa performed a numerical experiments using “Polytechnic RSC Tornado” (SPBSTU, Russia) with the support of the Russian Science Foundation Grant No. 21-71-20003.

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Authors and Affiliations

  1. Institute of Petroleum Geology and Geophysics SB RAS, Koptug ave. 3, Novosibirsk, 630090, Russia

    Dmitry Prokhorov

  2. Faculty of Science, Jan Evangelista Purkyně University in Ústí nad Labem, Pasteurova 3632/15, Ústí nad Labem, 400 96, Czech Republic

    Yaroslav Bazaikin

  3. Sobolev Institute of Mathematics SB RAS, 4 Koptug ave., Novosibirsk, 630090, Russia

    Vadim Lisitsa

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  1. Dmitry Prokhorov
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  2. Yaroslav Bazaikin
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Correspondence to Dmitry Prokhorov .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Basilicata, Potenza, Italy

    Francesco Scorza

  6. University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

  7. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

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Prokhorov, D., Bazaikin, Y., Lisitsa, V. (2023). Verification of the Domains Tracking Algorithm for Solving the System of Allen-Cahn and Cahn-Hilliard Equations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023 Workshops. ICCSA 2023. Lecture Notes in Computer Science, vol 14104. Springer, Cham. https://doi.org/10.1007/978-3-031-37105-9_46

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  • DOI: https://doi.org/10.1007/978-3-031-37105-9_46

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