Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review

I. Parallelism 1. Introduction 2. Parallel Computer Architectures 3. Parallel Programming Considerations II. Applications 4. General Application Issues 5. Parallel Computing in CFD 6. Parallel Computing in Environment and Energy 7. Parallel Computational Chemistry 8. Application Overviews III. Software technologies 9. Software Technologies 10. Message Passing and Threads 11. Parallel I/O 12. Languages and Compilers 13. Parallel Object-Oriented Libraries 14. Problem-Solving Environments 15. Tools for Performance Tuning and Debugging 16. The 2-D Poisson Problem IV. Enabling Technologies and Algorithms 17. Reusable Software and Algorithms 18. Graph Partitioning for Scientific Simulations 19. Mesh Generation 20. Templates and Numerical Linear Algebra 21. Software for the Scalable Solutions of PDEs 22. Parallel Continuous Optimization 23. Path Following in Scientific Computing 24. Automatic Differentiation V. Conclusion 25. Wrap-up and Features

Sourcebook of parallel computing

An accurate numerical analysis of the flows associated with rotor/stator configurations in turbomachinery can be very helpful in optimizing performance. In this study, the unsteady, thin-layer, Navier-Stokes equations are solved using a system of patched and overlaid grids for a rotor/stator configuration of an axial turbine. The equations necessary for an accurate transfer of information between the several grids are briefly described within the framework of an iterative, implicit algorithm. Results in the form of Mach number contours, time-averaged pressures, unsteady pressures, amplitudes, and phase are presented. The numerical results are also compared with experimental data and the agreement is found to be good. HE aerodynamic processes associated with the flow of fluid through turbomachines pose one of the toughest challenges to the computational fluid dynamicist. The un- steady nature of the flow, the complex geometries involved, the motion of some parts of the system relative to others, and the periodic transition of the flow from laminar to tur- bulent are some of the factors that contribute to the com- plexity of the problem. A clear understanding of these types of flows is essential for the optimization of the performance of turbomachiner y. In this study, an attempt is made to analyze two-dimensional flow past the rotor/stator con- figuration of an axial turbine using state-of-the-art computa- tional tools and computing facilities. The two-dimensional analysis of stator airfoils in isolation or rotor airfoils in isolation is a relatively straightforward task. Such an analysis is valid when the two rows of blades are set far enough apart so that the interaction effects are minimal. However, the desire to minimize engine length re- quires the stator and rotor airfoils to be closely spaced. Clearly, the interaction effects will become more important as the axial gap between the rows is reduced. In fact, the flow becomes periodically unsteady for small values of the axial gap. The experimental results of Ref. 1 show that the temporal pressure fluctuation (the difference between the minimum and maximum pressure values) near the leading edge of the rotor can be as much as 12% of the exit dynamic pressure when the axial gap is reduced to 15% of the chord length (for the operating conditions and geometry chosen). Hence, it is important that the rotor and stator airfoils be treated as a single system when the interaction effects become predominant. A computational tool that provides the design engineer with the necessary aerodynamic data can be used to great advantage in redesigning rotor and stator airfoils to enhance performance. Such a tool has to accurately simulate the unsteady flow associated with rotor/stator con- figurations exhibiting a strong interaction. A finite-differe nce solution to the Navier-Stokes equations requires the generation of a computational grid for the

Navier-Stokes Simulations of Rotor/Stator Interaction Using Patched and Overlaid Grids

A simulation of the flow about the integrated space shuttle vehicle in ascent mode has been undertaken for various flight conditions using the Chimera composite grid discretization approach. Overset body-conforming grids were used to represent each geometric component, and an implicit approximately factored finite-difference procedure was used to solve the three-dimensional thin-layer Navier-Stokes equations. The computational results have been compared with both wind tunnel and flight test data. Although relatively good agreement is obtained with the experimental data, further refinement and evaluation of numerical error is under way.

Numerical simulation of the integrated space shuttle vehicle in ascent

Grid generation equations formulated as hyperbolic partial differential equations are solved numerically to generate body conforming meshes. This grid generation procedure can be efficiently used to generate smoothly varying grids in which the user has good control of the grid clustering. Two-dimensional results are presented for typical external aerodynamic applications.

Generation of Body-Fitted Coordinates Using Hyperbolic Partial Differential Equations

A new computer code for the solution of the three-dimensional parabolized Navier-Stokes equations has been developed. The code employs a state-of-the-art upwind algorithm to capture strong shock waves. The algorithm is implicit, uses finite volumes, and is second-order accurate in the crossflow directions. The new code is validated through application to laminar hypersonic flows past two simple body shapes: a circular cone of 10 deg half-angle, and a generic all-body hypersonic vehicle. Cone flow solutions were computed at angles of attack of 12, 20, and 24 deg and results are in agreement with experimental data. Results are also presented for the flow past the all-body vehicle at angles of incidence of 0 and 10 deg.

Application of an upwind algorithm to the three-dimensional parabolized Navier-Stokes equations

An upwind algorithm for the parabolized Navier-Stokes equations

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.

Upwind Algorithm for the Parabolized Navier-Stokes Equations

Analytical techniques for the application of implicit boundary conditions for inviscid flows to shock and body boundary layer conditions involving the Euler equations are presented. The theory of characteristics is used to update boundary points with spatial second order accuracy. The method is useful for implicit schemes which feature approximate factorization, and as such is incorporated into an existing PNS code. Examples are provided in terms of flows over a cone, over a maneuverable reentry vehicle, and over a finned vehicle. Improvements in the convergence rate are demonstrated for the conical flow solutions.

Denny S. Chaussee

Papers

Generation of Body-Fitted Coordinates Using Hyperbolic Partial Differential Equations

Application of an upwind algorithm to the three-dimensional parabolized Navier-Stokes equations

An upwind algorithm for the parabolized Navier-Stokes equations

Upwind Algorithm for the Parabolized Navier-Stokes Equations

New implicit boundary procedures - Theory and applications