Modelling and Scientific Computing: environmental and societal applications.

In this module, three researchers will present part of their research activity in modeling and scientific computing in fields linked to the environment, energy and health.

mini-course 1: Some current issues in wave modeling (David Lannes, DR CNRS, IMB)

Understanding wave motion is at the heart of a number of environmental issues, such as the risks of submersion and erosion, as well as energy transition issues with marine renewable energies (offshore wind turbines, wave energy converters, etc.). In this course, we'll look at a few elements of wave motion modeling. We'll focus on the characteristic quantities that dictate the nature of wave propagation, and explain why, for example, a tsunami propagates in a qualitatively different way from ocean swell. A few simple numerical simulations will illustrate the main mechanisms involved. A few issues linked to the prospects for harnessing wave energy will also be addressed.

mini-course 2: Fluid-structure interactions for green energies (Michel Bergmann, DR INRIA, IMB)
The focus of this course will be on numerical modeling for renewable energies. In particular, we'll be talking about marine energy extractors and wind turbines. The specificity of these problems is the need to couple different models, having either different degrees of fidelity (compromise between accuracy and computation speed), or different physics (fluid or structure). Several model coupling strategies will be discussed to ensure numerical stability and accuracy of the overall model. These strategies will be studied in practical sessions.

mini-course 3: Multiscale modeling of electroporation: the contribution of mathematics to clinical practice (Clair Poignard, DR INRIA, IMB)
The exposure of a cell to a very intense and brief electric field (a few hundred V/cm for a few tens of microseconds) results in the destructuring of the lipid bilayer forming the cell membrane, making it permeable to extracellular molecules. From an electrical point of view, the membrane behaves like a capacitor in parallel with a conductor. This leads to Kirchoff's law describing the evolution of transmembrane voltage (TMV) and electric current. At the membrane scale, electroporation models involve writing a nonlinear law on membrane conductance. First, we'll show the different ways of modeling the phenomenon, from electrical circuit models to the latest phase-change approaches, and then we'll look at the mathematical challenges raised by percutaneous ablation of deep tumors (liver and pancreas), and the first recent results enabling fast, precise calculation in the treated zone during the clinical procedure.