The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.Comment: To appear in "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final publication is available at http://www.springerlink.co

Interactive calculation procedure for supersonic flows

An interactive procedure was developed for supersonic viscous flows that can be used for either two-dimensional or axisymmetric configurations. The procedure is directed to supersonic internal flows as well as those supersonic external flows that require consideration of mutual interaction between the outer flow and the boundary layer flow. The flow field is divided into two regions: an inner region which is highly viscous and mostly subsonic and an outer region where the flow is supersonic and in which viscous effects are small but not negligible. For the outer region a numerical solution is obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines. The inner region is treated by a system of equations of the boundary layer type that includes higher order effects such as longitudinal and transverse curvature and normal pressure gradients. These equations are coupled and solved simultaneously in the physical coordinates by using an implicit finite difference scheme. This system can also be used to calculate laminar and turbulent boundary layers using a scalar eddy viscosity concept

Integral-equation methods in steady and unsteady subsonic, transonic and supersonic aerodynamics for interdisciplinary design

Progress in the development of computational methods for steady and unsteady aerodynamics has perennially paced advancements in aeroelastic analysis and design capabilities. Since these capabilities are of growing importance in the analysis and design of high-performance aircraft, considerable effort has been directed toward the development of appropriate aerodynamic methodology. The contributions to those efforts from the integral-equations research program at the NASA Langley Research Center is reviewed. Specifically, the current scope, progress, and plans for research and development for inviscid and viscous flows are discussed, and example applications are shown in order to highlight the generality, versatility, and attractive features of this methodology

Computational fluid dynamics

An overview of computational fluid dynamics (CFD) activities at the Langley Research Center is given. The role of supercomputers in CFD research, algorithm development, multigrid approaches to computational fluid flows, aerodynamics computer programs, computational grid generation, turbulence research, and studies of rarefied gas flows are among the topics that are briefly surveyed

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described

Simulation of time-dependent compressible viscous flows using central and upwind-biased finite-difference techniques

Four time-dependent numerical algorithms for the prediction of unsteady, viscous compressible flows are compared. The analyses are based on the time-dependent Navier-Stokes equations expressed in a generalized curvilinear coordinate system. The methods tested include three traditional central-difference algorithms, and a new upwind-biased algorithm utilizing an implicit, time-marching relaxation procedure based on Newton iteration. Aerodynamic predictions are compared for internal duct-type flows and cascaded turbomachinery flows with spatial periodicity. Two-dimensional internal duct-type flow predictions are performed using an H-type grid system. Planar cascade flows are analyzed using a numerically generated, capped, body-centered, O-type grid system. Initial results are presented for critical and supercritical steady inviscid flow about an isolated cylinder. These predictions are verified by comparisons with published computational results from a similar calculation. Results from each method are then further verified by comparison with experimental data for the more demanding case of flow through a two-dimensional turbine cascade. Inviscid predictions are presented for two different transonic turbine cascade flows. All of the codes demonstrate good agreement for steady viscous flow about a high-turning turbine vane with a leading edge separation. The viscous flow results show a marked improvement over the inviscid results in the region near the separation bubble. Viscous flow results are then further verified in finer detail through comparison with the similarity solution for a flat plate boundary-layer flow. The usefulness of the schemes for the prediction of unsteady flows is demonstrated by examining the unsteady viscous flow resulting from a sinusoidally oscillating flat plate in the vicinity of a stagnant fluid. Predicted results are compared with the analytical solution for this flow. Finally, numerical results are compared with flow visualization and experimental data for the unsteady flow resulting from an impulsively started cylinder. Each algorithm demonstrates unique qualities which may be interpreted as either advantageous or disadvantageous, making it difficult to select an optimum scheme. The preferred method is perhaps best chosen based on the experience of the user and the particular application

Geophysical Fluid Dynamics

The workshop “Geophysical Fluid Dynamics” addressed recent advances in analytical, stochastic, modeling and computational studies of geophysical rotating fluids models. Of particular interest on the analytical and stochastic sides were the contributions concerning dispersive mechanism, regularity verses finite-time formation of singularities of certain viscous and inviscid geostrophic models, the primitive equations, Boussinesq approximation, boundary layers and fast rotating fluids. Model reductions, based on asymptotic, scaling analysis and variational methods, were presented. In addition, computational investigations were provided in support of the claim that three-dimensional geophysical turbulent flows exhibit two-dimensional features, at small Rosby numbers