UKACM2023 School Programme

Dr Radu Cimpeanu

Biography

Radu completed his B.Sc. in Applied and Computational Mathematics at Jacobs University Bremen in Germany. His dissertation work involved developing the mathematical models and numerical methods for high intensity focused ultrasound, working closely with the local Franhofer MeVis institute. He then moved to the United Kingdom where he spent six years in the Department of Mathematics at Imperial College London, completing his M.Sc., Ph.D. and a post-doctoral position while working on asymptotic and computational techniques for nonlinear interfacial flows, with a particular interest in electrohydrodynamics and impact phenomena. Following a period of two years as an independent Hooke Research Fellow in the Mathematical Institute at the University of Oxford, he then moved to the Mathematics Institute at the University of Warwick in 2019, where he is now a senior lecturer. His research activities span fluid mechanics, wave propagation and numerical methods for partial differential equations, and are complemented by a strong interest in industrial mathematics. He is also Deputy Director of the Warwick Fluid Dynamics Research Centre and executive committee member of the UK Fluids Network.

Course description

The session will address aspects at the interface between rigorous mathematical modelling, analysis, and high-performance computing in fluid mechanics. It will involve creating a framework that enables the construction and implementation of numerical tools, culminating in resolving the nonlinear dynamics of liquid film flows in a variety of contexts as canonical examples. Understanding the key conceptual steps required before engaging in any software engineering aspects, debugging and validation concepts will also be touched on. We will be using the open-source software Basilisk in order to navigate some of the key ideas in how the direct numerical solutions of multi-fluid flows can be tackled efficiently. Basic fluid dynamics knowledge will be assumed, however, no specific computational expertise, nor any specialist knowledge of the applications discussed, will be required. The course will be set in a friendly informal setting and will consist of a combination of delivered material, interactive mini-sessions, and small-scale group work.

Dr Laurence Brassart

Biography

Laurence Brassart is an Associate Professor in the Solid Mechanics & Materials Group of the Department of Engineering Science at the University of Oxford. She received her diploma in Mechanical Engineering from the University of Louvain in Belgium in 2007, followed by a PhD in Engineering Sciences from the same university in 2011. She then successively held postdoctoral positions at Harvard University (BAEF Fellowship) and the University of Louvain (FNRS Fellowship). From 2015 to 2019, she was a Senior Lecturer in the Department of Materials Science and Engineering at Monash University in Australia. Laurence’s research focuses on the micromechanical and constitutive modelling of engineering materials, including Polymers, Composites, Soft Materials, and Energy Materials. She is particularly interested in multiphysics and multiscale aspects. In 2022, Laurence was awarded a UKRI Future Leaders Fellowship focused on the chemo-mechanics of biodegradable polymers.

Course description

This course will focus on the modelling of coupled chemo-mechanical phenomena in solids, namely diffusion and chemical reactions coupled to large, possibly inelastic deformations. Emphasis will be placed on the formulation of governing equations within the framework of the Thermodynamics of Irreversible Processes (TIP) as a guide to identify coupled effects and to ensure thermodynamic consistency of constitutive models. The main couplings to be considered include diffusion- and reaction-induced deformations, and conversely the effect of stresses on the diffusion and reaction driving forces. Kinetic models will address diffusion, reaction and viscoplastic flow. The modelling framework will be illustrated in the context of polymer swelling and degradation in water, and in that of lithium transport in solid electrodes of Li-ion batteries. Computational aspects using the Finite Element Method will also be discussed. Emphasis will be placed on the development of the general thermodynamic framework for constitutive modelling, rather than on specialised constitutive models and applications. Basic knowledge of continuum mechanics and thermodynamics will be assumed.

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