Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations

Spectral methods for CFD

One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched

Flow Simulations About Steady-Complex and Unsteady Moving Configurations Using Structured-Overlapped and Unstructured Grids

The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary problems are evaluated. These are namely the structured-overlapped and the unstructured grid schemes. Both methods use a cell centered, finite volume, upwind approach. The structured-overlapped algorithm uses an approximately factored, alternating direction implicit scheme to perform the time integration, whereas, the unstructured algorithm uses an explicit Runge-Kutta method. To examine the accuracy, efficiency, and limitations of each scheme, they are applied to the same steady complex multicomponent configurations and unsteady moving boundary problems. The steady complex cases consist of computing the subsonic flow about a two-dimensional high-lift multielement airfoil and the transonic flow about a three-dimensional wing/pylon/finned store assembly. The unsteady moving boundary problems are a forced pitching oscillation of an airfoil in a transonic freestream and a two-dimensional, subsonic airfoil/store separation sequence. Accuracy was accessed through the comparison of computed and experimentally measured pressure coefficient data on several of the wing/pylon/finned store assembly\u27s components and at numerous angles-of-attack for the pitching airfoil. From this study, it was found that both the structured-overlapped and the unstructured grid schemes yielded flow solutions of comparable accuracy for these simulations. This study also indicated that, overall, the structured-overlapped scheme was slightly more CPU efficient than the unstructured approach

Navier-Stokes Simulations of Flows About Complex Configurations Using Domain Decomposition Techniques

An algorithm is developed to obtain numerical simulations of flows about complex configurations composed of multiple and nonsimilar components with arbitrary geometries. The algorithm uses a hybridization of the domain decomposition techniques for grid generation and to reduce the computer memory requirement. Three dimensional, Reynolds-averaged, unsteady, compressible, and complete Navier-Stokes equations are solved on each of the subdomains by a fully-vectorized, finite-volume, upwind-biased, approximately-factored, and multigrid method. The effect of Reynolds stresses is incorporated through an algebraic turbulence model with several modifications for interference flows. The present algorithm combines the advantages of an efficient, geometrically conservative, minimally and automatically dissipative algorithm with advantages and flexibility of domain decomposition techniques. The algorithm is used to simulate supersonic flows over two-dimensional profiles and a body of revolution at high angles of attack. This study is performed to examine the suitability of the baseline solution algorithm and gain a better understanding of this class of flows. The grid overlapping is tested by obtaining the solution of a supersonic flow over a blunt-nose-cylinder at high angles of attack using a composite of overlapped grids. This solution compares very well with the solution of the same flowfield obtained with no overlapping and the experimental data. The multigrid algorithm used for this case shows substantial savings in the computational time. To accomplish one of the main objectives of this study, the algorithm is then applied to simulate the supersonic flow over an ogive-nose-cylinder near and inside a cavity. The cylinder is attached to an offset L-shaped sting when placed above the cavity opening. The results of the time-accurate computations depict these complex flows and help understanding interference effects. The unsteady nature of these flowfields and the interaction of the cavity shear layer with the cylinder are simulated. These cases illustrate two significantly different and important interference characteristics for a store separating from its parent body. Unsteadiness of the cavity flow has a more pronounced effect on the normal forces acting on the cylinder when the cylinder is placed inside the cavity. A clearer understanding of the flow between the base of the cylinder and the cavity rear face is gained by eliminating the offset sting when the cylinder is inside the cavity. The time averaged surface pressures compare favorably with the wind tunnel data, despite the averaging time period for the computations being three orders of magnitude smaller than that of the experimental measurements. The results of the present computations contribute to the much needed database for the internal store carriage and separation