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An attempt is made to generalize results for arbitrary multidimensional difference schemes. Severe obstacles are encountered, however, for dissipative difference schemes the problem may be resolved.
Alternatives to Gaussian integration methods for multidimensional regions are presented. These rules preserve the convergence behavior of the exact integrated element but require fewer evaluation points than the Gauss methods. Numerical examples are given to verify the behavior of the new integration rules.
An approach to solution adaptive grid generation for use with finite difference techniques, previously demonstrated on model problems in one space dimension, has been extended to multidimensional problems. The method is based on the popular elliptic steady grid generators, but is 'dynamically' adaptive in the sense that a grid is maintained at all times satisfying the steady grid law driven by a solution-dependent source term. Testing has been carried out on Burgers' equation in one and two space dimensions. Results appear encouraging both for inviscid wave propagation cases and viscous boundary layer cases, suggesting that application to practical flow problems is now possible. In the course of the work, obstacles relating to grid correction, smoothing of the solution, and elliptic equation solvers have been largely overcome. Concern remains, however, about grid skewness, boundary layer resolution and the need for implicit integration methods. Also, the method in 3-D is expected to be very demanding of computer resources.
A full implicit continuous Eulerian (FICE) scheme is developed for solving multidimensional transient MHD flow problems. The physical system under consideration is a general case of a transient MHD flow in which an initial steady state is subject to a finite amplitude disturbance. The governing equations are described, their finite difference formulation is presented and the FICE algorithm is given. The boundary conditions are treated by classifying them into physical and computational ones. The usefulness of the FICE algorithm is demonstrated using a physical example concerning the dynamical response of the static solar atmosphere due to a representative photospheric disturbance.
A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.
A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.
Before an optimum layout of the facilities for the proposed Space Station can be designed, it is necessary to understand the functions that will be performed by the Space Station crew and the relationships among those functions. Five criteria for assessing functional relationships were identified. For each of these criteria, a matrix representing the degree of association of all pairs of functions was developed. The key to making inferences about the layout of the Space Station from these matrices was the use of multidimensional scaling (MDS). Applying MDS to these matrices resulted in spatial configurations of the crew functions in which smaller distances in the MDS configuration reflected closer associations. An MDS analysis of a composite matrix formed by combining the five individual matrices resulted in two dimensions that describe the configuration: a 'private-public' dimension and a 'group-individual' dimension. Seven specific recommendations for Space Station layout were derived from analyses of the MDS configurations. Although these techniques have been applied to the design of the Space Station, they can be applied to the design of any facility where people live or work.
The Space Shuttle Main Engine (SSME) consists of a large number of critical components each serving a special purpose. Any design change in one of these components not only alters its performance but also the performance of the ones in the upstream and in the downstream. To evaluate the effects of such a design change on the flow fields and on SSME's overall performance a multidomain and multidimensional analytical procedure has been developed and applied here to the series of components on the fuel side of the SSME. The results obtained from the multidomain analysis and their comparison with the single-domain solution when the SSME is operating at Full Power Load indicates that the multidomain model shows greater realism. It is concluded that this modeling technique would assist the designer significantly to achieve still higher performance levels of the SSME.
The rotordynamic behavior of turbomachinery is critically dependent on fluid dynamic rotor forces developed by various types of seals and bearings. The occurrence of self-excited vibrations often depends on the rotor speed and load. Misalignment and rotor wobbling motion associated with differential clearance were often attributed to stability problems. In general, the rotative character of the flowfield is a complex three dimensional system with secondary flow patterns that significantly alter the average fluid circumferential velocity. A multidimensional, nonorthogonal, body-fitted-grid fluid flow model is presented that describes the fluid dynamic forces and the secondary flow pattern development in seals and bearings. Several numerical experiments were carried out to demonstrate the characteristics of this complex flowfield. Analyses were performed by solving a conservation form of the three dimensional Navier-Stokes equations transformed to those for a rotating observer and using the general-purpose computer code PHOENICS with the assumptions that the rotor orbit is circular and that static eccentricity is zero. These assumptions have enabled a precise steady-state analysis to be used. Fluid injection from ports near the seal or bearing center increased fluid-film direct dynamic stiffness and, in some cases, significantly increased quadrature dynamic stiffness. Injection angle and velocity could be used for active rotordynamic control; for example, injection, when compared with no injection, increased direct dynamic stiffness, which is an important factor for hydrostatic bearings.
A new, nonoscillatory upwind scheme is developed for the multidimensional convection equation. The scheme consists of an upwind, nonoscillatory interpolation of data to the surfaces of an intermediate finite volume; a characteristic convection of surface data to a midpoint time level; and a conservative time integration based on the midpoint rule. This procedure results in a convection scheme capable of resolving discontinuities neither aligned with, nor convected along, grid lines.
A new, nonoscillatory upwind scheme is developed for the multidimensional convection equation. The scheme consists of an upwind, nonoscillatory interpolation of data to the surfaces of an intermediate finite volume; a characteristic convection of surface data to a midpoint time level; and a conservative time integration based on the midpoint rule. This procedure results in a convection scheme capable of resolving discontinuities neither aligned with, nor convected along, grid lines.
A fundamentally multidimensional convection scheme is described based on vector transient interpolation modeling rewritten in conservative control-volume form. Vector third-order upwinding is used as the basis of the algorithm; this automatically introduces important cross-difference terms that are absent from schemes using component-wise one-dimensional formulas. Third-order phase accuracy is good; this is important for coarse-grid large-eddy or full simulation. Potential overshoots or undershoots are avoided by using a recently developed universal limiter. Higher order accuracy is obtained locally, where needed, by the cost-effective strategy of adaptive stencil expansion in a direction normal to each control-volume face; this is controlled by monitoring the absolute normal gradient and curvature across the face. Higher (than third) order cross-terms do not appear to be needed. Since the wider stencil is used only in isolated narrow regions (near discontinuities), extremely high (in this case, seventh) order accuracy can be achieved for little more than the cost of a globally third-order scheme.
When a computer monitors a physical process, the computer uses sensors to determine the values of the physical variables that represent the state of the process. A sensor can sometimes fail, however, and in the worst case report a value completely unrelated to the true physical value. The work described is motivated by a methodology for transforming a process control program that can not tolerate sensor failure into one that can. In this methodology, a reliable abstract sensor is created by combining information from several real sensors that measure the same physical value. To be useful, an abstract sensor must deliver reasonably accurate information at reasonable computational cost. Sensors are considered that deliver multidimensional values (e.g., location or velocity in three dimensions, or both temperature and pressure). Geometric techniques are used to derive upper bounds on abstract sensor accuracy and to develop efficient algorithms for implementing abstract sensors.
Critical to the understanding of data is the ability to provide pictorial or visual representation of those data, particularly in support of correlative data analysis. Despite the advancement of visualization techniques for scientific data over the last several years, there are still significant problems in bringing today's hardware and software technology into the hands of the typical scientist. For example, there are other computer science domains outside of computer graphics that are required to make visualization effective such as data management. Well-defined, flexible mechanisms for data access and management must be combined with rendering algorithms, data transformation, etc. to form a generic visualization pipeline. A generalized approach to data visualization is critical for the correlative analysis of distinct, complex, multidimensional data sets in the space and Earth sciences. Different classes of data representation techniques must be used within such a framework, which can range from simple, static two- and three-dimensional line plots to animation, surface rendering, and volumetric imaging. Static examples of actual data analyses will illustrate the importance of an effective pipeline in data visualization system.
Progress made in the development of a genuinely multidimensional finite volume algorithm for problems in inviscid gas dynamics is presented. The approach entails: (1) the reconstruction of flowfield data using a planar wave pattern in which the strengths and orientations of the component waves are derived independently of the mesh geometry; and (2) the development of a flux formula which provides a numerical approximation to the flux at a finite volume cell face during the passage of waves which are in general oblique to the face. Several algorithms are outlined, and the most recent developments are included. The results of several numerical cases are also included.
Cobalt samples were analyzed for cosmic ray induced Co-60 with both an ultralow background germanium gamma ray spectrometer and with a large NaI(T1) multidimensional spectrometer using electronic anticoincidence shielding. Aluminum samples were analyzed for Na-22. The results are presented along with the relative sensitivities and precision afforded by the two methods.
Recent progress made in the development of a genuinely multidimensional finite-volume method for the Euler equations is reported. In this method, wave information is derived from a reconstruction procedure applied to the data on a triangle. The algorithm is therefore best suited to application on an unstructured grid. A flux formula which provides nearly-monotone solutions is also presented. The new method is tested on three simple 2D flows, and the results show that dominant-wave resolution is high, and that strong-wave transitions are nearly monotone.
Two reports describe elements of theory of multidimensional complex variables, with emphasis on three dimensions. First report introduces general theory. Second, presents further developments in theory of analytic functions of single three-dimensional variable and applies theory to representation of ideal flows. Results of preliminary studies suggest analytic functions of new three-dimensional complex variables useful in numerous applications, including representing of three-dimensional flows and potentials.