Search NASA⌕ Search

SEARCH · Search NASA

Results for “Flux reconstruction”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

New Capabilities and Improvements to the High-Order Glenn Flux Reconstruction Code

The Glenn Flux Reconstruction (GFR) code is a computational fluid dynamics (CFD) code under development at NASA Glenn Research Center. GFR is based on the high-order flux reconstruction (FR) method and provides a large-eddy simulation (LES) capability that is both accurate and efficient for complex aeropropulsion flows. Three significant new capabilities have been added to the code that improve its performance and functionality. First, a variety of explicit Runge-Kutta methods, including some with adaptive time stepping, were added to GFR with two methods offering a 33% improvement in time-to-solution. Second, GFR can now utilize fully unstructured, mixed-element meshes to more easily facilitate the grid generation process for complex geometries. Finally, a rotating reference frame capability has been added to GFR for solving rotating turbomachinery problems. A selection of results demonstrating these new capabilities are presented in this work. The Taylor-Green vortex problem is used to verify the new unstructured capability by showing similar accuracy and resolution for all element types. LES of the Turbulent Heat Flux Phase III (THX3) experiment with comparison to another high-order LES code and a popular Reynolds-averaged Navier-Stokes (RANS) code demonstrates the accuracy of the code for complex aeropropulsion flows. Finally, LES of a spacecraft cabin ventilation fan shows the ability of GFR to efficiently establish a fan performance map and identify operating points for further analysis at high orders of accuracy.

High-Order Methods↗
NASA NTRSDate not supplied

New Capabilities and Improvements to the High-Order Glenn Flux Reconstruction Code

The Glenn Flux Reconstruction (GFR) code is a computational fluid dynamics (CFD) code under development at NASA Glenn Research Center. GFR is based on the high-order flux reconstruction (FR) method and provides a large-eddy simulation (LES) capability that is both accurate and efficient for complex aeropropulsion flows. Three significant new capabilities have been added to the code that improve its performance and functionality. First, a variety of explicit Runge-Kutta methods, including some with adaptive time stepping, were added to GFR with two methods offering a 33% improvement in time-to-solution. Second, GFR can now utilize fully unstructured, mixed-element meshes to more easily facilitate the grid generation process for complex geometries. Finally, a rotating reference frame capability has been added to GFR for solving rotating turbomachinery problems. A selection of results demonstrating these new capabilities are presented in this work. The Taylor-Green vortex problem is used to verify the new unstructured capability by showing similar accuracy and resolution for all element types. LES of the Turbulent Heat Flux Phase III (THX3) experiment with comparison to another high-order LES code and a popular Reynolds-averaged Navier-Stokes (RANS) code demonstrates the accuracy of the code for complex aeropropulsion flows. Finally, LES of a spacecraft cabin ventilation fan shows the ability of GFR to efficiently establish a fan performance map and identify operating points for further analysis at high orders of accuracy.

Direct Numerical Simulations↗
NASA NTRS2009

Multi-Dimensional, Inviscid Flux Reconstruction for Simulation of Hypersonic Heating on Tetrahedral Grids

The quality of simulated hypersonic stagnation region heating on tetrahedral meshes is investigated by using a three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. Two test problems are investigated: hypersonic flow over a three-dimensional cylinder with special attention to the uniformity of the solution in the spanwise direction and hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problem provides a sensitive test for algorithmic effects on heating. This investigation is believed to be unique in its focus on three-dimensional, rotated upwind schemes for the simulation of hypersonic heating on tetrahedral grids. This study attempts to fill the void left by the inability of conventional (quasi-one-dimensional) approaches to accurately simulate heating in a tetrahedral grid system. Results show significant improvement in spanwise uniformity of heating with some penalty of ringing at the captured shock. Issues with accuracy near the peak shear location are identified and require further study.

Gnoffo, Peter A.↗
NASA NTRS2016

Overview of the NASA Glenn Flux Reconstruction Based High-Order Unstructured Grid Code

A computational fluid dynamics code based on the flux reconstruction (FR) method is currently being developed at NASA Glenn Research Center to ultimately provide a large- eddy simulation capability that is both accurate and efficient for complex aeropropulsion flows. The FR approach offers a simple and efficient method that is easy to implement and accurate to an arbitrary order on common grid cell geometries. The governing compressible Navier-Stokes equations are discretized in time using various explicit Runge-Kutta schemes, with the default being the 3-stage/3rd-order strong stability preserving scheme. The code is written in modern Fortran (i.e., Fortran 2008) and parallelization is attained through MPI for execution on distributed-memory high-performance computing systems. An h- refinement study of the isentropic Euler vortex problem is able to empirically demonstrate the capability of the FR method to achieve super-accuracy for inviscid flows. Additionally, the code is applied to the Taylor-Green vortex problem, performing numerous implicit large-eddy simulations across a range of grid resolutions and solution orders. The solution found by a pseudo-spectral code is commonly used as a reference solution to this problem, and the FR code is able to reproduce this solution using approximately the same grid resolution. Finally, an examination of the code's performance demonstrates good parallel scaling, as well as an implementation of the FR method with a computational cost/degree- of-freedom/time-step that is essentially independent of the solution order of accuracy for structured geometries.

High-Order Methods↗
NASA NTRSDate not supplied

Large Eddy Simulations of a Single-Injector Cooling Flow Using the High-Order Flux Reconstruction Method

A single-injector cooling flow into a heated crossflow was used as a validation case for large eddy simulations (LES) from two high-order CFD codes with comparisons to a state-of-the-art Reynolds averaged Navier-Stokes (RANS) turbulence model. The focus of this paper is on the validation of LES for one of the high-order CFD codes, namely the GFR (Glenn Flux Reconstruction) code that is being developed at NASA Glenn Research Center. Fourth-order LES were performed for the single-injector cooling flow configuration at blowing ratios of both 1.0 and 2.0, and a fifth-order LES was also performed with a blowing ratio of 1.0. The GFR simulations agree very well with the experiment mean quantities and reasonably well with the experiment turbulence quantities. The LES solutions from GFR and the other high-order CFD code, FDL3DI, agreed very closely for nearly every flow quantity examined, despite the fact that these two codes use completely different numerical methods, different grid geometries and domains, and different inflow boundary conditions. Finally, both LES show a significant accuracy improvement over RANS turbulence models for flows with large temperature gradients, where the standard gradient diffusion approximation is insufficient for temperature predictions.

Large Eddy Simulation↗
NASA NTRSDate not supplied

Large-Eddy Simulations of a Single-Injector Cooling Flow Using the High-Order Flux Reconstruction Method

A single-injector cooling flow into a heated crossflow was used as a validation case for large eddy simulations (LES) from two high-order CFD codes with comparisons to a state-of-the-art Reynolds averaged Navier-Stokes (RANS) turbulence model. The focus of this paper is on the validation of LES for one of the high-order CFD codes, namely the GFR (Glenn Flux Reconstruction) code that is being developed at NASA Glenn Research Center. Fourth-order LES were performed for the single-injector cooling flow configuration at blowing ratios of both 1.0 and 2.0, and a fifth-order LES was also performed with a blowing ratio of 1.0. The GFR simulations agree very well with the experiment mean quantities and reasonably well with the experiment turbulence quantities. The LES solutions from GFR and the other high-order CFD code, FDL3DI, agreed very closely for nearly every flow quantity examined, despite the fact that these two codes use completely different numerical methods, different grid geometries and domains, and different inflow boundary conditions. Finally, both LES show a significant accuracy improvement over RANS turbulence models for flows with large temperature gradients, where the standard gradient diffusion approximation is insufficient for temperature predictions.

Large Eddy Simulations↗
NASA NTRS2010

Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids

The quality of simulated hypersonic stagnation region heating with tetrahedral meshes is investigated by using an updated three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. An earlier implementation of this algorithm provided improved symmetry characteristics on tetrahedral grids compared to conventional reconstruction methods. The original formulation however displayed quantitative differences in heating and shear that were as large as 25% compared to a benchmark, structured-grid solution. The primary cause of this discrepancy is found to be an inherent inconsistency in the formulation of the flux limiter. The inconsistency is removed by employing a Green-Gauss formulation of primitive gradients at nodes to replace the previous Gram-Schmidt algorithm. Current results are now in good agreement with benchmark solutions for two challenge problems: (1) hypersonic flow over a three-dimensional cylindrical section with special attention to the uniformity of the solution in the spanwise direction and (2) hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problems provide a sensitive indicator for algorithmic effects on heating. Additional simulations on a sharp, double cone and the shuttle orbiter are then presented to demonstrate the capabilities of the new algorithm on more geometrically complex flows with tetrahedral grids. These results provide the first indication that pure tetrahedral elements utilizing the updated, three-dimensional, upwind reconstruction algorithm may be used for the simulation of heating and shear in hypersonic flows in upwind, finite volume formulations.

Gnoffo, Peter A.↗
NASA NTRS2015

De-Aliasing Through Over-Integration Applied to the Flux Reconstruction and Discontinuous Galerkin Methods

High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).

High-Order↗
NASA NTRS2016

The May 17, 2012 Solar Event: Back-Tracing Analysis and Flux Reconstruction with PAMELA

The PAMELA space experiment is providing first direct observations of Solar Energetic Particles (SEPs) with energies from about 80 MeV to several GeV in near-Earth orbit, bridging the low energy measurements by other spacecrafts and the Ground Level Enhancement (GLE) data by the worldwide network of neutron monitors. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies associated to SEP events. The analysis is supported by an accurate back-tracing simulation based on a realistic description of the Earth's magnetosphere, which is exploited to estimate the SEP energy spectra as a function of the asymptotic direction of arrival with respect to the Interplanetary Magnetic Field (IMF). In this work we report the results for the May 17, 2012 event.

Bruno, A.↗
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 NTRS2006

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Gnoffo, Peter A.↗
NASA NTRS2015

Investigation of Benthic Foraminiferal Non-Traditional Stable Isotopes to Reconstruct Methane Fluxes in Sedimentary Environments

Methane (CH4) is an important greenhouse gas, with a global warming potential much higher than carbon dioxide (CO2) on a short time scale. Even if the residence time of CH4 in the atmosphere is relatively short (tens of years), one of the products of CH4 oxidation is CO2, a greenhouse gas with a much longer residence time in the atmosphere (tens to hundreds of years). CH4 has been proposed as one of the trigger mechanisms for rapid global climate change today and in the geological past. With regards to the geological past, numerous studies proposed the benthic foraminiferal carbon isotope ratio (Delta13C) as a tool to reconstruct the impact of marine CH4 on rapid climate changes; however, the investigation of modern benthic foraminiferal Delta13C have produced inconclusive results. CH4 has a distinctive hydrogen isotope (Delta(D)) and Delta13C signature compared to seawater, and sulfate reduction, often coupled to CH4 anaerobic oxidation in sediments, changes the sulfur isotope signature (Delta34S) of the remaining sulfate in porewater. Therefore, we hypothesize that the Delta(D) and Delta34S signature of infaunal benthic foraminiferal species can provide a complementary approach to Delta13C to study CH4 dynamics in sedimentary environments. Here, we present the preliminary results obtained analyzing Uvigerina peregrina Delta(D) and Delta34S from three different locations at Hydrate Ridge, offshore Oregon. Unfortunately, the lack of chemical data related to the moment of foraminiferal calcification makes difficult to build a robust relationship among the U. peregrina stable isotopes and the CH4 fluxes at the sampling sites. However, our results look very promising, as each site is characterized by a different Delta(D) and Delta34S signature. We emphasize that this study represents the first step in the development of new proxies (Delta(D)) and Delta34S), which may complement the more traditional benthic foraminiferal Delta13C values, to reconstruct marine CH4 fluxes in the geological past.

Borrelli, C.↗
NASA NTRS2021

Comparing Commercial and Research Computational Fluid Dynamic Codes Using High-Order Workshop Benchmark Problems

The commercial computational fluid dynamic (CFD) code ANSYS Fluent and multiple research CFD codes (ez4d with uses the conservation element and solution element (CESE) method and codes that use the flux reconstruction (FR) method) were tested using three different benchmark problems from the International Workshop for High-Order CFD Methods. The benchmark problems included the transonic Ringleb flow, vortex transport by uniform flow, and laminar boundary layer on a flat plate. Simulation results from all three benchmark problems showed that the Fluent solutions had less error than the ez4d solutions for a given degree of freedom. As expected, both the Fluent and ez4d solutions had larger errors for a given degree of freedom than the simulations that used the FR method because both Fluent and ez4d utilized a second-order scheme whereas the FR codes utilized a fourth-order scheme.

CFD↗
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 NTRS2021

FUMES. II. Ly α Reconstructions of Young, Active M Dwarfs

The H I Ly α (1215.67 Å) emission line dominates the far-UV spectra of M dwarf stars, but strong absorption from neutral hydrogen in the interstellar medium makes observing Ly α challenging even for the closest stars. As part of the Far-Ultraviolet M-dwarf Evolution Survey, the Hubble Space Telescope has observed 10 early-to-mid M dwarfs with ages ranging from ∼24 Myr to several Gyr in order to evaluate how the incident UV radiation evolves through the lifetime of exoplanetary systems. We reconstruct the intrinsic Ly α profiles from STIS G140L and E140M spectra, and achieve reconstructed fluxes with 1σ uncertainties ranging from 5% to a factor of two for the low-resolution spectra (G140L) and 3%–20% for the high-resolution spectra (E140M). We observe broad, 500–1000 km s −1 wings of the Ly α line profile, and analyze how the line width depends on stellar properties. We find that stellar effective temperature and surface gravity are the dominant factors influencing the line width with little impact from the star's magnetic activity level, and that the surface flux density of the Ly α wings may be used to estimate the chromospheric electron density. The Ly α reconstructions on the G140L spectra are the first attempted on λ/Δλ ∼ 1000 data. We find that the reconstruction precision is not correlated with the signal-to-noise ratio of the observation—rather, it depends on the intrinsic broadness of the stellar Ly α line. Young, low-gravity stars have the broadest lines and therefore provide more information at low spectral resolution to the fit to break degeneracies among model parameters.

Allison Youngblood↗
NASA NTRSDate not supplied

Turbulent Simulations of Cooling Jets in Crossflow

Turbulent flow simulations were completed of the THX-III single hole film cooling experiment performed at NASA Glenn Research Center (GRC). Two different Large-Eddy Simulation (LES) approaches were completed along with a RANS based study. The first LES approach utilizes the Flux Reconstruction (FR) based finite element code GFR, while the second approach makes use of the compact difference solver FDL3DI. Both LES codes were run on grids larger than 1.5 Billion degrees of freedom (DoF). The RANS simulations used FUN3D and included a grid convergence as a turbulence closure study. A summary of the computational approaches and key findings are presented along with the experimental measurements. Significant progress has been made towards the completion of this work, as all but one simulation have been completed. The preliminary findings have shown the LES approaches have excellent agreement with each other, and closely follow the trends of the experiment. The Reynolds stress RANS closure, while the best of the RANS results, had difficulty matching the results of the LES and experimental measurements.

High-Order Methods↗