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318 records · Page 18

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NASA NTRS2003

Validation of a High-Order Prefactored Compact Code on Nonlinear Flows with Complex Geometries

A finite-difference time domain solution of the airfoil gust problem is obtained using a high-accuracy nonlinear computational aeroacoustics code. For computational efficiency, the equations are cast in chain-rule curvilinear form, and a structured multiblock solver is used in parallel. In order to fully investigate the performance of this solver, a test matrix of eight problems are computed (two airfoil geometries, two gust frequencies, and two gust configurations). These results are compared to solutions obtained by the GUST3D frequency-domain solver both on the airfoil surface and in the far field. Grid density and domain size studies are included.

Hixon, R.↗

NASA NTRS2006

Track-Level-Compensation Look-Up Table Improves Antenna Pointing Precision

This article presents the improvement of the beam-waveguide antenna pointing accuracy due to the implementation of the track-level-compensation look-up table. It presents the development of the table, from the measurements of the inclinometer tilts to the processing of the measurement data and the determination of the threeaxis alidade rotations. The table consists of three axis rotations of the alidade as a function of the azimuth position. The article also presents the equations to determine the elevation and cross-elevation errors of the antenna as a function of the alidade rotations and the antenna azimuth and elevation positions. The table performance was verified using radio beam pointing data. The pointing error decreased from 4.5 mdeg to 1.4 mdeg in elevation and from 14.5 mdeg to 3.1 mdeg in cross-elevation. I. Introduction The Deep Space Station 25 (DSS 25) antenna shown in Fig. 1 is one of NASA s Deep Space Network beam-waveguide (BWG) antennas. At 34 GHz (Ka-band) operation, it is necessary to be able to track with a pointing accuracy of 2-mdeg root-mean-square (rms). Repeatable pointing errors of several millidegrees of magnitude have been observed during the BWG antenna calibration measurements. The systematic errors of order 4 and lower are eliminated using the antenna pointing model. However, repeatable pointing errors of higher order are out of reach of the model. The most prominent high-order systematic errors are the ones caused by the uneven azimuth track. The track is shown in Fig. 2. Manufacturing and installation tolerances, as well as gaps between the segments of the track, are the sources of the pointing errors that reach over 14-mdeg peak-to-peak magnitude, as reported in [1,2]. This article presents a continuation of the investigations and measurements of the pointing errors caused by the azimuth-track-level unevenness that were presented in [1] and [2], and it presents the implementation results. Track-level-compensation (TLC) look-up tables were created for the DSS 25, DSS 26, DSS 34, and DSS 55 antennas. To date, the most complete and detailed results were obtained for the DSS 25 and DSS 55 antennas. In this article, for brevity of presentation, we present the DSS 25 antenna results only. 1 Communications Ground Systems Section. The research described in this publication was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

Gawronski, W.↗

NASA NTRS2008

High-Order Energy Stable WENO Schemes

A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

Yamaleev, Nail K.↗

NASA NTRS2009

Parametric Optimization of Ares I Propellant Slosh Characteristics Using Frequency Response Criteria

A novel technique for developing propellant slosh damping requirements with respect to the stability characteristics of large flexible launch vehicles is presented. A numerical algorithm is devised which allows an automated software program to rapidly converge to pseudo-optimal solutions that minimize required propellant slosh damping for multiple tanks while maintaining constraints on the frequency response characteristics of a particular open-loop plant transfer function. An implementation of the algorithm using a high-order linear model of the Ares I plant dynamics considers all relevant dynamic interactions of flexible body modes, propellant slosh, and nozzle inertia effects. A high-resolution propellant damping requirements table is produced that can be used for baffle design. The method is demonstrated to provide exceptional speed and accuracy when compared with the alternative human-in-the-loop approach.

Orr, Jeb S.↗

NASA NTRS2011

Development and Validation of a Multidisciplinary Tool for Accurate and Efficient Rotorcraft Noise Prediction (MUTE)

A physics-based, systematically coupled, multidisciplinary prediction tool (MUTE) for rotorcraft noise was developed and validated with a wide range of flight configurations and conditions. MUTE is an aggregation of multidisciplinary computational tools that accurately and efficiently model the physics of the source of rotorcraft noise, and predict the noise at far-field observer locations. It uses systematic coupling approaches among multiple disciplines including Computational Fluid Dynamics (CFD), Computational Structural Dynamics (CSD), and high fidelity acoustics. Within MUTE, advanced high-order CFD tools are used around the rotor blade to predict the transonic flow (shock wave) effects, which generate the high-speed impulsive noise. Predictions of the blade-vortex interaction noise in low speed flight are also improved by using the Particle Vortex Transport Method (PVTM), which preserves the wake flow details required for blade/wake and fuselage/wake interactions. The accuracy of the source noise prediction is further improved by utilizing a coupling approach between CFD and CSD, so that the effects of key structural dynamics, elastic blade deformations, and trim solutions are correctly represented in the analysis. The blade loading information and/or the flow field parameters around the rotor blade predicted by the CFD/CSD coupling approach are used to predict the acoustic signatures at far-field observer locations with a high-fidelity noise propagation code (WOPWOP3). The predicted results from the MUTE tool for rotor blade aerodynamic loading and far-field acoustic signatures are compared and validated with a variation of experimental data sets, such as UH60-A data, DNW test data and HART II test data.

Liu, Yi↗

NASA NTRS2013

Performance of Improved High-Order Filter Schemes for Turbulent Flows with Shocks

The performance of the filter scheme with improved dissipation control κ has been demonstrated for different flow types. The scheme with local κ is shown to obtain more accurate results than its counterparts with global or constant κ. At the same time no additional tuning is needed to achieve high accuracy of the method when using the local κ technique. However, further improvement of the method might be needed for even more complex and/or extreme flows.

Flows↗

NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗

NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗

NASA NTRS2016

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Mazaheri, Alireza↗

NASA NTRSDate not supplied

Scale-Resolving Simulations of a Supersonic Retro-Propulsion Concept For Mars Entry, Descent, and Landing

Supersonic retro-propulsion (SRP) is a deceleration technology that could enable largerpayloads and potentially humans to be brought from space to the surface of Mars safely.Accurate and reliable CFD predictions are needed to help design future Mars entry, descent,and landing (EDL) vehicles due to the cost and limitations of wind tunnel tests. TypicalCFD approaches struggle at points along the Mars EDL trajectory with high enough altitude(low enough ambient pressure) that the SRP motor plumes are over-expanded. This workdemonstrates how high-order scale-resolving simulations on Cartesian AMR grids can provideaccurate and reliable time-averaged aerodynamic loads on the vehicle for this challengingflow regime. Greater than second order convergence in the time-averaged integrated axialforce𝐶𝐴is obtained across the three finest mesh resolutions simulated, and the estimateduncertainty is smaller than the unsteady standard deviation – demonstrating the accuracy andreliability of the method. Although costly, this approach can yield higher confidence in𝐶𝐴thanpreviously obtained in a reasonable turnaround time and is within reach for a few points in thetrajectory (i.e. Mach 2.4, 2.52, and 2.78). Further computational performance and numericalmethods improvements are needed to reduce the cost enough to bring this method into the EDLengineering design cycle.

S&M↗

NASA NTRSDate not supplied

Shock Capturing via Limiting for High-Order Methods Including Discontinuous Galerkin

As is well-known, popular high-order methods such as discontinuous Galerkin (DG) and flux reconstruction (FR) tend to generate oscillations near shocks and discontinuities, which can lead to negative pressure or density, ultimately causing code breakdown. For standard second-order methods, one approach to mitigating oscillations is to impose constraints on the calculated slopes, ensuring they do not become excessively steep. This limiting process is rooted in the idea of preserving monotonicity introduced by Van Leer (1974): when the data are monotone, limiting the slopes result in a monotone piecewise linear solution. However, a drawback of this approach is the loss of accuracy near extrema, where the non-monotone solution is somewhat flattened and achieves only first-order accuracy.

numerical methods↗

DOE OSTI2022

High-order diamond differencing schemes for the Boltzmann Fokker-Planck equation in 3D Cartesian geometries

The Boltzmann Fokker-Planck, an approximate form of the linear Boltzmann equation is commonly used to treat efficiently the transport of charged particles in matter. This paper introduces the application of high-order diamond differencing schemes (HODD), specifically the DD1 and DD2 schemes which are 4- and 6-order accurate respectively, to handle the spatial discretization of that equation in 3D Cartesian geometries. The energy deposition solutions for the coupled transport of electrons and photons presented in this work shows that HODD, compared to classical DD scheme, provides correction to the oscillations and a reduced propensity to yield negative fluxes. They are useful tools to minimize local error, notably in regions with abrupt variations of the flux solution. They also can be used to reduced execution time by decreasing the needed number of voxels to obtain a fixed accuracy. On the tested benchmarks, the DD1 scheme is 87%- 92%-91% more accurate than the classical DD scheme for total, mean per-voxels and maximum deviation of energy deposition values respectively. For comparison, a calculation with 8 times more voxels, requiring roughly 2.5 times more time to execute, is 92%-90%-77% more accurate. (authors)

97 MATHEMATICS AND COMPUTING↗