Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth. (English) Zbl 1439.76003
Summary: In this work we consider the discretization of our recently formulated [Eur. J. Appl. Math. 28, No. 3, 499–534 (2017; Zbl 1375.92030)] 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 [loc. cit.] 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.
MSC:
| 76-10 | Mathematical modeling or simulation for problems pertaining to fluid mechanics |
| 74L15 | Biomechanical solid mechanics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76T99 | Multiphase and multicomponent flows |
| 76Z05 | Physiological flows |
| 92C42 | Systems biology, networks |
Citations:
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