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NASA NTRS1995

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1994

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1995

Nonlinear Control and Discrete Event Systems

As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.

Meyer, George↗
NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Bart, Timothy J.↗
NASA NTRS1995

Remote Visualization and Remote Collaboration On Computational Fluid Dynamics

A new technology has been developed for remote visualization that provides remote, 3D, high resolution, dynamic, interactive viewing of scientific data (such as fluid dynamics simulations or measurements). Based on this technology, some World Wide Web sites on the Internet are providing fluid dynamics data for educational or testing purposes. This technology is also being used for remote collaboration in joint university, industry, and NASA projects in computational fluid dynamics and wind tunnel testing. Previously, remote visualization of dynamic data was done using video format (transmitting pixel information) such as video conferencing or MPEG movies on the Internet. The concept for this new technology is to send the raw data (e.g., grids, vectors, and scalars) along with viewing scripts over the Internet and have the pixels generated by a visualization tool running on the viewer's local workstation. The visualization tool that is currently used is FAST (Flow Analysis Software Toolkit).

Watson, Val↗
NASA NTRS1995

Bringing "Scientific Expeditions" Into the Schools

Two new technologies, the FASTexpedition and Remote FAST, have been developed that provide remote, 3D, high resolution, dynamic, interactive viewing of scientific data (such as simulations or measurements of fluid dynamics). The FASTexpedition permits one to access scientific data from the World Wide Web, take guided expeditions through the data, and continue with self controlled expeditions through the data. Remote FAST permits collaborators at remote sites to simultaneously view an analysis of scientific data being controlled by one of the collaborators. Control can be transferred between sites. These technologies are now being used for remote collaboration in joint university, industry, and NASA projects in computational fluid dynamics (CFD) and wind tunnel testing. Also, NASA Ames Research Center has initiated a project to make scientific data and guided expeditions through the data available as FASTexpeditions on the World Wide Web for educational purposes. Previously, remote visualiZation of dynamic data was done using video format (transmitting pixel information) such as video conferencing or MPEG movies on the Internet. The concept for this new technology is to send the raw data (e.g., grids, vectors, and scalars) along with viewing scripts over the Internet and have the pixels generated by a visualization tool running on the viewer's local workstation. The visualization tool that is currently used is FAST (Flow Analysis Software Toolkit). The advantages of this new technology over using video format are: 1. The visual is much higher in resolution (1280xl024 pixels with 24 bits of color) than typical video format transmitted over the network. 2. The form of the visualization can be controlled interactively (because the viewer is interactively controlling the visualization tool running on his workstation). 3. A rich variety of guided expeditions through the data can be included easily. 4. A capability is provided for other sites to see a visual analysis of one site as the analysis is interactively performed. Control of the analysis can be passed from site to site. 5. The scenes can be viewed in 3D using stereo vision. 6. The network bandwidth used for the visualization using this new technology is much smaller than when using video format. (The measured peak bandwidth used was 1 Kbit/sec whereas the measured bandwidth for a small video picture was 500 Kbits/sec.)

Watson, Val↗
NASA NTRS1996

Fast 3D Net Expeditions: Tools for Effective Scientific Collaboration on the World Wide Web

Two new technologies, the FASTexpedition and Remote FAST, have been developed that provide remote, 3D (three dimensional), high resolution, dynamic, interactive viewing of scientific data. The FASTexpedition permits one to access scientific data from the World Wide Web, take guided expeditions through the data, and continue with self controlled expeditions through the data. Remote FAST permits collaborators at remote sites to simultaneously view an analysis of scientific data being controlled by one of the collaborators. Control can be transferred between sites. These technologies are now being used for remote collaboration in joint university, industry, and NASA projects. Also, NASA Ames Research Center has initiated a project to make scientific data and guided expeditions through the data available as FASTexpeditions on the World Wide Web for educational purposes. Previously, remote visualization of dynamic data was done using video format (transmitting pixel information) such as video conferencing or MPEG (Motion Picture Expert Group) movies on the Internet. The concept for this new technology is to send the raw data (e.g., grids, vectors, and scalars) along with viewing scripts over the Internet and have the pixels generated by a visualization tool running on the viewers local workstation. The visualization tool that is currently used is FAST (Flow Analysis Software Toolkit). The advantages of this new technology over using video format are: (1) The visual is much higher in resolution (1280x1024 pixels with 24 bits of color) than typical video format transmitted over the network. (2) The form of the visualization can be controlled interactively (because the viewer is interactively controlling the visualization tool running on his workstation). (3) A rich variety of guided expeditions through the data can be included easily. (4) A capability is provided for other sites to see a visual analysis of one site as the analysis is interactively performed. Control of the analysis can be passed from site to site. (5) The scenes can be viewed in 3D using stereo vision. (6) The network bandwidth for the visualization using this new technology is much smaller than when using video format. (The measured peak bandwidth used was 1 Kbit/sec whereas the measured bandwidth for a small video picture was 500 Kbits/sec.) This talk will illustrate the use of these new technologies and present a proposal for using these technologies to improve science education.

Watson, Val↗
NASA NTRS2002

Multi-dimensional Upwind Fluctuation Splitting Scheme with Mesh Adaption for Hypersonic Viscous Flow

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably, the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local, compact, anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.

Wood, William A., III↗
NASA NTRS2001

Overview of the NCC

A multi-disciplinary design/analysis tool for combustion systems is critical for optimizing the low-emission, high-performance combustor design process. Based on discussions between then NASA Lewis Research Center and the jet engine companies, an industry-government team was formed in early 1995 to develop the National Combustion Code (NCC), which is an integrated system of computer codes for the design and analysis of combustion systems. NCC has advanced features that address the need to meet designer's requirements such as "assured accuracy", "fast turnaround", and "acceptable cost". The NCC development team is comprised of Allison Engine Company (Allison), CFD Research Corporation (CFDRC), GE Aircraft Engines (GEAE), NASA Glenn Research Center (LeRC), and Pratt & Whitney (P&W). The "unstructured mesh" capability and "parallel computing" are fundamental features of NCC from its inception. The NCC system is composed of a set of "elements" which includes grid generator, main flow solver, turbulence module, turbulence and chemistry interaction module, chemistry module, spray module, radiation heat transfer module, data visualization module, and a post-processor for evaluating engine performance parameters. Each element may have contributions from several team members. Such a multi-source multi-element system needs to be integrated in a way that facilitates inter-module data communication, flexibility in module selection, and ease of integration. The development of the NCC beta version was essentially completed in June 1998. Technical details of the NCC elements are given in the Reference List. Elements such as the baseline flow solver, turbulence module, and the chemistry module, have been extensively validated; and their parallel performance on large-scale parallel systems has been evaluated and optimized. However the scalar PDF module and the Spray module, as well as their coupling with the baseline flow solver, were developed in a small-scale distributed computing environment. As a result, the validation of the NCC beta version as a whole was quite limited. Current effort has been focused on the validation of the integrated code and the evaluation/optimization of its overall performance on large-scale parallel systems.

Liu, Nan-Suey↗
NASA NTRS1997

A DSMC Study of Low Pressure Argon Discharge

Work toward a self-consistent plasma simulation using the DSMC (Direct Simulation Monte Carlo) method for examination of the flowfields of low-pressure high density plasma reactors is presented. Presently, DSMC simulations for these applications involve either treating the electrons as a fluid or imposing experimentally determined values for the electron number density profile. In either approach, the electrons themselves are not physically simulated. Self-consistent plasma DSMC simulations have been conducted for aerospace applications but at a severe computational cost due in part to the scalar architectures on which the codes were employed. The present work attempts to conduct such simulations at a more reasonable cost using a plasma version of the object-oriented parallel Cornell DSMC code, MONACO, on an IBM SP-2. Due to availability of experimental data, the GEC reference cell is chosen to conduct preliminary investigations. An argon discharge is chosen to conduct preliminary investigations. An argon discharge is examined thus affording a simple chemistry set with eight gas-phase reactions and five species: Ar, Ar(+), Ar(*), Ar(sub 2), and e where Ar(*) is a metastable.

Hash, David B.↗
NASA NTRS2002

The Statistical Mechanics of Ideal Homogeneous Turbulence

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

Shebalin, John V.↗
NASA NTRS1998

Atomization Energies of SO and SO2; Basis Set Extrapolation Revisted

The addition of tight functions to sulphur and extrapolation to the complete basis set limit are required to obtain accurate atomization energies. Six different extrapolation procedures are tried. The best atomization energies come from the series of basis sets that yield the most consistent results for all extrapolation techniques. In the variable alpha approach, alpha values larger than 4.5 or smaller than 3, appear to suggest that the extrapolation may not be reliable. It does not appear possible to determine a reliable basis set series using only the triple and quadruple zeta based sets. The scalar relativistic effects reduce the atomization of SO and SO2 by 0.34 and 0.81 kcal/mol, respectively, and clearly must be accounted for if a highly accurate atomization energy is to be computed. The magnitude of the core-valence (CV) contribution to the atomization is affected by missing diffuse valence functions. The CV contribution is much more stable if basis set superposition errors are accounted for. A similar study of SF, SF(+), and SF6 shows that the best family of basis sets varies with the nature of the S bonding.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1998

Direct Volume Rendering of Curvilinear Volumes

Direct volume rendering can visualize sampled 3D scalar data as a continuous medium, or extract features. However, it is generally slow. Furthermore, most algorithms for direct volume rendering have assumed rectilinear gridded data. This paper discusses methods for using direct volume rendering when the original volume is curvilinear, i.e. is divided into six-sided cells which are not necessarily equilateral hexahedra. One approach is to ray-cast such volumes directly. An alternative approach is to interpolate the sample volumes to a rectilinear grid, and use this regular volume for rendering. Advantages and disadvantages of the two approaches in terms of speed and image quality are explored.

Vaziri, Arsi↗
NASA NTRS2001

Precision Measurement of Large Scale Structure

The purpose of this grant was to develop and to start to apply new precision methods for measuring the power spectrum and redshift distortions from the anticipated new generation of large redshift surveys. A highlight of work completed during the award period was the application of the new methods developed by the PI to measure the real space power spectrum and redshift distortions of the IRAS PSCz survey, published in January 2000. New features of the measurement include: (1) measurement of power over an unprecedentedly broad range of scales, 4.5 decades in wavenumber, from 0.01 to 300 h/Mpc; (2) at linear scales, not one but three power spectra are measured, the galaxy-galaxy, galaxy-velocity, and velocity-velocity power spectra; (3) at linear scales each of the three power spectra is decorrelated within itself, and disentangled from the other two power spectra (the situation is analogous to disentangling scalar and tensor modes in the Cosmic Microwave Background); and (4) at nonlinear scales the measurement extracts not only the real space power spectrum, but also the full line-of-sight pairwise velocity distribution in redshift space.

Hamilton, A. J. S.↗
NASA NTRS1998

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗
NASA NTRS2002

System and Method for Measuring the Transfer Function of a Guided Wave Device

A method/system are provided for measuring the NxN scalar transfer function elements for an N-port guided wave device. Optical energy of a selected wavelength is generated at a source and directed along N reference optical paths having N reference path lengths. Each reference optical path terminates in one of N detectors such that N reference signals are produced at the N detectors. The reference signals are indicative of amplitude, phase and frequency of the optical energy carried along the N reference optical paths. The optical energy from the source is also directed to the N-ports of the guided wave device and then on to each of the N detectors such that N measurement optical paths are defined between the source and each of the N detectors. A portion of the optical energy is modified in terms of at least one of the amplitude and phase to produce N modified signals at each of the N detectors. At each of the N detectors, each of the N modified signals is combined with a corresponding one of the N reference signals to produce corresponding N combined signals at each of the N detectors. A total of N(sup 2) measurement signals are generated by the N detectors. Each of the N(sup 2) measurement signals is sampled at a wave number increment (Delta)k so that N(sup 2) sampled signals are produced. The NxN transfer function elements are generated using the N(sup 2) sampled signals. Reference and measurement path length constraints are defined such that the N combined signals at each of the N detectors are spatially separated from one another in the time domain.

Mark E Froggatt↗
NASA NTRS2002

Extreme Wind Velocity Measurement System

A wind velocity measurement system employs two different principles of physics to measure wind speed: (1) the aerodynamic force imparted to a low profile, rigidly mounted cylindrical rod, and (2) the vibrating frequency of the rod as vortices are shed from the rod's cylindrical surface. A set of strain gages is used as a common sensor for both measurements, and these provide force measurements imparted by the wind on the rod. The signals generated by the strain gages are fed to processing circuitry that calculates the wind speed and direction from the signals. The force measurement is proportional to the square of the wind speed. Since it is a vector quantity, it can also be used to derive wind direction. The vortex shedding frequency is a scalar quantity and is linearly proportional to wind speed. This frequency can be calculated by analyzing the force measurements generated by the strain gages over time. Both of the wind velocity calculations can be advantageously used by the processing circuitry to generate an accurate wind velocity reading.

Jan A Zysko↗
NASA NTRS1998

The Heats of Formation of GaCl3 and its Fragments

The heats of formation of GaC13 and its fragments are computed. The geometries and frequencies are obtained at the B3LYP level. The CCSD(T) approach is used to solve the correlation problem. The effect of Ga 3d correlation is studied, and found to affect the bond energies by up to 1 kcal/mol. Both basis set extrapolation and bond functions are considered as ways to approach the basis set limit. Spin-orbit and scalar relativistic effects are also considered.

Bauschlicher, Charles W., Jr.↗