European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
15:45   MS50: Numerical methods to advance mathematical biology research (Part 3)
Chair: Alf Gerisch
25 mins
Numerical approximations of a tractable mathematical model for tumour growth
Vanessa Styles
Abstract: We consider a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We derive sharp interface and diffuse interface finite element approximations of this model and present some numerical results.
25 mins
Multiscale dynamics of bulk and leading edge in cancer invasion
Dumitru Trucu
Abstract: In this talk I will present a novel multiscale moving boundary approach for cancer invasion that accounts for cell-adhesion in the context of the multiphase nature of the ECM dynamics. This connects the tissue-scale macro-dynamics with both the proteolytic cell- scale dynamics occurring at the tumour invasive edge and the micro-scale ECM fibres dynamic degradation and realignment occurring inside the tumour domain. The new modelling framework, will be accompanied by details of the computational approach and a discussion of the numerical simulation results.
25 mins
Numerical study of the fracture diffusion-dispersion coefficient for passive transport in fractured porous media
Florent CHAVE
Abstract: We propose a new definition of the normal fracture diffusion-dispersion coefficient for a reduced model of passive transport in fractured porous media.
25 mins
Comparison of the Influence of Conifer and Deciduous Trees on Dust Concentration Emitted From Low-lying Highway by CFD
Ludek Benes
Abstract: The influence of different types of vegetative barriers along a highway notch on dustiness was studied. The mathematical model is based on RANS equations for turbulent fluid flow in Boussinesq approximation completed by the standard k-$\epsilon$ model. Pollutants, considered as passive scalar, were modelled by additional transport equation. Three effects of the vegetation should be considered: effect on the air flow, i.e. slowdown or deflection of the flow, influence on turbulence levels inside and near the vegetation and filtering of the particles present in the flow. Deposition velocity reflects four main processes by which particles depose on the leaves: Brownian diffusion, interception, impaction and gravitational settling. The numerical method is based on finite volume formulation and uses AUSM+up scheme for convective terms. Two fractions of pollutants, PM10 and PM75, emitted from a four--lane highway were numerically simulated. 49 cases of conifer-type forest differing in density, width and height were studied. A new simplified LAD profile for this type of vegetation was developed and tested. Main processes playing role in modelled cases are described. The differences between the conifer and deciduous trees on pollutants deposition were studied.