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Place CentraleSupélec - Amphi V - Eiffel Building
On the numerical approximation of hyperbolic nonlinear problems, with a focus on compressible fluid mechanics: a little history, some current scientific perspectives
In this talk, I will present a historical perspective on the numerical approximation of the hyperbolic with a focus on compressible fluid mechanics.
I will explain the interaction between mathematics and physics: to understand the nature of a solution to the Euler equations or the Navier-Stokes equations, you need to understand where the equations come from and have some knowledge of thermodynamics.
This knowledge was acquired during a long process, which began with L. Euler and continued with scientists such as Riemann, Reynolds, Prandlt, Lax and many others.
I will also touch on the history of the numerical approximation of nonlinear hyperbolic partial differential equations, a process that began during the First World War and has accelerated since the Second World War, initially thanks to the Manhattan Project.
Over the years, increasingly complex problems have been studied. I will conclude by describing some recent developments.