The development of modern computational fluid dynamics (CFD) began with the advent of the digital computer in the early 1950s. Finite difference methods (FDM) and finite element methods (FEM), which are the basic tools used in the solution of partial differential equations in general and CFD in particular, have different origins. ENGINEERING MECHANICS

In 1910, at the Royal Society of London, Richardson presented a paper on the first FDM solution for the stress analysis of a masonry dam. In contrast, the first FEM work was published in the Aeronautical Science Journal by Turner, Clough, Martin, and Topp for applications to aircraft stress analysis in 1956. Since then, both methods have been developed extensively in fluid dynamics, heat transfer, and related areas.FLUID DYNAMICS

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Earlier applications of FDM in CFD include Courant, Friedrichs, and Lewy [1928], Evans and Harlow [1957], Godunov [1959], Lax and Wendroff [1960], MacCormack [1969], Briley and McDonald [1973], van Leer [1974], Beam and Warming [1978], Harten [1978, 1983], Roe [1981, 1984], Jameson [1982], among many others. The literature on FDM in CFD is adequately documented in many text books such as Roache [1972, 1999], Patankar [1980], Peyret and Taylor [1983], Anderson, Tannehill, and Pletcher
[1984, 1997], Hoffman [1989], Hirsch [1988, 1990], Fletcher [1988], Anderson [1995], and Ferziger and Peric [1999], among others.FLUID DYNAMICS

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Earlier applications of FEM in CFD include Zienkiewicz and Cheung [1965], Oden [1972, 1988], Chung [1978], Hughes et al. [1982], Baker [1983], Zienkiewicz and Taylor [1991], Carey and Oden [1986], Pironneau [1989], Pepper and Heinrich [1992]. Other contributions of FEM in CFD for the past two decades include generalized PetrovGalerkin methods [Heinrich et at 1977; Hughes, Franca, and Mallett, 1986; Johnson, 1987], Taylor-Galerkin methods [Donea, 1984; Lohner, Morgan, and Zienkiewicz, 1985], ยจ
adaptive methods [Oden et al., 1989], characteristic Galerkin methods [Zienkiewicz et al., 1995], discontinuous Galerkin methods [Oden, Babuska, and Baumann, 1998], and incompressible flows [Gresho and Sani, 1999], among others.INTERNAL COMBUSTION ENGINE

There is a growing evidence of benefits accruing from the combined knowledge of both FDM and FEM. Finite volume methods (FVM), because of their simple data structure, have become increasingly popular in recent years, their formulations being related to both FDM and FEM. The flowfield-dependent variation (FDV) methods [Chung, 1999] also point to close relationships between FDM and FEM. Therefore, in this book we are seeking to recognize such views and to pursue the advantage of studying FDM and FEM together on an equal footing.ELECTRICAL TECHONOLOGY

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Historically, FDMs have dominated the CFD community. Simplicity in formulations and computations contributed to this trend. FEMs, on the other hand, are known to be more complicated in formulations and more time-consuming in computations. However, this is no longer the case in many of the recent developments in FEM applications.

Many examples of superior performance of FEM have been demonstrated. Our ultimate goal is to be aware of all advantages and disadvantages of all available methods so that if and when supercomputers grow manyfold in speed and memory storage, this knowledge will be an asset in determining the computational scheme capable of rendering the most accurate results, and not be limited by computer capacity. In the meantime, one may
always be able to adjust his or her needs in choosing between suitable computational schemes and available computing resources. It is toward this flexibility and desire that this text is geared.ADVANCED METHOD OF STRUCTURAL ANALYSIS

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This book covers the basic concepts, procedures, and applications of computational methods in fluids and heat transfer, known as computational fluid dynamics (CFD). Specifically, the fundamentals of finite difference methods (FDM) and finite element methods (FEM) are included in Parts Two and Three, respectively. Finite volume methods (FVM) are placed under both FDM and FEM as appropriate.SOFTWARE TESTING AND QUALITY ASSURANCE

This is because FVM can be formulated using either FDM or FEM. Grid generation, adaptive methods, and computational techniques are covered in Part Four. Applications to various physical problems in fluids and heat transfer are included in Part FiveDATA STRUCTURES WITH JAVA

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