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At least 163 records · Page 9

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NASA NTRS1995

Towards Distributed Fluids/Controls Simulations

Computational prototyping of aircraft in nonlinear regimes will require the coupling of high-order disciplines on high performance computers. This effort investigates the coupling of the Reynolds-averaged Navier-Stokes equations with six degree-of-freedom nonlinear body dynamics and controls on distributed architectures. Towards this goal, solutions obtained on a wide-node IBM SP-2, an Ethernet-linked cluster of workstations, and a Cray C90 are compared in terms of accuracy and throughput.

Atwood, Christopher A.↗

NASA NTRS2000

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

Three benchmark problems are solved using a sixth-order prefactored compact scheme employing an explicit 10th-order filter with optimized fourth-order Runge-Kutta time stepping. The problems solved are the following: (1) propagation of sound waves through a transonic nozzle; (2) shock-sound interaction; and (3) single airfoil gust response. In the first two problems, the spatial accuracy of the scheme is tested on a stretched grid, and the effectiveness of boundary conditions is shown. The solution stability and accuracy near a shock discontinuity is shown as well. Also, 1-D nonlinear characteristic boundary conditions will be evaluated. In the third problem, a nonlinear Euler solver will be used that solves the equations in generalized curvilinear coordinates using the chain rule transformation. This work, continuing earlier work on flat-plate cascades and Joukowski airfoils, will focus mainly on the effect of the grid and boundary conditions on the accuracy of the solution. The grids were generated using a commercially available grid generator, GridPro/az3000.

Hixon, Ray↗

NASA NTRS1995

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗

NASA NTRS2002

High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

Bryson, Steve↗

NASA NTRS2002

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

We present the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi equations. Unlike most of the commonly used high order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov-Tadmor and Kurganov-Tadmor-Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spacial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton-Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations.

Bryson, Steve↗

NASA NTRS2002

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Liu, Yen↗

NASA NTRS2003

Computational Methods for Jet Noise Simulation

The purpose of our project is to develop, analyze, and test novel numerical technologies central to the long term goal of direct simulations of subsonic jet noise. Our current focus is on two issues: accurate, near-field domain truncations and high-order, single-step discretizations of the governing equations. The Direct Numerical Simulation (DNS) of jet noise poses a number of extreme challenges to computational technique. In particular, the problem involves multiple temporal and spatial scales as well as flow instabilities and is posed on an unbounded spatial domain. Moreover, the basic phenomenon of interest, the radiation of acoustic waves to the far field, involves only a minuscule fraction of the total energy. The best current simulations of jet noise are at low Reynolds number. It is likely that an increase of one to two orders of magnitude will be necessary to reach a regime where the separation between the energy-containing and dissipation scales is sufficient to make the radiated noise essentially independent of the Reynolds number. Such an increase in resolution cannot be obtained in the near future solely through increases in computing power. Therefore, new numerical methodologies of maximal efficiency and accuracy are required.

Goodrich, John W.↗

NASA NTRS2004

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Shu, Chi-Wang↗

NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

Liu, Yen↗

NASA NTRS2005

Multi-Dimensional Spectral Difference Method for Unstructured Grids

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.

Liu, Yen↗

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↗