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NASA NTRS1987

On similarity solutions of a boundary layer problem with an upstream moving wall

The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.

Hussaini, M. Y.↗

NASA NTRS1987

Cellular automatons applied to gas dynamic problems

This paper compares the results of a relatively new computational fluid dynamics method, cellular automatons, with experimental data and analytical results. This technique has been shown to qualitatively predict fluidlike behavior; however, there have been few published comparisons with experiment or other theories. Comparisons are made for a one-dimensional supersonic piston problem, Stokes first problem, and the flow past a normal flat plate. These comparisons are used to assess the ability of the method to accurately model fluid dynamic behavior and to point out its limitations. Reasonable results were obtained for all three test cases, but the fundamental limitations of cellular automatons are numerous. It may be misleading, at this time, to say that cellular automatons are a computationally efficient technique. Other methods, based on continuum or kinetic theory, would also be very efficient if as little of the physics were included.

Long, Lyle N.↗

NASA NTRS1987

An adaptive pseudo-spectral method for reaction diffusion problems

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

Bayliss, A.↗

NASA NTRS1986

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Warming, Robert F.↗

NASA NTRS1987

A general solution to the silhouette problem

In displaying computer-generated graphics, it is advantageous to have the facility to render any subset of polygons as a silhouette with respect to itself. While the silhouette problem has been addressed before, there has been no completely general solution. In this report, the silhouette problem for calligraphic drawings is solved for the most general case. This solution offers all possible combinations of silhouette and non-silhouette specifications for an arbitrary solid. It allows the flexibility to enhance the clarity of any three-dimensional scene presented in two dimensions.

Hedgley, David R., Jr.↗

NASA NTRS1987

Development of a coupled expert system for the spacecraft attitude control problem

A majority of the current expert systems focus on the symbolic-oriented logic and inference mechanisms of artificial intelligence (AI). Common rule-based systems employ empirical associations and are not well suited to deal with problems often arising in engineering. Described is a prototype expert system which combines both symbolic and numeric computing. The expert system's configuration is presented and its application to a spacecraft attitude control problem is discussed.

Kawamura, K.↗

NASA NTRS1988

A unified framework for approximation in inverse problems for distributed parameter systems

A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results.

Banks, H. T.↗

NASA NTRS1988

Accurate boundary conditions for exterior problems in gas dynamics

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Hagstrom, Thomas↗

NASA NTRS1988

The design of aircraft using the decision support problem technique

The Decision Support Problem Technique for unified design, manufacturing and maintenance is being developed at the Systems Design Laboratory at the University of Houston. This involves the development of a domain-independent method (and the associated software) that can be used to process domain-dependent information and thereby provide support for human judgment. In a computer assisted environment, this support is provided in the form of optimal solutions to Decision Support Problems.

Mistree, Farrokh↗

NASA NTRS1987

Measurement from satellites of land surface parameters and fluxes in the thermal infrared bands: Problems and methods

The main problems arising in the elaboration of accurate and reliable algorithms for extracting land surface parameters and flux from their measured radiances are discussed. Methods of solution in the thermal infrared spectral domain are described. Particular interest is given to the inversion of thermal models and to the problems resulting from the heterogeneity of the observed surfaces.

Becker, F.↗

NASA NTRS1988

Boundary shape identification problems in two-dimensional domains related to thermal testing of materials

The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is reported. The domain identification problem treated here is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Results of numerical experiments to demonstrate the efficacy of the theoretical ideas are reported.

Banks, H. T.↗

NASA NTRS1987

Exact image theory for the problem of dielectric/magnetic slab

Exact image method, recently introduced for the exact solution of electromagnetic field problems involving homogeneous half spaces and microstrip-like geometries, is developed for the problem of homogeneous slab of dielectric and/or magnetic material in free space. Expressions for image sources, creating the exact reflected and transmitted fields, are given and their numerical evaluation is demonstrated. Nonradiating modes, guided by the slab and responsible for the loss of convergence of the image functions, are considered and extracted. The theory allows, for example, an analysis of finite ground planes in microstrip antenna structures.

Lindell, I. V.↗

NASA NTRS1988

Solving time-dependent two-dimensional eddy current problems

Results of transient eddy current calculations are reported. For simplicity, a two-dimensional transverse magnetic field which is incident on an infinitely long conductor is considered. The conductor is assumed to be a good but not perfect conductor. The resulting problem is an interface initial boundary value problem with the boundary of the conductor being the interface. A finite difference method is used to march the solution explicitly in time. The method is shown. Treatment of appropriate radiation conditions is given special consideration. Results are validated with approximate analytic solutions. Two stringent test cases of high and low frequency incident waves are considered to validate the results.

Lee, Min Eig↗

NASA NTRS1988

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

Banks, H. T.↗

NASA NTRS1988

Computational methods for the problems of the tip vortex

The tip vortex problem for helicopter rotors in transonic flow was studied. The first model was that of potential flow past a single blade in parallel transonic flow. The incidence on the wing of a vortex sheet trailing from a blade in front was studied by modeling the incident sheet by a single vortex filament. A 3-D potential flow code was written to incorporate the usual boundary conditions at infinity together with the model of such a vortex filament and to analyze the resulting flow over the wing. The code was used to study the effect of the vortex filament on the production of shocks at the tip of the wing. Another problem studied within the framework of potential flow theory was the rollup of the vortex sheet behind the wing. A comparison was made of flow models described by the potential equation, by the Euler equations for steady flow, and by the Navier-Stokes equations. The question was also studied as to whether there is an advantage in solving the Navier-Stokes equations rather than the Euler equations for steady flow.

Garabedian, Paul R.↗

NASA NTRS1988

Hybrid transfinite element modeling/analysis of nonlinear heat conduction problems involving phase change

The present paper describes the applicability of hybrid transfinite element modeling/analysis formulations for nonlinear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modeling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modeled using enthalpy formulations to enable a physically realistic approximation to be dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modeling/analysis of nonlinear heat conduction problems involving phase change.

Tamma, Kumar K.↗

NASA NTRS1987

A fixed grid numerical methodology for phase change problems involving a moving heat source

A numerical method for solving phase change problems involving a moving heat source is presented and illustrated by a two-dimensional example. The method uses a fixed grid and does not require the implementation of the Stefan condition at the solid-liquid interface; the procedure can thus be easily implemented using existing fixed grid codes. The problem considered as an example involves natural convection flow in the molten metal during tungsten inert gas welding.

Prakash, C.↗

NASA NTRS1987

On the reliable and flexible solution of practical subset regression problems

A new algorithm for solving subset regression problems is described. The algorithm performs a QR decomposition with a new column-pivoting strategy, which permits subset selection directly from the originally defined regression parameters. This, in combination with a number of extensions of the new technique, makes the method a very flexible tool for analyzing subset regression problems in which the parameters have a physical meaning.

Verhaegen, M.↗