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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Comparitive Study of High-Order Positivity-Preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density ρ and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ρ may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

Schemes↗
NASA NTRS2020

Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations via Order-Reduction Techniques

The High-Fidelity Generalized Method of Cells (HFGMC) is one technique, distinct from traditional finite element approaches, for accurately simulating nonlinear composite material behavior. In this work, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents has been reduced in size through the novel application of a Petrov-Galerkin Proper Orthogonal Decomposition order-reduction scheme in order to improve its computational efficiency. Order-reduced models of an E-glass/Nylon 12 composite led to a 4.8 to 6.3x speedup in the equation assembly/solution runtime while maintaining model accuracy. This corresponded to a 21 to 38 percent reduction in total runtime. The significant difference in assembly/solution and total runtimes was attributed to the evaluation of integration point inelastic field quantities; this step was identical between the unreduced and order-reduced models. Nonetheless, order-reduced techniques offer the potential to significantly improve the computational efficiency of multiscale calculations.

Ricks, Trenton M.↗
NASA NTRS2017

Dynamic Testbed Demonstration of WFIRST Coronagraph Low Order Wavefront Sensing and Control (LOWFS/C)

To maintain the required performance of WFIRST Coronagraph in a realistic space environment, a Low Order Wavefront Sensing and Control (LOWFS/C) subsystem is necessary. The LOWFS/C uses a Zernike wavefront sensor (ZWFS) with the phase shifting disk combined with the starlight rejecting occulting mask. For wavefront error corrections, WFIRST LOWFS/C uses a fast steering mirror (FSM) for line-of-sight (LoS) correction, a focusing mirror for focus drift correction, and one of the two deformable mirrors (DM) for other low order wavefront error (WFE) correction. As a part of technology development and demonstration for WFIRST Coronagraph, a dedicated Occulting Mask Coronagraph (OMC) testbed has been built and commissioned. With its configuration similar to the WFIRST flight coronagraph instrument the OMC testbed consists of two coronagraph modes, Shaped Pupil Coronagraph (SPC) and Hybrid Lyot Coronagraph (HLC), a low order wavefront sensor (LOWFS), and an optical telescope assembly (OTA) simulator which can generate realistic LoS drift and jitter as well as low order wavefront error that would be induced by the WFIRST telescope’s vibration and thermal changes. In this paper, we will introduce the concept of WFIRST LOWFS/C, describe the OMC testbed, and present the testbed results of LOWFS sensor performance. We will also present our recent results from the dynamic coronagraph tests in which we have demonstrated of using LOWFS/C to maintain the coronagraph contrast with the presence of WFIRST-like line-of-sight and low order wavefront disturbances.

Zhou, Hanying↗
NASA NTRS2018

Efficient Runtime Verification of First-Order Temporal Properties

Runtime verification allows monitoring the execution of a system against a temporal property, raising an alarm if the property is violated. In this paper we present a theory and system for runtime verification of a first-order past time linear temporal logic. The first-order nature of the logic allows a monitor to reason about events with data elements. While runtime verification of propositional temporal logic requires only a fixed amount of memory, the first-order variant has to deal with a number of data values potentially growing unbounded in the length of the execution trace. This requires special compactness considerations in order to allow checking very long executions. In previous work we presented an efficient use of BDDs for such first-order runtime verification, implemented in the tool DEJAVU. We first summarize this previous work. Subsequently, we look at the new problem of dynamically identifying when data observed in the past are no longer needed, allowing to reclaim the data elements used to represent them. We also study the problem of adding relations over data values. Finally, we present parts of the implementation, including a new concept of user defined property macros.

Peled, Doron↗
NASA NTRS2018

WFIRST Low Order Wavefront Sensing and Control Testbed Performance under Flight Like Photon Flux

To maintain the required performance for the WFIRST Coronagraph Instrument (CGI) in a realistic space environment, a Low Order Wavefront Sensing and Control (LOWFS/C) subsystem is necessary. The WFIRST CGI LOWFS/C subsystem would use the Zernike wavefront sensor, which has the phase-shifting disk combined with the coronagraph’s focal plane mask, to sense the low-order wavefront drift and line-of-sight (LoS) error using the rejected starlight. The dynamic tests on JPL’s on the Occulting Mask Coronagraph (OMC) Testbed have demonstrated that LOWFS/C can maintain coronagraph contrast to better than 10-8 in presence of WFIRST-like line of sight and low order wavefront disturbances in both Shaped Pupil Coronagraph (SPC) and Hybrid Lyot Coronagraph (HLC) modes. However, the previous dynamic tests have been done using a bright source with photon flux equivalent to stellar magnitude of Mv = -3.5. The LOWFS/C technology development continues on the OMC testbed especially in evaluating and improving the LOWFS/C performance under the realistic photon flux that is equivalent to WFIRST Coronagraph target stars. Our recent testbed tests have demonstrated that the LOWFS/C can work cohesively with the stellar light suppression wavefront control, which brings broad band coronagraph contrast from 1x10-6 to 6x10-9, while LOWF/C is simultaneously suppressing the WFIRST like LoS and low order wavefront drift disturbances on a source that photon flux is equivalent to a Mv = 2 star. This demonstration mimics the CGI initial dark hole establish process on a bright reference star. We also demonstrated on the testbed that LOWFS/C can maintain the coronagraph contrast by suppressing the WFIRST like line-of-sight disturbances on a fainter Mv = 5 star. This mimics scenario of CGI science target observations. In this paper we will present the recent testbed results on LOWFS/C LoS loops and low order wavefront error correction loop performance on the flight like photon flux.

Truong, Tuan↗
NASA NTRS2017

Order-Reduced Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations

The High-Fidelity Generalized Method of Cells (HFGMC) is one technique for accurately simulating nonlinear composite material behavior. The HFGMC uses a higher-order approximation for the subcell displacement field that allows for a more accurate determination of the subcell stressstrain fields at the cost of some computational efficiency. In order to reduce computational costs associated with the solution of the ensuing system of simultaneous equations, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents was reduced in size through the use of a Petrov-Galerkin-based Proper Orthogonal Decomposition order-reduction scheme. A number of cases were presented that address the computational feasibility of using order-reduction techniques to solve solid mechanics problems involving complex microstructures.

order-reduction↗
NASA NTRS2024

High-Order/Low-Dissipation Chain-Rule Flux Solution Reconstruction Schemes in FUN3D

In this paper, we report progress in the development of economically high-order flux-solution-reconstruction (FSR) schemes, which are second-order accurate on general unstructured grids but achieve high-order accuracy when a grid is regular, i.e., has the same stencil (with the same spacing) throughout the domain. Two variants of the FSR schemes are discussed: chain-rule-flux-solution reconstruction (CFSR) and quadratic-form-flux-solution reconstruction (QFSR), where the former is based on the chain rule and the latter on the flux reconstruction expressed as a function of solution variables. These schemes are tested for flows with shock waves with a limiter incorporated in the flux and solution reconstructions. Improved results, compared with second-order methods are demonstrated for inviscid and viscous flows with smooth grids.

high-order↗
NASA NTRSDate not supplied

Extending an Economical Third-Order Inviscid Nodal-Gradient Cell-Centered Finite-Volume Method to Mixed-Element Grids

In this paper, we extend an economical third-order nodal-gradient cell-centered finite-volume method, originally developed for tetrahedral grids, to mixed-element grids. It is shown that the efficient quadratic interpolation formula essential to eliminating second derivatives from a third-order accurate discretization can be easily extended to an arbitrary cell type. For the surface flux integration, we consider a split-face approach, where a quadrilateral face is split into two triangles, and the third-order method for tetrahedra is directly applied. Also, we derive a second-derivative-free, high-order, volume quadrature formula for an arbitrary cell. Numerical results are presented for accuracy verification and applications with three-dimensional nontetrahedral grids.

Computational Fluid Dynamics↗
NASA NTRS1972

Ordering Effects in NbC and TaC

By means of transmission electron microscopy and electron diffraction, evidence has been obtained for the existence of long range carbon atom ordering in single-crystal niobium carbide that has a carbon-to-metal ratio close to the integral composition Nb6C5. The ordering, which gives rise to superlattice and domain structures similar to those observed in V6C5, appears, however, only in samples that have been cooled slowly through the order-disorder temperature of 1025 C. In TaC of similar composition, the ordering, although present, remains very imperfect even after the crystals are subjected to the same thermal treatment. The results are interpreted in terms of the electronic structure of the transition metal carbides as it is currently understood, and their relevance to the mechanical properties of NbC and TaC are discussed.

Venables, J. D.↗
NASA NTRS1971

Second-order electro-optic effect in diamond.

Observation of a second-order electrooptic effect in diamond, leading to the determination of an order of magnitude for the appropriate second-order electrooptic coefficient of diamond. A linear effect, forbidden by symmetry, is also observed and attributed to random residual strains, an average estimate of which is obtained as .00001 for the particular sample used in this experiment. Birefringence due to second-order dispersion effects is also discussed.

Anastassakis, E.↗
NASA NTRS1972

Electron paramagnetic resonance studies of a viscous nematic liquid crystal: Evidence counter to a second-order phase change

The ordering in a viscous, nematic, liquid crystal was studied using vanadyl acetyl acetonate and several nitroxides as paramagnetic probes. The ordering curve for VAAC at both K-band and X-band shows a slope discontinuity at a reduced temperature of 0.85. This discontinuity is caused by the tumbling time of the VAAC becoming comparable with the hyperfine splitting. The slope discontinuity is not present in the ordering curves of the nitroxides. The results are taken as evidence counter to the presence of a second-order phase transition.

Shutt, W. E.↗
NASA NTRS1972

Generation and application of the equations of condition for high order Runge-Kutta methods

This thesis develops the equations of condition necessary for determining the coefficients for Runge-Kutta methods used in the solution of ordinary differential equations. The equations of condition are developed for Runge-Kutta methods of order four through order nine. Once developed, these equations are used in a comparison of the local truncation errors for several sets of Runge-Kutta coefficients for methods of order three up through methods of order eight.

Haley, D. C.↗
NASA NTRS1974

Development of a second order closure model for computation of turbulent diffusion flames

A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions.

Varma, A. K.↗
NASA NTRS1974

A second-order theory of an artificial satellite under the influence of the oblateness of the earth

The general theory of the method of averaging is used to study the effect of the oblateness of the earth on the motion of an artificial satellite. The first-order harmonic J2 and the second-order harmonics J3 and J4 are included in the analysis. The first-order, periodic variations together with the second-order, averaged and secular variations are derived for all the six orbital elements. Alternative orbital elements and necessary relations are introduced to deal with circular orbits, orbits at critical inclination and equatorial orbits. Essential transformations and initialization procedures are also outlined.

Liu, J. J. F.↗
NASA NTRS1973

Aircraft maneuver optimization of reduced-order approximation

Review of recent work in recasting the energy type of approximation to aircraft flight in terms of singular perturbation theory and in extending this theory to three-dimensional maneuvers. Singular perturbations for differential equations arising in optimal control are first examined for a system of fairly general form but low order. The attitude dynamics for optimal flight of a rocket in vacuum is then studied as an introductory, and fairly transparent, example. The question of the choice of variables is then discussed. Finally, optimal aircraft flight in various reduced-order approximations is investigated. In particular, the problem of three-dimensional aircraft flight is formulated for singular perturbation treatment, and possibilities for decoupling into several lower-order problems are illustrated. The use of reduced-order approximation facilitates numerical computations by reducing the number of multiplier initial values that must be determined simultaneously and by improving the conditioning of the differential equations.

Kelley, H. J.↗
NASA NTRS1974

Equations of condition for high order Runge-Kutta-Nystrom formulae

Derivation of the equations of condition of order eight for a general system of second-order differential equations approximated by the basic Runge-Kutta-Nystrom algorithm. For this general case, the number of equations of condition is considerably larger than for the special case where the first derivative is not present. Specifically, it is shown that, for orders two through eight, the number of equations for each order is 1, 1, 1, 2, 3, 5, and 9 for the special case and is 1, 1, 2, 5, 13, 34, and 95 for the general case.

Bettis, D. G.↗
NASA NTRS1974

Second-order small disturbance theory for hypersonic flow over power-law bodies

A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.

Townsend, J. C.↗
NASA NTRS1976

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗