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The hyperbolic scheme is used to efficiently generate smoothly varying grids with good step size control near the body. Although only two dimensional applications are presented, the basic concepts are shown to extend to three dimensions.
The development of an interactive/batch gridded information system (array of cells georeferenced to USGS quad sheets) and interfacing application programs (e.g., hydrologic models) is discussed. This system allows non-programer users to request any data set(s) stored in the data base by inputing any random polygon's (watershed, political zone) boundary points. The data base information contained within this polygon can be used to produce maps, statistics, and define model parameters for the area. Present/proposed conditions for the area may be compared by inputing future usage (land cover, soils, slope, etc.). This system, known as the Hydrologic Analysis Program (HAP), is especially effective in the real time analysis of proposed land cover changes on runoff hydrographs and graphics/statistics resource inventories of random study area/watersheds.
The effect of non-uniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme based on a finite volume formulation is considered. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are presented in both two- and three-space dimensions. Applications to finite difference and implicit algorithms are also given.
The effect of nonuniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme is considered based on a finite volume formuation. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are pesented in both two- and three-space dimensions. Applications to finite difference and impicit algorithms are also given.
The Fluid Dynamics Panel of AGARD arranged a Symposium on Applications of Computational Fluid Dynamics in Aeronautics, on 7 to 10 April 1986 in Aix-en-Provence, France. The purpose of the Symposium was to provide an assessment of the status of CFD in aerodynamic design and analysis, with an emphasis on emerging applications of advanced computational techniques to complex configurations. Sessions were devoted specifically to grid generation, methods for inviscid flows, calculations of viscous-inviscid interactions, and methods for solving the Navier-Stokes equations. The 31 papers presented at the meeting are published in AGARD Conference Proceedings CP-412 and are listed in the Appendix of this report. A brief synopsis of each paper and some general conclusions and recommendations are given.
A package of computer codes for analysis of flow fields for waverider configurations is described. The package consists of a surface/volume grid generator and a finite-volume flow solver. The grid generator defines body geometries and computational grids by an algebraic homotopy procedure. The algebraic procedure is versatile in its application and can readily generate configurations in the class of blended wing-body geometries. This code has the ability to produce a wide variety of geometries in the given class with varying geometrical attributes. The flow solver employs a finite-volume formation and solves the explicit, Runge-Kutta integration technique. The method or flow simulation incorporates several techniques for acceleration of the convergence of the interaction process and an entropy corrected enthalpy damping procedure for efficient computation of high Mach number flows.
A computer program, ISOLEV, allows interactive visualization of CFD scalar and vector functions by means of user-specified sections of the data. The application is based on table lookups which govern both isosurface generation on hexahedral grid cells and recursive subdivision of the cells. The program supports Gouraud-shaded color maps of the data, surface-on-surface maps, and deformation surfaces of vector fields. The execution of the code for animated sweeps is improved by resorting to the cells in the database and maintaining an active set of cells to be rendered.
A solution-adaptive grid method has been developed for computing tip-vortex flowfields around rectangular wings. This method uses subdivision in order to locally refine the grid in regions with high vorticity. Two different flow solvers are used. Each solves the three-dimensional Euler equations on unstructured grids. Computed results are compared to experimentally measured surface pressures and vortex velocities on a NACA 0015 rectangular wing. Predicted results for surface pressures and integrated lift agree well with the experimental data. The predicted size of the rotational vortex core is larger than the experimentally-measured value and the peak velocities are less. This discrepancy appears to be caused by deficiencies in the inviscid Euler-equation model. This model cannot capture the complex viscous effects at the tip that determine the detailed structure of the resulting vortex. In spite of this limitation, the present Euler unstructured adaptive-grid method demonstrates the ability to convert vortical flows with low numerical diffusion. Applications for modeling helicopter rotor wake systems are discussed.
The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
Unstructured grids lead to unstructured communication on distributed memory parallel computers, a problem that has been considered difficult. Here, we consider adaptive, offline communication routing for a SIMD processor grid. Our approach is empirical. We use large data sets drawn from supercomputing applications instead of an analytic model of communication load. The chief contribution of this paper is an experimental demonstration of the effectiveness of certain routing heuristics. Our routing algorithm is adaptive, nonminimal, and is generally designed to exploit locality. We have a parallel implementation of the router, and we report on its performance.
In a variety of potential flow applications, the modal element method has been shown to significantly reduce the numerical grid, employ a more precise grid termination boundary condition, and give theoretical insight to the flow physics. The method employs eigenfunctions to replace the numerical grid over significant portions of the flow field. Generally, a numerical grid is employed around obstacles with complex geometry while eigenfunctions are applied to regions in the flow field where the boundary conditions can easily be satisfied. To handle a wider class of computational fluid dynamics (CFD) problems, the present paper extends the modal element to include function approximations which do not satisfy the governing differential equation. To accomplish this task, a double modal series approximation and weighted residual constraints are developed to force the comparison functions to satisfy the governing differential equation and to interface properly with the finite element solution. As an example, the method is applied to the problem of potential flow in a channel with two-dimensional cylindrical like obstacles. The calculated flow fields are in excellent agreement with exact analytical solutions.
A combined geometric approach for solving the Navier-Stokes equations is presented for the analysis of planar, unsteady flow about mechanisms with components in moderate relative motion. The approach emphasizes the relationships between the geometry model, grid, and flow model for the benefit of the total dynamics problem. One application is the analysis of the restart operation of a variable-geometry, high-speed inlet.
A combined geometric approach for computational fluid dynamics is presented for the analysis of unsteady flow about mechanisms in which its components are in moderate relative motion. For a CFD analysis, the total dynamics problem involves the dynamics of the aspects of geometry modeling, grid generation, and flow modeling. The interrelationships between these three aspects allow for a more natural formulation of the problem and the sharing of information which can be advantageous to the computation of the dynamics. The approach is applied to planar geometries with the use of an efficient multi-block, structured grid generation method to compute unsteady, two-dimensional and axisymmetric flow. The applications presented include the computation of the unsteady, inviscid flow about a hinged-flap with flap deflections and a high-speed inlet with centerbody motion as part of the unstart / restart operation.
The stretched-grid approach provides an efficient down-scaling and consistent interactions between global and regional scales due to using one variable-resolution model for integrations. It is a workable alternative to the widely used nested-grid approach introduced over a decade ago as a pioneering step in regional climate modeling. A variable-resolution General Circulation Model (GCM) employing a stretched grid, with enhanced resolution over the US as the area of interest, is used for simulating two anomalous regional climate events, the US summer drought of 1988 and flood of 1993. The special mode of integration using a stretched-grid GCM and data assimilation system is developed that allows for imitating the nested-grid framework. The mode is useful for inter-comparison purposes and for underlining the differences between these two approaches. The 1988 and 1993 integrations are performed for the two month period starting from mid May. Regional resolutions used in most of the experiments is 60 km. The major goal and the result of the study is obtaining the efficient down-scaling over the area of interest. The monthly mean prognostic regional fields for the stretched-grid integrations are remarkably close to those of the verifying analyses. Simulated precipitation patterns are successfully verified against gauge precipitation observations. The impact of finer 40 km regional resolution is investigated for the 1993 integration and an example of recovering subregional precipitation is presented. The obtained results show that the global variable-resolution stretched-grid approach is a viable candidate for regional and subregional climate studies and applications.
The development of and results obtained with a variable resolution stretched-grid GCM for the regional climate simulation mode, are presented. A global variable resolution stretched- grid used in the study has enhanced horizontal resolution over the U.S. as the area of interest The stretched-grid approach is an ideal tool for representing regional to global scale interaction& It is an alternative to the widely used nested grid approach introduced over a decade ago as a pioneering step in regional climate modeling. The major results of the study are presented for the successful stretched-grid GCM simulation of the anomalous climate event of the 1988 U.S. summer drought- The straightforward (with no updates) two month simulation is performed with 60 km regional resolution- The major drought fields, patterns and characteristics such as the time averaged 500 hPa heights precipitation and the low level jet over the drought area. appear to be close to the verifying analyses for the stretched-grid simulation- In other words, the stretched-grid GCM provides an efficient down-scaling over the area of interest with enhanced horizontal resolution. It is also shown that the GCM skill is sustained throughout the simulation extended to one year. The developed and tested in a simulation mode stretched-grid GCM is a viable tool for regional and subregional climate studies and applications.
The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.
Different aspects of advanced surface mount package technology have been investigated for aerospace applications. Three key areas included the assembly reliability of conventional Surface Mount, Ball Grid Arrays (BGAs), and Chip Scale Packages.
We have developed a technique that allows SIM to measure relative stellar positions with an accuracy of 1 micro-arcsecond at any time during its 5-yr mission. Unlike SIM's standard narrow-angle approach, Gridless Narrow Angle Astrometry (GNAA) does not rely on the global reference frame of grid stars that reaches full accuracy after 5 years. GNAA is simply the application of traditional single-telescope narrow angle techniques to SIM's narrow angle optical path delay measurements. In GNAA, a set of reference stars and a target star are observed at several baseline orientations. A linearized model uses delay measurements to solve for star positions and baseline orientations. A conformal transformation maps observations at different epochs to a common reference frame. The technique works on short period signals (P=days to months), allowing it to be applied to many of the known extra-solar planets, intriguing radio/X- ray binaries, and other periodic sources. The technique's accuracy is limited in the long-term by false acceleration due to a combination of reference star and target star proper motion. The science capability 1 micro-arcsecond astrometric precision - is unique to SIM.