Direct Numerical Simulations

To understand and model the turbulent behavior of flowing fluids is one of the most fascinating, intriguing, annoying, and most important problems of engineering and physics. Admittedly most of the fluid flows are turbulent. In the known universe, turbulence is evident at the macroscopic scale and the microscopic scale in identical proportions. Turbulence is manifested in many places, such as: a plethora of technological devices, atmospheres and ocean currents, astronomical or galactic motions, and biological systems like circulation or respiration. With the continuum as an assumption, the equations that define the physics of fluid flow are the Navier-Stokes equations modeled during the mid-19th Century by Claude-Louis Navier and Sir George Gabriel Stokes. These equations define all flows, even turbulent flows, yet there is no analytical solution to even the simplest turbulent flow possible. However, the numerical solution of the Navier-Stokes equation is able to describe the flow variable as a function of space and time. It is called direct numerical simulations (DNS), which is the subject matter of this book.