Approximate formulas for the computation of turbulent boundary-layer momentum thicknesses in compressible flows
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Tetervin, Neal↗
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Results for “approximate computing”
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An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow
The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.
Desmarais, R. N.↗
An accurate and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow
This paper describes an accurate economical method for generating approximations to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the non elementary integrals in the kernel by exponential approximations and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term approximations are tabulated in the report. Also, since the method is automated, it can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.
Desmarais, R. N.↗
Design and performance analysis of solid-propellant rocket motors using a simplified computer program
An analysis and a computer program are presented which represent a compromise between the more sophisticated programs using precise burning geometric relations and the textbook type of solutions. The program requires approximately 900 computer cards including a set of 20 input data cards required for a typical problem. The computer operating time for a single configuration is approximately 1 minute and 30 seconds on the IBM 360 computer. About l minute and l5 seconds of the time is compilation time so that additional configurations input at the same time require approximately 15 seconds each. The program uses approximately 11,000 words on the IBM 360. The program is written in FORTRAN 4 and is readily adaptable for use on a number of different computers: IBM 7044, IBM 7094, and Univac 1108.
Sforzini, R. H.↗
Computation of general planetary perturbations, part ii- a comparison of components
Improving convergence of successive approximations when computing perturbations in rectangular coordinates
PERTURBATION↗
On the Convergence of Numerical Computations for Both Exact and Approximate Solutions for Electromagnetic Scattering by Nonspherical Dielectric Particles
We summarize the size parameter range of the applicability of four lightscattering computational methods for nonspheric dielectric particles. These methods include two exact methods - the extended boundary condition method (EBCM) and the invariant imbedding T-matrix method (II-TM) and two approximate approaches - the physical-geometric optics method (PGOM) and the improved geometric optics method (IGOM). For spheroids, the single-scattering properties computed by EBCM and II-TM agree for size parameters up to 150, and the comparison gives us confidence in using IITM as a benchmark for size parameters up to 150 for other geometries (e.g., hexagonal columns) because the applicability of II-TM with respect to particle shape is generic, as demonstrated in our previous studies involving a complex aggregate. This study demonstrates the convergence of the exact II-TM and approximate PGOM solutions for the complete set of single-scattering properties of a nonspherical shape other than spheroids and circular cylinders with particle sizes of ~48λ, specifically a hexagonal column with a size parameter of length as kL=300, where k=2π/λ and L is the column length. IGOM is also quite accurate except near the exact 180º backscattering direction. This study demonstrates that a synergetic combination of the numerically-exact II-TM and the approximate PGOM can seamlessly cover the entire size parameter range of practical interest. To demonstrate the applicability of the approach, we compute the optical properties of dust particles with a downstream application to the retrieval of dust aerosol optical thickness and effective particle size from polarimetric observations.
Ping Yang↗
Towards Accurate Prediction of Turbulent, Three-Dimensional, Recirculating Flows with the NCC
The National Combustion Code (NCC) was used to calculate the steady state, nonreacting flow field of a prototype Lean Direct Injection (LDI) swirler. This configuration used nine groups of eight holes drilled at a thirty-five degree angle to induce swirl. These nine groups created swirl in the same direction, or a corotating pattern. The static pressure drop across the holes was fixed at approximately four percent. Computations were performed on one quarter of the geometry, because the geometry is considered rotationally periodic every ninety degrees. The final computational grid used was approximately 2.26 million tetrahedral cells, and a cubic nonlinear k - epsilon model was used to model turbulence. The NCC results were then compared to time averaged Laser Doppler Velocimetry (LDV) data. The LDV measurements were performed on the full geometry, but four ninths of the geometry was measured. One-, two-, and three-dimensional representations of both flow fields are presented. The NCC computations compare both qualitatively and quantitatively well to the LDV data, but differences exist downstream. The comparison is encouraging, and shows that NCC can be used for future injector design studies. To improve the flow prediction accuracy of turbulent, three-dimensional, recirculating flow fields with the NCC, recommendations are given.
Iannetti, A.↗
Programs For Modeling Fault-Tolerant Computing Systems
Pade Approximation with Scaling, (PAWS) and Scaling Taylor Exponential Matrix (STEM) computer programs are software tools for design and validation. Provide flexible, user-friendly, language-based interface for input of Markov mathematical methods describing behaviors of fault-tolerant computer systems. Markov models include both recovery from faults via reconfiguration and behaviors of such systems when faults occur. PAWS and STEM produce exact solutions of probability of system failure and provide conservative estimate of number of significant digits in solution. Written in PASCAL and FORTRAN.
Butler, Ricky W.↗
Wave refraction diagrams for the Baltimore Canyon region of the mid-Atlantic continental shelf computed by using three bottom topography approximation techniques
The Langley Research Center and Virginia Institute of Marine Science wave refraction computer model was applied to the Baltimore Canyon region of the mid-Atlantic continental shelf. Wave refraction diagrams for a wide range of normally expected wave periods and directions were computed by using three bottom topography approximation techniques: quadratic least squares, cubic least squares, and constrained bicubic interpolation. Mathematical or physical interpretation of certain features appearing in the computed diagrams is discussed.
Poole, L. R.↗
Reducing Drift In Computation Of Spacecraft Attitude
Error in approximation less than computer truncation error. Report discusses scheme for reduction of computational drift in estimation of attitude of spacecraft from strapdown-gyroscope measurements.
Huang, Whittak H.↗
Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. I: Approach Based on the Far-Field Foldy Equations
In this paper, we revisit, with further enhancements and clarifications, the self-consistent first-principles approach developed previously for deriving the vector radiative transfer theory for a discrete random medium with a sparse concentration of particles. We specifically consider the case of a plane-parallel particulate layer embedded in an otherwise homogeneous unbounded medium. The solution method is based on the far-field Foldy equations, an order-of-scattering expansion for the total field derived under the Twersky approximation, the computation of the coherent field by assuming that the positions of the particles are uncorrelated, and the ladder approximation for the coherency dyadic. The latter yields an integral equation for the diffuse specific coherency dyadic, defined through an angular spectrum repre- sentation for the coherency dyadic, which in turn, gives the vector radiative transfer equation for the diffuse specific intensity column vector. We analyze specifically the computation of the coherent field for inhomogeneous particulate media and multiple species of particles, the continuous extension of the far-field representation to the near field, the Foldy approximation, and the Foldy integral equation for the coherent field. Finally, we discuss the transition from the vector to the scalar radiative transfer equation.
Doicu, Adrian↗
A simple formulation of oxygen absorption at centimeter wavelengths
Carefully performed experiments by a number of investigators have supported the Van Vleck line shape theory for oxygen absorption in the lower-frequency wing (0-50 GHz). In view of the frequent need to compute oxygen absorption at centimeter wavelengths and lower a computationally simple four-line absorption model based on the Van Vleck theory is offered. The approximation yields computational accuracy better than 1% over the entire range of atmospheric pressures and temperatures for frequencies less than 30 GHz when it is compared with the Van Vleck 45-line expression. The versatility of the model in adapting to various line-broadening expressions is also shown. Instead of refining the present theories, this communication is mainly intended to propose a more convenient formulation to compute oxygen absorption.
Claassen, J. P.↗
Computer program describing turbine aerodynamic requirements, approximate external blade geometries, and coolant flow requirements for a two stage axial flow turbine
Computer program to generate turbine aerodynamic requirements, approximate external blade geometries, and coolant flow requirements for two stage axial flow turbine
Evans, D. G.↗
Study of the mapping of Navier-Stokes algorithms onto multiple-instruction/multiple-data-stream computers
Implicit approximate-factored algorithms have certain properties that are suitable for parallel processing. A particular computational fluid dynamics (CFD) code, using this algorithm, is mapped onto a multiple-instruction/multiple-data-stream (MIMD) computer architecture. An explanation of this mapping procedure is presented, as well as some of the difficulties encountered when trying to run the code concurrently. Timing results are given for runs on the Ames Research Center's MIMD test facility which consists of two VAX 11/780's with a common MA780 multi-ported memory. Speedups exceeding 1.9 for characteristic CFD runs were indicated by the timing results.
Eberhardt, D. S.↗
Metamodels for Computer-Based Engineering Design: Survey and Recommendations
The use of statistical techniques to build approximations of expensive computer analysis codes pervades much of todays engineering design. These statistical approximations, or metamodels, are used to replace the actual expensive computer analyses, facilitating multidisciplinary, multiobjective optimization and concept exploration. In this paper we review several of these techniques including design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning, and kriging. We survey their existing application in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of statistical approximation techniques in given situations and how common pitfalls can be avoided.
Simpson, Timothy W.↗
Catalytic ignition model in a monolithic reactor with in-depth reaction
Two transient models have been developed to study the catalytic ignition in a monolithic catalytic reactor. The special feature in these models is the inclusion of thermal and species structures in the porous catalytic layer. There are many time scales involved in the catalytic ignition problem, and these two models are developed with different time scales. In the full transient model, the equations are non-dimensionalized by the shortest time scale (mass diffusion across the catalytic layer). It is therefore accurate but is computationally costly. In the energy-integral model, only the slowest process (solid heat-up) is taken as nonsteady. It is approximate but computationally efficient. In the computations performed, the catalyst is platinum and the reactants are rich mixtures of hydrogen and oxygen. One-step global chemical reaction rates are used for both gas-phase homogeneous reaction and catalytic heterogeneous reaction. The computed results reveal the transient ignition processes in detail, including the structure variation with time in the reactive catalytic layer. An ignition map using reactor length and catalyst loading is constructed. The comparison of computed results between the two transient models verifies the applicability of the energy-integral model when the time is greater than the second largest time scale of the system. It also suggests that a proper combined use of the two models can catch all the transient phenomena while minimizing the computational cost.
Tien, Ta-Ching↗
Experimental and computational flow-field results for an all-body hypersonic aircraft
A comprehensive test program is defined which is being implemented in the NASA/Ames 3.5 foot Hypersonic Wind Tunnel for obtaining data on a generic all-body hypersonic vehicle for computational fluid dynamics (CFD) code validation. Computational methods (approximate inviscid methods and an upwind parabolized Navier-Stokes code) currently being applied to the all-body model are outlined. Experimental and computational results on surface pressure distributions and Pitot-pressure surveys for the basic sharp-nose model (without control surfaces) at a free-stream Mach number of 7 are presented.
Cleary, Joseph W.↗
Statistical linearization for multi-input/multi-output nonlinearities
Formulas are derived for the computation of the random input-describing functions for MIMO nonlinearities; these straightforward and rigorous derivations are based on the optimal mean square linear approximation. The computations involve evaluations of multiple integrals. It is shown that, for certain classes of nonlinearities, multiple-integral evaluations are obviated and the computations are significantly simplified.
Lin, Ching-An↗