This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engineers to get useful information on CFD for their activities. The procedural details are given with respect to particular tasks from the authors’ field of research, for example simulations of liquid propellant rocket engine subsystems, turbo-pumps and the blood circulations in the human brain as well as the design of artificial heart devices. However, those examples serve as illustrations of computational and physical challenges relevant to many other fields. Unlike other books on incompressible flow simulations, no abstract mathematics are used in this book. Assuming some basic CFD knowledge, readers can easily transfer the insights gained from specific CFD applications in engineering to their area of interest.

Introduction to the Numerical Analysis of Incompressible Viscous Flows treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier-Stokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. This book provides the foundation for understanding the interconnection of the physics, mathematics, and numerics of the incompressible case, which is essential for progressing to the more complex flows not addressed in this book (e.g., viscoelasticity, plasmas, compressible flows, coating flows, flows of mixtures of fluids, and bubbly flows). With mathematical rigor and physical clarity, the book progresses from the mathematical preliminaries of energy and stress to finite element computational fluid dynamics in a format manageable in one semester. Audience: this unified treatment of fluid mechanics, analysis, and numerical analysis is intended for graduate students in mathematics, engineering, physics, and the sciences who are interested in understanding the foundations of methods commonly used for flow simulations.

A unified treatment of fluid mechanics, analysis and numerical analysis appropriate for first year graduate students.

Both laminar and turbulent flows in strongly curved ducts, channels, and pipes are studied by numerical methods. The study concentrates on the curved square-duct geometry and flow conditions for which detailed measurements have been obtained recently by Taylor, Whitelaw, and Yianneskis. The solution methodology encompasses solution of the compressible ensemble-averaged Navier-Stokes equations at low Mach number using a split linearized block implicit (LBI) scheme, and rapid convergence on the order of 80 noniterative time steps is obtained. The treatment of turbulent flows includes resolution of the viscous sublayer region. A series of solutions for both laminar and turbulent flow and for both two- and three-dimensional geometries of the same curvature are presented. The accuracy of these solutions is explored by mesh refinement and by comparison with experiment. In summary, good qualitative and reasonable quantitative agreement between solution and experiment is obtained. Collectively, this sequence of results serves to clarify the physical structure of these flows and hence how grid selection procedures might be adjusted to improve the numerical accuracy and experimental agreement. For a three-dimensional flow of considerable complexity, the relatively good agreement with experiment obtained for the turbulent flow case despite a coarse grid must be regarded as encouraging. (Author).