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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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177 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

On the Statistics of Elsasser Increments in Solar Wind and Magnetohydrodynamic Turbulence

In this Letter we investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets of WIND data (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous reduced MHD turbulence on a 2048 3 rectangular mesh. A large statistical sample of Alfvénic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power laws of the form α l ∝ l –μ , where l is the scale size, with μ between 0.17 and 0.25 for observations and 0.43 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results point to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative approach to investigate high-order statistics in solar wind observations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

High-order numerical solutions using cubic splines

The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.

Rubin, S. G.↗
NASA NTRS1986

A spectral multi-domain technique with application to generalized curvilinear coordinates

Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic and fluid mechanic problems. The high order accuracy and resolution shown by these methods allows one to obtain engineering accuracy solutions on coarse meshes, or alternatively, to obtain solutions with very small error. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be preserved. Additionally even smooth stretching transformations can decrease the accuracy of a spectral method, if the stretching is severe. A further difficulty with spectral methods was in their implementation on parallel processing computers, where efficient spectral algorithms were lacking. The above restrictions are overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of the mesh spacing between regions to be several orders of magnitude higher than allowable in a single domain. Such stretchings would be required to resolve the thin viscous region in an external aerodynamic problem. Adjoining regions are interfaced by enforcing a global flux balance which preserves high-order continuity of the solution, regardless of the type of the equations being solved.

Macaraeg, M. G.↗
NASA NTRS1989

A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

Liou, Meng-Sing↗
NASA NTRS1993

A comparison of two formulations for high-order accurate essentially non-oscillatory schemes

The finite-volume and finite-difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

Casper, J.↗
NASA NTRS1993

Some aspects of high-order numerical solutions of the linear convection equation with forced boundary conditions

A six-stage low-storage Runge-Kutta time-marching method is presented and shown to be an efficient method for use with high-accuracy spatial difference operators for wave propagation problems. The accuracy of the method for inhomogeneous ordinary differential equations is demonstrated through numerical solutions of the linear convection equation with forced boundary conditions. Numerical experiments are presented simulating a sine wave and a Gaussian pulse propagating into and through the domain. For practical levels of mesh refinement corresponding to roughly ten points per wavelength, the six-stage Runge-Kutta method is more accurate than the popular fourth-order Runge-Kutta method. Further numerical experiments are presented which show that the numerical boundary scheme at an inflow boundary can be a significant source of error when high-accuracy spatial discretizations are used.

Zingg, D. W.↗
NASA NTRS1993

A comparison of two formulations for high-order accurate essentially non-oscillatory schemes

The finite-volume and finite-difference implementations of high-order accurate essentially non-oscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

Casper, Jay↗
NASA NTRS2000

An Application of the Quadrature-Free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.

Lockard, David P.↗
NASA NTRS2014

Parallel Adaptive High-Order CFD Simulations Characterizing Cavity Acoustics for the Complete SOFIA Aircraft

This paper presents one-of-a-kind MPI-parallel computational fluid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft of a Boeing 747SP. These simulations focus on how the unsteady flow field inside and over the cavity interferes with the optical path and mounting of the telescope. A temporally fourth-order Runge-Kutta, and spatially fifth-order WENO-5Z scheme was used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh refinement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32,000 cores and 4 billion cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregularities caused by the highly complex geometry. Limits to scaling beyond 32K cores are identified, and targeted code optimizations are discussed.

Acoustics↗
NASA NTRS2016

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

Swanson, R. C.↗
NASA NTRS2016

Parallel Adjective High-Order CFD Simulations Characterizing SOFIA Cavity Acoustics

This paper presents large-scale MPI-parallel computational uid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft fuselage of a Boeing 747SP. These simulations focus on how the unsteady ow eld inside and over the cavity interferes with the optical path and mounting structure of the telescope. A temporally fourth-order accurate Runge-Kutta, and spatially fth-order accurate WENO- 5Z scheme was used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh re nement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32k CPU cores and 4 billion compu- tational cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregular numerical cost associated with blocks con- taining boundaries. Limits to scaling beyond 32k cores are identi ed, and targeted code optimizations are discussed.

CFD↗
NASA NTRS2016

Improving Fidelity of Launch Vehicle Liftoff Acoustic Simulations

Launch vehicles experience high acoustic loads during ignition and liftoff affected by the interaction of rocket plume generated acoustic waves with launch pad structures. Application of highly parallelized Computational Fluid Dynamics (CFD) analysis tools optimized for application on the NAS computer systems such as the Loci/CHEM program now enable simulation of time-accurate, turbulent, multi-species plume formation and interaction with launch pad geometry and capture the generation of acoustic noise at the source regions in the plume shear layers and impingement regions. These CFD solvers are robust in capturing the acoustic fluctuations, but they are too dissipative to accurately resolve the propagation of the acoustic waves throughout the launch environment domain along the vehicle. A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed to improve such liftoff acoustic environment predictions. The framework combines the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin (DG) solver, Loci/THRUST, developed in the same computational framework. Loci/THRUST employs a low dissipation, high-order, unstructured DG method to accurately propagate acoustic waves away from the source regions across large distances. The DG solver is currently capable of solving up to 4th order solutions for non-linear, conservative acoustic field propagation. Higher order boundary conditions are implemented to accurately model the reflection and refraction of acoustic waves on launch pad components. The DG solver accepts generalized unstructured meshes, enabling efficient application of common mesh generation tools for CHEM and THRUST simulations. The DG solution is coupled with the CFD solution at interface boundaries placed near the CFD acoustic source regions. Both simulations are executed simultaneously with coordinated boundary condition data exchange.

Liever, Peter↗
NASA NTRS2017

Navier-Stokes Simulation of UH-60A Rotor/Wake Interaction Using Adaptive Mesh Refinement

High-resolution simulations of rotor/vortex-wake interaction for a UH60-A rotor under BVI and dynamic stallconditions were carried out with the OVERFLOW Navier-Stokes code.a. The normal force and pitching moment variation with azimuth angle were in good overall agreementwith flight-test data, similar to other CFD results reported in the literature.b. The wake-grid resolution did not have a significant effect on the rotor-blade airloads. This surprisingresult indicates that a wake grid spacing of (Delta)S=10% ctip is sufficient for engineering airloads predictionfor hover and forward flight. This assumes high-resolution body grids, high-order spatial accuracy, anda hybrid RANS/DDES turbulence model.c. Three-dimensional dynamic stall was found to occur due the presence of blade-tip vortices passing overa rotor blade on the retreating side. This changed the local airfoil angle of attack, causing stall, unlikethe 2D perspective of pure pitch oscillation of the local airfoil section.

CFD Validation↗
NASA NTRS2015

Parallel Adaptive High-Order CFD Simulations Characterizing SOFIA Cavitiy Acoustics

This paper presents large-scale MPI-parallel computational uid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft fuselage of a Boeing 747SP. These simulations focus on how the unsteady ow eld inside and over the cavity interferes with the optical path and mounting structure of the telescope. A tempo- rally fourth-order accurate Runge-Kutta, and a spatially fth-order accurate WENO-5Z scheme were used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh re nement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32k CPU cores and 4 billion compu- tational cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregular numerical cost associated with blocks con- taining boundaries. Limits to scaling beyond 32k cores are identi ed, and targeted code optimizations are discussed.

Parallell↗
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↗