Eur. Phys. J. Special Topics 226, 3303–3314 (2017)
https://doi.org/10.1140/epjst/e2016-60323-x

Regular Article

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

¹ Centre for Atmospheric Sciences (CCA), National Autonomous University of Mexico (UNAM), Av. Universidad #3000, Cd. Universitaria, Mexico City, C.P. 04510, Mexico
² Sceptica Scientific Ltd, Carpenter Court, 1 Maple Road, Bramhall, Stockport, Cheshire SK7 2DH, UK

^a e-mail: denis.filatov@sceptica.co.uk

Received: 20 October 2016
Received in final form: 4 February 2017
Published online: 28 December 2017

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.