Governing equations of fluid dynamics

Abstract

The cornerstone of computational fluid dynamics is the fundamental governingequations of fluid dynamics-the continuity, momentum and energy equations.These equations speak physics. They are the mathematical statements of three fundamentalphysical principles upon which all of fluid dynamics is based:(1) mass is conserved;(2) F = ma (Newton's second law);(3) energy is conserved.The purpose of this chapter is to derive and discuss these equations.The purpose of taking the time and space to derive the governing equations offluid dynamics in this course are three-fold:(1) Because all of CFD is based on these equations, it is important for each studentto feel very comfortable with these equations before continuing further with hisor her studies, and certainly before embarking on any application of CFD to aparticular problem.(2) This author assumes that the attendees of the present VKI short course comefrom varied background and experience. Some of you may not be totally familiarwith these equations, whereas others may use them every day. For theformer, this chapter will hopefully be some enlightenment; for the latter, hopefullythis chapter will be an interesting review.(3) The governing equations can be obtained in various different forms. For mostaerodynamic 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) inthe numerical results, or even instability. Therefore, in the world of CFD, thevarious forms of the equations are of vital interest. In turn, it is important toderive these equations in order to point out their differences and similarities,and to reflect on possible implications in their application to CFD. © Springer-Verlag Berlin Heidelberg 2009.