Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth

Collis, Joe; Hubbard, Matthew E.; O'Dea, Reuben D.

Abstract

In this work we consider the discretization of a recently formulated (Collis et al., [22]) 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. [22] 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.

Citation

Collis, J., Hubbard, M. E., & O'Dea, R. D. (2016). Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth. Computer Methods in Applied Mechanics and Engineering, 309, https://doi.org/10.1016/j.cma.2016.06.015

• Journal Article Type: Article
• Acceptance Date: Jun 11, 2016
• Online Publication Date: Jun 21, 2016
• Publication Date: Sep 1, 2016
• Deposit Date: Jul 19, 2016
• Publicly Available Date: Jul 19, 2016
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Electronic ISSN: 1879-2138
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 309
• DOI: https://doi.org/10.1016/j.cma.2016.06.015
• Keywords: Numerical simulations; Finite elements; Porous media; Cancer modelling
• Public URL: https://nottingham-repository.worktribe.com/output/802786
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0045782516305746
• Contract Date: Jul 19, 2016