Governing Equations of Fluid Dynamics

(1) Because all of CFD is based on these equations, it is important for each student to feel very comfortable with these equations before continuing further with his or her studies, and certainly before embarking on any application of CFD to a particular problem. (2) This author assumes that the attendees of the present VKI short course come from varied background and experience. Some of you may not be totally familiar with these equations, whereas others may use them every day. For the former, this chapter will hopefully be some enlightenment; for the latter, hopefully this chapter will be an interesting review. (3) The governing equations can be obtained in various different forms. For most aerodynamic theory, the particular form of the equations makes little difference. However, for CFD, the use of the equations in one form may lead to success, whereas the use of an alternate form may result in oscillations (wiggles) in the numerical results, or even instability. Therefore, in the world of CFD, the various forms of the equations are of vital interest. In turn, it is important to derive these equations in order to point out their differences and similarities, and to reflect on possible implications in their application to CFD.