**2. A brief history of CFD**

Computational Fluid Dynamics (CFD) refers to a broad set of methods that are used to solve the coupled nonlinear equations that govern fluid motion. To our best knowledge, the first attempt to calculate fluid flow was set forth by Lewis Fry Richardson, with applications for weather prediction. He envisioned a "forecast factory" that included 64,000 human "computers". Each "computer" was positioned at tiered elevations around a spherical globe, occupying computational cells that corresponded to map locations, as shown below for northern Europe. His method involved inputting weather observation data to the corresponding grid locations and then solving the forward-stepping equations.

Based on Richardson's description, the following image provides the imagined weather prediction system, commonly referred to as the "fantastic weather factory" of Lewis Richardson. Each of the red and white grid cells represents a human calculator. They are arranged across the surface of a sphere (which represents the Earth). In the center, a conductor uses spotlights to highlight calculated results at each grid cell. It was acknowledged that for such a system to work, each human calculator would be required to perform their calculations at the same speed. That is, if one human calculator was either faster or slower than its neighbors, it would send information to the neighbors at a faster or slower rate which would consequently cause numerical instability; a concept that is important even today as we will show. In the image, the blue spotlight identifies calculators that are operating too slowly, and the red spotlight identifies those that are too fast.

While the vision of Richardson is somewhat fanciful, it nevertheless provides the foundation for modern day numerical simulation. His vision was remarkably prescient.

It was not until electric computers were developed that CFD could really begin its development and the human computers of Richardson could be replaced by digital computation. This generally commenced in the 1940s with the ENIAC programmable digital computer. Small scale simulations began to appear in the scientific literature in the early 1950s (for example [1]).
