P. Barral

Existence and uniqueness of a thermoelastic problem with variable parameters

The aim of this article is to study the existence and uniqueness of solution for a quasistatic fully coupled thermoelastic problem arising from some metallurgical processes. We consider mixed boundary conditions for both submodels, and a Robin boundary condition for the thermal one. Furthermore, the reference temperature, the thermal conductivity and the Lames parameters are assumed to depend on the material point.

Reports about 8 selected benchmark cases of model hierarchies

Based on the multitude of industrial applications, benchmarks for model hierarchies will be created that will form a basis for the interdisciplinary research and for the training programme. These will be equipped with publically available data and will be used for training in modelling, model testing, reduced order modelling, error estimation, efficiency optimization in algorithmic approaches, and testing of the generated MSO/MOR software. The present document includes the description about the selection of (at least) eight benchmark cases of model hierarchies. Disclaimer & acknowledgment This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 765374. This document reflects the views of the author(s) and does not necessarily reflect the views or policy of the European Commission. The REA cannot be held responsible for any use that may be made of the information this document contains. Reproduction and translation for non-commercial purposes are authorised, provided the source is acknowledged and the publisher is given prior notice and sent a copy.

19th European Conference on Mathematics for Industry: book of Abstracts, June, 13-17, 2016, Santiago de Compostela (Spain)

In the last decades, the biomedical relevance of mathematical models has been demonstrated and comparison of experiments against computer simulations has been encouraged. Blood circulation in the human liver and in particular perfusion, the process of delivering blood to the capillary bed, is an open problem and inherently multiscale in nature. Models currently available in the literature [2, 1] either present a macroscale approach in which liver is assumed as a homogeneous anisotropic porous medium and therefore flow within it is simulated using Darcy’s equation, or they work at the microscale where the vascular and extravascular domains need to be treated differently solving Stokes’ equation in the former and Darcy’s equation in the latter and applying suitable coupling condition at the interface. In this communication, instead, we present an approach where the Darcy-Stokes-Brinkmann [3] equation is used on the entire computational domain, different areas of the tissue being represented by a (possibly discontinuous) friction coefficient. This approach allows to run simulations at the capillary scale on real-life geometries deduced from medical images avoiding complex and costly preprocessing such as edge detection, and mesh generation. The peculiar properties of IsoGeometric discretization methods [4, 5] such as stability and ability to provide exactly divergence free velocity are exploited in the simulation. After validating the numerical method on 2D and 3D test cases based on syntetic images, we apply it to actual micro-CT images of the liver and perform an upscaling procedure to determine the macroscale parameters of the tissue such as the local permeability tensor.