Generally, the fundamental problem of CFD is solving the Navier-Stokes equations. Historically, the first method developed was 2D flow around an airfoil using conformal transformation, which was developed in the 1930s.
Lewis Fry Richardson used the idea of calculating using finite differences. In 1922, he divided the physical space into cells in the book Weather Prediction by Numerical Process, although the prediction was not entirely satisfactory.
From 1957 to the late 1960s, a group at Los Alamos National Lab, the T3 group led by Francis H. Harlow, developed three-dimensional methods such as particle-in-cell, fluid-in-cell, vorticity stream function, and marker-and-cell methods.
The first paper with a three-dimensional model was published in 1967 by John Hess and A.M.O. Smith of Douglas Aircraft. Panel methods are a method of discretizing the surface of the geometry with panels. The lifting panel code (A230) was described in a paper by Paul Rubbert and Gary Saaris in Boeing 1968. From this, more advanced methods were developed to be used in the development of submarines, surface ships, automobiles, helicopters, aircraft, and wind turbines.
In the early 1980s, Richard Eppler developed the PROFILE code, partly with NASA funding. This code performs 2D airfoil analysis with boundary layer analysis, including viscous effects. Mark Drela’s XFOIL code soon followed it.
Also, in the early 1980s, an intermediate step between Panel and full potential codes was used to transonic small disturbance equations, the 3D WIBCO code, developed by Charlie Boppe of Grumman aircraft.
Developers turned to Full potential codes because the Panel method could not calculate non-linear flow at transonic speeds. Frances Bauer, Paul Garabedian, and David Korn from New York University (NYU) wrote a series of 2D full potential airfoil codes that were widely used, the most important being Program H. Antony Jameson, also from NYU, worked with David Caughey to develop the important 3D Full potential code FLO22 in 1975. Many full potential codes emerged after this, culminating in Boeing’s Tranair (A633) code.
In 1981, Jameson developed the 3D FLO57 code from Lockheed’s TEAM program based on the Euler equation. The program uses structured cartesian mesh code, while most others use structured body-fitted grids.
Recent CFD codes can solve granular materials using chemical processes and physical models.
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