By Charles Hirsch

The second one variation of Numerical Computation of inner and exterior Flows is a self-contained advent to computational fluid dynamics (CFD). It covers the basics of the topic required in an introductory path for senior undergraduate or graduate point scholars. it's also perfect for readers who want a complete connection with CFD conception and perform, or because the foundation for extra complex learn and simulation improvement.

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These differences are crucial to the understanding of the physics of flows, but also to the rules for discretization and to essential properties of CFD numerical schemes. We can already mention here a most fundamental rule of numerical discretizations, which will be elaborated further in the following chapters, namely: The properties of a numerical discretization scheme may NEVER be in contradiction with the physics it aims to describe. It is therefore of uttermost importance to clearly understand the physical properties of the equations to be discretized and the mathematical translation of these properties.

It is of importance to note that the basic flow equations being three-dimensional any description with less than three space variables will be obtained by disregarding the flow variations with respect to the corresponding space coordinate and this can be formulated mathematically by averaging out the equations over that space variable. Therefore, the averaging process, here over space, is again essential. In this space averaging, we will obtain equations in a two- or one-dimensional region, which contain terms describing the averaged influence of the full three-dimensional motion.

An averaging is performed over the turbulent fluctuations, since we are concerned in that case with variations of the flow slower that the turbulent fluctuations and hence, with time constants much larger than the time constant of these fluctuations. Through this procedure, extra terms appear in the equation, the Reynolds stresses, which are averaged products of fluctuations, and for which external information will have to be provided. Along similar lines, in Large Eddy Simulations, known as the LES approximation, the turbulent fluctuations are averaged only over part of their spectrum, namely the small scales are modeled while the larger turbulent motion, associated with the lower frequencies, is directly simulated.

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