As a branch of fluid mechanics, fluid dynamics deals with fluid flow, that is, liquids and gasses in motion. In the following sections of this chapter, different types of flows will be introduced first without heavily referring to the mathematical equations. The purpose is to offer a clear picture regarding the basic concepts in fluid dynamics and computational fluid dynamics (CFD) simulations. Presented next will be the introduction to the Navier-Stokes (N-S) equations. To make the introduction clear and complete, the general equations will be explained first, followed by the derivations of various common forms of the N-S equations, which correspond to different types of flows. Both the mass and momentum equations will be derived from the basic conservation law. Different constitutive relationships will be added to show different forms of the N-S equations for different fluids. Then, a section will be used to describe many concepts more in-depth with more mathematical details. The turbulent models will also be briefly introduced to complete the theoretical framework. Finally, a benchmark problem will be provided for practicing the numerical simulation of fluid dynamics.
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