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A numerical study of nonlinear diffusion phenomena in heterogeneous media: energy transfer at diverse blow-up modes and self-organisation processes

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Abstract

A detailed analysis of a new method for numerical simulation of nonlinear diffusion phenomena is carried out. The method is based on operator splitting performed in time and space, and yields highly accurate solutions in complex 2D and 3D computational domains. After providing a circumstantial mathematical description of the developed method, we test it in several numerical experiments aimed, firstly, to model energy transfer at diverse modes of evolution of the dynamical system, and, secondly, to simulate self-organisation processes typical for real-world applications. A discussion of the outcomes of the numerical experiments is given. This is a follow-up paper of our recent original results presented at the 19th European conference on mathematics for industry.

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Authors and Affiliations

  1. Centre for Atmospheric Sciences (CCA), National Autonomous University of Mexico (UNAM), Av. Universidad #3000, Cd. Universitaria, Mexico City, C.P. 04510, Mexico

    Yuri N. Skiba

  2. Sceptica Scientific Ltd, Carpenter Court, 1 Maple Road, Bramhall, Stockport, Cheshire, SK7 2DH, UK

    Denis M. Filatov

Authors
  1. Yuri N. Skiba
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  2. Denis M. Filatov
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Correspondence to Denis M. Filatov.

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Skiba, Y.N., Filatov, D.M. A numerical study of nonlinear diffusion phenomena in heterogeneous media: energy transfer at diverse blow-up modes and self-organisation processes. Eur. Phys. J. Spec. Top. 226, 3303–3314 (2017). https://doi.org/10.1140/epjst/e2016-60323-x

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  • DOI: https://doi.org/10.1140/epjst/e2016-60323-x

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