8/22/2023 0 Comments Gmsh define dirichletbc fenicsOn the one hand, a competitive solver requires the right choice of discretisation, iterative method and pre-conditioner. The development of a modern, efficient finite element solver is an undertaking that requires expertise in many different areas of mathematics and computer science: Rapid development of finite element solvers in Firedrake and FEniCS You will also learn about cutting edge code-generation technology that allows for rapid algorithm research and development, which the team at Oxford exploited to develop these ideas so quickly. Keep reading if you would like to learn how this was done. I find this very exciting as in my F1 days we used to do an inordinate amount of work iterating to find the optimal design while this process has automatically emerged with a novel and optimised shape. Starting from a standard Naca aerofoil, we obtain a final shape that is very different to what you might expect and certainly not something I would have come up with. The picture below shows the shape of the airfoil at the beginning and end of the process, where the colours indicate the velocity obtained by solving for laminar flow conditions. The goal is to obtain the design that fully occupies the extent of the box and yields a large amount of lift while having low drag. The objective we consider is the airfoil's aerodynamic efficiency, that is the ratio of the lift and drag while we enforce box constraints on the airfoil. (It would be trivial to extend the analysis to optimise an aerofoil loss bucket). Note that for this example we did not vary the angle of attack so the leading edge is a rather incidence sensitive shape, but this does allow us to demonstrate more clearly how the technology works. Similarly my experience in road cars where inconveniences like gearbox casings or suspension legs tended to get in the way of my inspired diffuser design!Īs a test problem we have explored the optimisation of an aerofoil at a fixed onset flow within a geometrical box (like those used in the F1 rules). This was motivated by my experience of Formula 1, where aerodynamic devices are typically constrained to occupy a fixed geometric space by the technical regulations. We sought to explore the potential for applying the exciting field of geometric differentiation to the constrained optimisation of aerodynamic devices. The challenge of constrained optimisation Here we describe recent developments in open source finite element libraries that allow for the rapid development of solvers and optimisation algorithms in fluid dynamics. LCS-FAST has been working with the Mathematical Institute at the University of Oxford on researching novel shape optimisation techniques for aerodynamic and hydrodynamic design. Fast aerodynamic design using automatic differentiation
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