TAILIEUCHUNG - Ebook Fluid mechanics and Its applications: Part 2

(BQ) Part 2 book "Fluid mechanics and Its applications" has contents: Discretization of the convection term, high resolution schemes, fluid flow computation - Compressible flows, turbulence modeling, closing remarks, fluid flow computation - Compressible flows,.and other contents. | Chapter 11 Discretization of the Convection Term Abstract So far, the discretization of the general steady diffusion equation has been formulated on orthogonal, non-orthogonal, structured, and unstructured grids. Another important term, the convection term represented by the divergence operator, is the focus of this chapter. Initially this term is discretized using a symmetrical linear profile similar to the one adopted for the discretization of the diffusion term. The shortcomings of this profile are delineated and a remedy is suggested through the use of an upwind profile. Even though it leads to physically plausible predictions, the upwind profile is shown to be highly diffusive generating results that are first order accurate. To increase accuracy, higher order profiles that are upwind biased are introduced. While reducing the discretization error, higher order profiles are shown to give rise to another type of error known as the dispersion error. Methods dealing with this error will be dealt with in the next chapter. Moreover, the flow field, which represents the driving catalyst of the convection term, is assumed to be known. The computation of the flow field will be the subject of later chapters. Introduction Although the convection term looks simple, its discretization presents a number of difficulties that have occupied researchers for more than three decades now. Their work has shed light on the problems that hindered its discretization and resulted in the development of a large number of convection schemes. The body of literature is so large that two chapters are devoted for the analysis of this term. In this chapter the basic concepts are introduced and High Order (HO) [1–3] upwind biased schemes are discussed. The bounding of the convective flux, which made possible the development of non-oscillatory convection schemes of high order of accuracy, denoted by High Resolution (HR) schemes, will be discussed in the next chapter. For clarity, the presentation .

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