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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:

Zbl 1375.92030

Software:

Triangle; MUMPS
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Full Text: DOI Link

References:

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