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Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course that the author has developed over twenty years, the text is split into three parts. The quick introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, the representation of surfaces, the boundary integral method, the multigrid method, domain decomposition, the fast multipole method, particle methods and wavelets.
THIS IS ONE OF THE LONGER chapters in this book and should be revisited many times at various levels. To cover in detail the subject of the properties of gases and liquids would take an entire book. Reference [1] is a classic example of such a book. We begin our study of properties by defining a few basic terms and concepts. We follow this by examining ideal-gas properties that originate from the equation of state and calorific equations of state. Various approaches for obtaining properties of nonideal gases, liquids, and solids follow. We emphasize the properties of substances that have coexisting liquid and vapor phases. The concept of illustrating processes graphically, using thermodynamic property coordinates (i.e., T– and P– coordinates), is developed.
IN THIS CHAPTER, we extend the overarching mass and energy conservation principles to reacting systems. In addition to conserving mass in an overall sense, the mass of individual elements must also be conserved in the transformation of reactants to products. Complicating energy conservation (the first law of thermodynamics) is the need to account for the potential energies associated with the making and breaking of chemical bonds. To accomplish this, we introduce the concept of standardized enthalpies. We introduce other new concepts related to mass conservation (e.g., various measures of stoichiometry) and energy conservation (e.g., adiabatic flame temperatures and fuel heating values). The chapter also applies the theoretical developments to practical steady-flow systems (e.g., furnaces, boilers, and combustors). Although the chapter focuses on combustion, the ideas developed here apply to other reacting systems as well.