History of theoretical fluid dynamics

In 1759 Leonhard Euler published equations of motion for a fluid, applying Newton's second law of motion, which states that the product of mass and acceleration of a body equals the external forces acting on it. Euler's idea to express knowledge about fluid dynamics in the form of partial differential equations was a major breakthrough. A practical shortcoming of his flow model, however, was that it did not consider friction forces.

George Stokes came with more advanced equations in 1845. These equations where already introduced in 1822 by Claude Navier, but only for incompressible fluids. With the freshly introduced equations, today called Navier-Stokes equations, understanding and controlling a large class of fluid flows seemed close at hand. The problem was reduced to the mathematical solution of these basic differential equations.

Although the Navier-Stokes equations meant a considerable theoretical advance, the analytic mathematical solution of the full equations proved one bridge too far. This led to a fragmentation into a large number of simplified equations, derived from Navier-Stokes for special cases, equations which could be tackled analytically, i.e., with pen and paper. However, these different models all described the motion of the same fluid - a theoretically most undesirable situation.

No experiments anymore, only computations?
The invention of the digital computer led to many changes. John von Neumann, one of the founding fathers of CFD, predicted already in 1946 that ‘automatic computing machines' would replace the analytic solution of simplified flow equations by a ‘numerical' solution of the full nonlinear flow equations for arbitrary geometries. Von Neumann suggested that this numerical approach would even make experimental fluid dynamics obsolete.

Von Neumann's prediction did not fully come true, in the sense that both analytic theoretical and experimental research still coexist with CFD. Crucial properties of CFD methods such as consistency, stability and convergence need mathematical study. At present much fundamental research must still be done to increase CFD's accuracy, efficiency and robustness. Since many years, CWI actively partakes in this research and applies its results to challenging flow problems.