Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth
Collis, Joe and Hubbard, Matthew E. and O'Dea, Reuben D. (2016) Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth. Computer Methods in Applied Mechanics and Engineering, 309 . pp. 554-578. ISSN 1879-2138
In this work we consider the discretization of a recently formulated (Collis et al., ) multiscale model for drug- and nutrient-limited tumour growth. The key contribution of this work is the proposal of a discontinuous Galerkin finite element scheme which incorporates a non-standard coupling across a singular surface, and the presentation of full details of a suitable discretization for the coupled flow and transport systems, such as that arising in Collis et al.  and other similar works. We demonstrate the application of the proposed discretizations via representative numerical experiments; furthermore, we present a short numerical study of convergence for the proposed microscale scheme, in which we observe optimal rates of convergence for sufficiently smooth data.
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