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NASA NTRS1996

Numerical simulation of iodine speciation in relation to water disinfection aboard manned spacecraft I. Equilibria

Elemental iodine (I2) is currently used as the drinking water disinfectant aboard the Shuttle Orbiter and will also be incorporated into the water recovery and distribution system for the International Space Station Alpha. Controlled release of I2 is achieved using the Microbial Check Valve (MCV), a flow-through device containing an iodinated polymer which imparts a bacteriostatic residual concentration of approximately 2mg/L to the aqueous stream. During regeneration of MCV canisters, I2 concentrations of approximately 300 mg/L are used. Dissolved iodine undergoes a series of hydrolytic disproportionation and related reactions which result in the formation of an array of inorganic species including: I-, I3-, HOI, OI-, IO3-, HIO3, I2OH-, I2O(-2), and H2OI+. Numerical estimation of the steady-state distribution of inorganic iodine containing species in pure water at 25 degrees C has been achieved by simultaneous solution of the multiple equilibrium expressions as a function of pH. The results are reported herein.

NASA Discipline Environmental Health↗

NASA NTRS1979

Numerical solutions of the trans-relativistic shock relations

Using a slight modification of the Taub adiabat procedure, the paper solves the relativistic Rankine-Hugoniot (RH) relations for transrelativistic shocks in a nondegenerate Fermi gas. A parametric survey of numerical solutions of the RH relations is presented, making it possible to infer by interpolation from graphical displays the solutions to a variety of shocks. In addition, the transrelativistic nature of the solutions is explicit because when the upstream pressure is low, the shocks first approach those given by nonrelativistic strong shock theory and then approach the relativistic strong shock limit as the Mach number increases.

Fujimura, F. S.↗

NASA NTRS2007

Results from Binary Black Hole Simulations in Astrophysics Applications

Present and planned gravitational wave observatories are opening a new astronomical window to the sky. A key source of gravitational waves is the merger of two black holes. The Laser Interferometer Space Antenna (LISA), in particular, is expected to observe these events with signal-to-noise ratio's in the thousands. To fully reap the scientific benefits of these observations requires a detailed understanding, based on numerical simulations, of the predictions of General Relativity for the waveform signals. New techniques for simulating binary black hole mergers, introduced two years ago, have led to dramatic advances in applied numerical simulation work. Over the last two years, numerical relativity researchers have made tremendous strides in understanding the late stages of binary black hole mergers. Simulations have been applied to test much of the basic physics of binary black hole interactions, showing robust results for merger waveform predictions, and illuminating such phenomena as spin-precession. Calculations have shown that merging systems can be kicked at up to 2500 km/s by the thrust from asymmetric emission. Recently, long lasting simulations of ten or more orbits allow tests of post-Newtonian (PN) approximation results for radiation from the last orbits of the binary's inspiral. Already, analytic waveform models based PN techniques with incorporated information from numerical simulations may be adequate for observations with current ground based observatories. As new advances in simulations continue to rapidly improve our theoretical understanding of the systems, it seems certain that high-precision predictions will be available in time for LISA and other advanced ground-based instruments. Future gravitational wave observatories are expected to make precision.

Baker, John G.↗

NASA NTRS1992

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Yu, Sheng-Tao↗

NASA NTRS2001

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

NASA NTRS2002

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

NASA NTRS2004

Reliability of Complex Nonlinear Numerical Simulations

This work describes some of the procedure to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

NASA NTRS2005

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

Yee, H. C.↗

NASA NTRS1974

Evaluation of approximate relations for Delta /Q/ using a numerical solution of the Boltzmann equation

Data obtained from a numerical solution of the Boltzmann equation for shock-wave structure are used to test the accuracy of accepted approximate expressions for the two moments of the collision integral Delta (Q) for general intermolecular potentials in systems with a large translational nonequilibrium. The accuracy of the numerical scheme is established by comparison of the numerical results with exact expressions in the case of Maxwell molecules. They are then used in the case of hard-sphere molecules, which are the furthest-removed inverse power potential from the Maxwell molecule; and the accuracy of the approximate expressions in this domain is gauged. A number of approximate solutions are judged in this manner, and the general advantages of the numerical approach in itself are considered.

Nathenson, M.↗

NASA NTRS2006

Processing-Related Issues for the Design and Lifing of SiC/SiC Hot-Section Components

For successful SiC/SiC engine components, numerous process steps related to the fiber, fiber architecture, interphase coating, and matrix need to be optimized. Under recent NASA-sponsored programs, it was determined that many of these steps in their initial approach were inadequate, resulting in less than optimum thermostructural and life properties for the as-fabricated components. This presentation will briefly review many of these process issues, the key composite properties they degrade, their underlying mechanisms, and current process remedies developed by NASA and others.

DiCarlo, J.↗

NASA NTRS1977

The influence of the directional energy distribution on the nonlinear dispersion relation in a random gravity wave field

The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.

Huang, N. E.↗

NASA NTRS1988

On the dynamic estimation of relative weights for observation and forecast in numerical weather prediction

The problem of merging direct and remotely sensed (indirect) data with forecast data to get an estimate of the present state of the atmosphere for the purpose of numerical weather prediction is examined. To carry out this merging optimally, it is necessary to provide an estimate of the relative weights to be given to the observations and forecast. It is possible to do this dynamically from the information to be merged, if the correlation structure of the errors from the various sources is sufficiently different. Some new statistical approaches to doing this are described, and conditions quantified in which such estimates are likely to be good.

Wahba, Grace↗

NASA NTRS1976

A method for generating numerical pilot opinion ratings using the optimal pilot model

A method for generating numerical pilot opinion ratings using the optimal pilot model is introduced. The method is contained in a rating hypothesis which states that the numerical rating which a human pilot assigns to a specific vehicle and task can be directly related to the numerical value of the index of performance resulting from the optimal pilot modeling procedure as applied to that vehicle and task. The hypothesis is tested using the data from four piloted simulations. The results indicate that the hypothesis is reasonable, but that the predictive capability of the method is a strong function of the accuracy of the pilot model itself. This accuracy is, in turn, dependent upon the parameters which define the optimal modeling problem. A procedure for specifying the parameters for the optimal pilot model in the absence of experimental data is suggested.

Hess, R. A.↗

NASA NTRS1993

Effects of detailed droplet heating models on turbulent sprays vaporization behavior

The effects of three different droplet heating models on the vaporization history and internal structure of turbulent liquid fuel sprays were investigated. The models considered were the infinite-diffusion, diffusion-limit, and effective-conductivity models. A numerical solution for the models was developed and implemented in the KIVA-II computer code. Low temperature and relatively high temperature numerical studies were conducted. The low temperature computations were compared with existing experimental data. The comparisons showed that while the infinite-diffusion and diffusion-limit models respectively overpredicted and underpredicted the fuel vapor peak concentration and distribution in the combustor, the effective-conductivity model gave results that were in better agreement with measurements. A limited study for the high temperature case was performed due to lack of experimental data and predictions using the three models were compared with each other.

Mawid, M. A.↗

NASA NTRS1967

On the stability of numerical solutions of ordinary differential equations

Relative and absolute stability regions determined for numerical solutions of ordinary differential equations

STABILITY↗

NASA NTRS1988

Numerical Arc Segmentation Algorithm for a Radio Conference-NASARC (version 4.0) technical manual

The information contained in the NASARC (Version 4.0) Technical Manual and NASARC (Version 4.0) User's Manual relates to the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through November 1, 1988. The Technical Manual describes the NASARC concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions were incorporated in the Version 4.0 software over prior versions. These revisions have further enhanced the modeling capabilities of the NASARC procedure and provide improved arrangements of predetermined arcs within the geostationary orbits. Array dimensions within the software were structured to fit within the currently available 12 megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 4.0) allows worldwide planning problem scenarios to be accommodated within computer run time and memory constraints with enhanced likelihood and ease of solution.

Whyte, Wayne A., Jr.↗

NASA NTRS1987

The ion-ion acoustic instability

This paper considers the linear theory of ion-acoustic-like instabilities in a homogeneous Vlasov plasma with two ion components, a less dense beam and a more dense core, with a relative drift velocity. Numerical solutions of the full electrostatic dispersion equation are presented, and the properties of the ion-ion acoustic instability are studied in detail. At relatively cold beam temperatures, the instability is fluid-like, but it becomes a beam resonant kinetic instability as the beam temperature becomes of the order of the core temperature; if the mode is unstable, its threshold lies well below the threshold of the electron-ion acoustic instability. An electron temperature anisotropy enhances the instability, and at sufficiently large beam-core relative drift speeds, electron magnetization can either detract from or enhance the instability.

Gary, S. Peter↗

NASA NTRS1987

A linear MHD instability analysis of solar mass ejections with gravitation

The linear MHD instability of a cylindrical plasma is used to investigate the origin of solar mass ejections, and the dispersion relation is solved numerically. The initial plasma-flow velocity is found to have a significant effect on the instability criteria and growth rate, and the instability growth-rate is shown to be larger in cases where plasma flow exists, relative to the static case. Results suggest that the plasma column may break into small pieces. Assuming a thin-tube approximation, gravity is found to have little effect on the instability of quasi-horizontal ejection, but to have considerable effect on the vertical ejection. In considering the gravitational force, an exact analytical solution is found for the vertical case, while asymptotic solutions are given for the horizontal and oblique cases.

Song, M. T.↗