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A moving mesh approach for modelling avascular tumour growth

Lee, T. E., Baines, M. J., Langdon, S. and Tindall, M. J. (2013) A moving mesh approach for modelling avascular tumour growth. Applied Numerical Mathematics, 72. pp. 99-114. ISSN 01689274

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To link to this item DOI: 10.1016/j.apnum.2013.06.001


A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.

Item Type:Article
Divisions:Interdisciplinary centres and themes > Institute for Cardiovascular and Metabolic Research (ICMR)
Life Sciences > School of Biological Sciences > Biomedical Sciences
Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:36174

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