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A novel fully adaptive truly explicit time-marching methodology for the solution of hyperbolic bioheat conduction models

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Abstract

In this work, a truly explicit time-marching methodology is discussed for the time-domain solution for heat propagation considering the dual-phase-lag (DPL) bioheat model. The proposed technique considers self-adjustable time integration parameters, and it is approached together with automated calculations of domain decomposition and subcycling, providing a very versatile fully adaptive solution algorithm. The discussed domain decomposition procedure automatically divides the domain model into different subdomains (according to the properties of the discretized problem), in which different time-step values are applied, enabling more efficient (yet stable) explicit analyses. Expressions for the adaptive time integration parameters of the method and for the critical time steps of the subdomains of the model are presented and discussed. At the end of the paper, benchmark and applied examples are studied, showing the excellent performance of the proposed approach and the great effectiveness of the discussed fully adaptive formulation.

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Acknowledgements

The financial support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais), PRH-ANP (Programa de Recursos Humanos da Agência Nacional do Petróleo, Gás Natural e Biocombustíveis) and PETROBRAS (CENPES – 21066) is greatly acknowledged.

Funding

CNPq, CAPES, FAPEMIG, PRH-ANP, Petrobras.

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Authors and Affiliations

  1. Civil Engineering Department, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, CEP 21941-611, Brazil

    Lucas Ruffo Pinto & Webe João Mansur

  2. Structural Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, MG, CEP 36036-330, Brazil

    Delfim Soares Jr.

Authors
  1. Lucas Ruffo Pinto
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  2. Delfim Soares Jr.
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  3. Webe João Mansur
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Correspondence to Delfim Soares Jr..

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Pinto, L.R., Soares Jr., D. & Mansur, W.J. A novel fully adaptive truly explicit time-marching methodology for the solution of hyperbolic bioheat conduction models. Engineering with Computers 38, 4183–4206 (2022). https://doi.org/10.1007/s00366-022-01739-x

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