Euler equations from the birth of CFD to present codes for multiphysics and complex geometry in aerospace and ground transportation engineering

Pierre Perrier, Dassault Aviation

The birth of Computational Fluid Dynamics appeared really with the Euler equations in the beginning of seventies with finite difference multiphysics numerical simulations of flow fields in hypersonic flow in the simple geometry of an axi-symmetric blunt body in competition with other analytical, empirical or numerical methods; however extension to more complex geometries let appear soon a lot of problems that required more than twenty years to be solved or only identified; parts was specific to an equation containing some drawbacks when put in discrete stable algorithms; the increase in speed of super-computers helped then to test in international workshops and validate versus experiments many promising new solvers. A survey of the improvements in numerical methods over years shows a parallel increase in engineering applications; particularly the discovery of some very interesting properties of the tridimensional Euler codes in the tracking of vortical flows has opened the way to predict the drag of blunt bodies, like cars, trucks or trains. However if the coupling with boundary layers on the body and with turbulent dissipation in wakes is necessary for better simulation it requires specific care; applications in aero-acoustics and in combustion continue to be in development and for the long years where speed of computers will not allow significant complexity of the geometries of vehicles to be tested.

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