European Numerical Mathematics and
 15:45 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. 16:10 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. 16:35 25 mins Hybrid High-Order methods in the framework of fractured porous media Florent CHAVE, Daniele A. Di Pietro, Luca Formaggia Abstract: In this work, we propose a model for the passive transport of a solute in a fractured porous medium, for which we develop a Hybrid High-Order (HHO) space discretization. We consider, for the sake of simplicity, the case where the flow problem is fully decoupled from the transport problem. The novel transmission conditions in our model mimic at the discrete level the property that the advection terms do not contribute to the energy balance. This choice enables us to handle the case where the concentration of the solute jumps across the fracture. The HHO discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture for the flow problem, and on a primal formulation both in the bulk region and inside the fracture for the transport problem. Relevant features of the method include the treatment of nonconforming discretizations of the fracture, as well as the support of arbitrary approximation orders on fairly general meshes. 17:00 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.