P. Quintela

A numerical method for simulation of thermal stresses during casting of aluminium slabs

Abstract We present a numerical study of a quasistatic evolution problem for a system of partial differential equations modelling the thermomechanical behaviour of a direct chill (DC) or electromagnetic (EMC) casting of aluminium. It is a quasistatic evolution problem of a three-dimensional elastic-viscoplastic solid with contact. This model can be used to predict and assess the most fundamental variables in the casting process: casting speed, alloy composition, cooling conditions, mould shape, ... To solve the discrete problem at each time step, we propose a discretization by a tetrahedral finite element method and an iterative algorithm. At each iteration, one must solve a linear elasticity problem. To validate the proposed algorithm it has been applied to some test examples with known analytical solutions. Finally, we present the results of calculations corresponding to a real industrial casting process.

Numerical solution of a three-dimensional thermoelectric problem taking place in an aluminium electrolytic cell

Abstract In this paper we solve a free boundary problem for a system of partial differential equations modelling the thermoelectrical behaviour of an aluminium electrolytic cell. A fixed domain method is proposed which relies upon a weak formulation of this system. A discretisation is introduced by using pentahedral finite elements of six degrees of freedom. To solve the discretised system an iterative algorithm is proposed. Numerical results are given both for a test example and a real industrial situation.

Numerical simulation of some problems related to aluminium casting

Abstract In this paper we present several models describing some thermal, mechanical, electromagnetic and hydrodynamic phenomena arising from electromagnetic aluminium casting process. A numerical solution of these models is proposed and numerical results are given for industrial castings.

A numerical algorithm for prediction of thermomechanical deformation during the casting of aluminium alloy ingots

This paper describes a numerical algorithm predicting three-dimensional deformation during direct chill or electromagnetic casting of aluminium alloy ingots. Its predictions are compared with experimental results for both the initial and stationary phases of the casting process.

Numerical analysis of a viscoplastic problem with contact condition taking place in an aluminium casting

We consider a viscoplastic problem with contact condition modelling the thermomechanical deformations during casting of aluminium alloy slabs. We introduce a fictitious domain method to impose the metallostatic pressure on the thermal free boundary. Finally, we present some numerical results for a particular casting process during both the start and stationary stages.

Existence of solution for a free boundary problem in a nonlinear piecewise homogeneous medium

A free boundary problem arising from the bidimensional thermal modelling of aluminium electrolytic cells is studied. The medium is assumed piecewise homogeneous and nonlinear. A fixed domain method is proposed which leads to a weak formulation of the problem. Existence of weak solution is proved by regularizing the contact condition between the homogeneous subdomains and passing to the limit.

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.

Minisymposium: EU-MATHS-IN: Success Stories of Mathematical Technologies in Societal Challenges and Industry

The development of new products, production processes or improvements in the society today is dominated by the use of simulation and optimization methods that, based on a detailed mathematical modeling, support or even replace the costly production of prototypes and classical trial-and-error methods. To address this development and following the Recommendations of the Forward Look ‘Mathematics and Industry’ published by the European Science Foundation, several European research networks have established a new organization to increase the impact of mathematics on innovations in key technologies and to foster the development of new modeling, simulation and optimization tools.