Computational fluid dynamics physical boundary conditions

Before proceeding to such types of analysis and computations in the sections that follow, we begin with a statement of the full problem with as much of the physics represented as possible. Our approach is to work with macroscopic models of the interface separating the fluid phases. This approach represents the interface by a sharp dynamic surface embedded in three-dimensional space, across which flow and concentration variables can jump in a manner specified by physical boundary conditions. The alternative microscopic approach seeks to describe the three-dimensional thin transition layer between the two phases using statistical or continuum mechanical methods. The reader is referred to Chapters 15-18 of the text by Edwards, Brenner and Wasan as well as the many references therein. 

With their strength tied to available computer speed, simulations continue to become a more powerful tool. A letter to the Journal of Chemical Physics by B. J. Alder and T. E. Wainwright in 1957 was the first work that reported results from molecular dynamics simulations. The Lawrence Radiation Laboratory scientists studied two different sized systems with 32 and 108 hard spheres. They modeled bulk fluid phases using periodic boundary conditions. In the paper they mention that they counted 7000 and 2000 particle collisions for 32 and 108 particle systems, respectively. This required one hour on a UNIVAC computer. Incidentally, this was the fifth such commercial computer delivered out of the 46 ever produced. The computer cost around 200 000 in 1952 and each of ten memory units held 100 words or bytes. Nowadays, a 300 personal computer with a memory of approximately 500000000 bytes can complete this simulation in less than 1 second. And Moore s empirical law that computer power doubles every 18 months still holds. 

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