Numerical Fluid Dynamics
Garrett Birkhoff · SIAM Review · 1983
By 1755, Euler was explicitly envisaging analytical fluid dynamics as a mathematical science, that of integrating the Euler–Lagrange equations. But by 1915, at least seven different analytical models were being used to explain the behavior of real fluids. From 1945 on, von Neumann was trying to “arithmetize” the approximate solution of the equations associated with these models, with the help of large-scale, high-speed computers. Thus he was envisaging numerical fluid dynamics as a mathematical science. After briefly reviewing the gradual disintegration of Euler’s concept of analytical fluid dynamics as a mathematical science, this survey article tries to assess the present status and future prospects of numerical fluid dynamics, through a series of case studies.