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At least 343 records · Page 19

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NASA NTRS2014

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

electric propulsion↗

DOE OSTI2020

Unitary Bethe-Salpeter Methods in Two- and Three-Body Systems

The study of resonances, unstable particles formed in particle scattering, is motivated by the questions about the strong interaction and the composition of hadrons. In order to advance this study in the intermediate energy region, a variety of techniques are used. In this thesis, we present work done on two different analyses that use the principle of unitarity and the Bethe-Salpeter equation to study the resonances Lambda(1405), Sigma(1385), and a1(1260). Firstly, we perform a simultaneous analysis of Sand P-waves of the Strangeness = -1 two-body meson-baryon scattering amplitude using all low-energy data. For the first time, differential cross section data are included for chiral unitary coupled-channel models. From this model, S- and P-wave amplitudes are extracted and we observe both well-known I(JP)=0(1/2^-) S-wave states as well as a new I(JP)=1(1/2^+) state absent in quark models and lattice QCD results. Multiple statistical and phenomenological tests suggest that, while the data clearly require an I =1 P-wave resonance, the new state just accounts for the absence of the decuplet Sigma(1385)3/2+ in the model which is subsequently included in the parameterization. Secondly, we formulate the final state interaction of the a1(1260) resonance decay in a manifestly three-body-unitary parameterization and fit it to the a1(1260) lineshape measured by the ALEPH experiment. Dalitz plots calculated from this fit are presented. The work demonstrates the feasibility to numerically solve a previously derived amplitude and its generalization to isobars with spin and coupled channels. The model is a good test case because it can also be applied to other meson decays including exotic states and modified for the finite-volume problem as it arises in lattice QCD due to its manifest unitarity. The understanding of the resonances being analyzed in both the two-body work and the three-body work gives a better understanding of intermediate energy QCD.

Sadasivan, Daniel↗

DOE OSTI2022

A multi-resolution approach to hydraulic fracture simulation

Abstract We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

58 GEOSCIENCES↗

DOE OSTI2022

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. Further, the method is demonstrated through calculations of the binding energies of nuclei with atomic number A ϵ {2,3,4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and infinite-volume effective field theory calculations of A ϵ {2,3,4,5,6} systems based on this matching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

Research at NASA Lewis Research Center gave the opportunity to incorporate new control volumes in the Denton 3-D finite-volume time marching code. For duct flows, the new control volumes require no transverse smoothing and this allows calculations with large transverse gradients in properties without significant numerical total pressure losses. Possibilities for improving the Denton code to obtain better distributions of properties through shocks were demonstrated. Much better total pressure distributions through shocks are obtained when the interpolated effective pressure, needed to stabilize the solution procedure, is used to calculate the total pressure. This simple change largely eliminates the undershoot in total pressure down-stream of a shock. Overshoots and undershoots in total pressure can then be further reduced by a factor of 10 by adopting the effective density method, rather than the effective pressure method. Use of a Mach number dependent interpolation scheme for pressure then removes the overshoot in static pressure downstream of a shock. The stability of interpolation schemes used for the calculation of effective density is analyzed and a Mach number dependent scheme is developed, combining the advantages of the correct perfect gas equation for subsonic flow with the stability of 2-point and 3-point interpolation schemes for supersonic flow.

Moore, J.↗

NASA NTRS1987

Supercomputing of supersonic flows using upwind relaxation and MacCormack schemes

The performance of two numerical solution schemes, (1) an implicit upwind relaxation with a finite-volume discretization (Thomas and Walters, 1985) and (2) an explicit-implicit MacCormack (1981) scheme with a finite-difference discretization, is compared in two-dimensional simulations of supersonic flow past a flat plate with leading edge, a rearward-facing step, a 10-deg compression corner, a NACA 0012 airfoil at high angle of attack, and a cavity. The algebraic turbulence model, the solution methods, and the boundary conditions and SIMD coding are explained, and the results are presented in tables and graphs and characterized with reference to published experimental data. Scheme (1) is found to converge more rapidly and to give more accurate results than (2) in a wide range of problem types.

Baysal, O.↗

NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗

NASA NTRS1990

A comparison of two central difference schemes for solving the Navier-Stokes equations

Five viscous transonic airfoil cases were computed by two significantly different computational fluid dynamics codes: An explicit finite-volume algorithm with multigrid, and an implicit finite-difference approximate-factorization method with Eigenvector diagonalization. Both methods are described in detail, and their performance on the test cases is compared. The codes utilized the same grids, turbulence model, and computer to provide the truest test of the algorithms. The two approaches produce very similar results, which, for attached flows, also agree well with experimental results; however, the explicit code is considerably faster.

Maksymiuk, C. M.↗

NASA NTRS1992

Freestream capturing for moving coordinates in three dimensions

A detailed formula is developed that can be used in both finite-volume (FV) and finite-difference (FD) methods for constructing freestream capturing metrics in space and time. It is shown that, considering an FV cell on the FD grid, the freestream capturing metrics in space and time can be constructed from the FD formulation. The approach is costly but guarantees the global conservation for an arbitrary motion of the grid.

Obayashi, Shigeru↗

NASA NTRS1995

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

Hollis, Brian R.↗

NASA NTRS1998

Analysis of Linear Aerospike Plume Induced X-33 Base Heating Environment

Computational analysis is conducted to study the effect of an linear aerospike engine plume on the X-33 base-heating environment during ascent flight. To properly account for the freestream-body interaction and to allow for potential plume-induced flow-separation, the thermo-flowfield of the entire vehicle at several trajectory points is computed. A sequential grid-refinement technique is used in conjunction with solution-adaptive, patched, and embedded grid methods to limit the model to a manageable size. The computational methodology is based on a three-dimensional, finite-difference, viscous flow, chemically reacting, pressure-based computational fluid dynamics formulation, and a three-dimensional, finite-volume, spectral-line based weighted-sum-of-gray-gases absorption, computational radiation heat transfer formulation. The computed forebody and afterbody surface pressure coefficients and base pressure characteristic curves are compared with those of a cold-flow test. The predicted convective and radiative base-heat fluxes, the effect of base-bleed, and the potential of plume-induced flow separation are presented.

Wang, Ten-See↗

NASA NTRS1999

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Bui, Trong T.↗

NASA NTRS1996

Challenges and Accomplishments of Viscous Incompressible Flow Computations in Aerospace and Beyond

Recent progress in incompressible Navier-Stokes solution methods will be presented. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. Both steady- and unsteady-solution algorithms and their salient features are discussed. A summary of our recent progress in flow solver development is given followed by numerical studies of a few example problems of our current interest. Solvers discussed here are based on structured-grid approach using finite-difference or finite-volume frame work. This short course will be delivered in three one-our lectures. The material in the course are collected from the work performed by the Incompressible Navier-Stokes group at NASA Ames Research Center over the past several years, and can be found in our publications widely disseminated in the US and abroad. This short course is sponsored by AGARD Consultant and Exchange Program under Support Project P-110.

Kwak, Dochan↗

NASA NTRS2002

Incompressible Navier-Stokes Solvers in Primative Variables and their Applications to Steady and Unsteady Flow Simulations

This paper reviews recent progress made in incompressible Navier-Stokes simulation procedures and their application to problems of engineering interest. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. A summary of efforts in flow solver development is given followed by numerical studies of a few example problems of current interest. Both steady and unsteady solution algorithms and their salient features are discussed. Solvers discussed here are based on a structured-grid approach using either a finite -difference or a finite-volume frame work. As a grand-challenge application of these solvers, an unsteady turbopump flow simulation procedure has been developed which utilizes high performance computing platforms. In the paper, the progress toward the complete simulation capability of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of two parallel computing algorithms that have been implemented in the INS3D code. The relative motion of the grid systems for the rotorstator interaction was obtained using overact grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on SCSI Origin 3000 systems at NASA Ames Research Center. The same procedure has been extended to the development of NASA-DeBakey Ventricular Assist Device (VAD) that is based on an axial blood pump. Computational, and clinical analysis of this device are presented.

Kiris, Cetin C.↗

NASA NTRS2013

File Specification for GEOS-5 FP (Forward Processing)

The GEOS-5 FP Atmospheric Data Assimilation System (GEOS-5 ADAS) uses an analysis developed jointly with NOAA's National Centers for Environmental Prediction (NCEP), which allows the Global Modeling and Assimilation Office (GMAO) to take advantage of the developments at NCEP and the Joint Center for Satellite Data Assimilation (JCSDA). The GEOS-5 AGCM uses the finite-volume dynamics (Lin, 2004) integrated with various physics packages (e.g, Bacmeister et al., 2006), under the Earth System Modeling Framework (ESMF) including the Catchment Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a three-dimensional variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic, inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003). The GSI implementation for GEOS-5 FP incorporates a set of recursive filters that produce approximately Gaussian smoothing kernels and isotropic correlation functions. The GEOS-5 ADAS is documented in Rienecker et al. (2008). More recent updates to the model are presented in Molod et al. (2011). The GEOS-5 system actively assimilates roughly 2 × 10(exp 6) observations for each analysis, including about 7.5 × 10(exp 5) AIRS radiance data. The input stream is roughly twice this volume, but because of the large volume, the data are thinned commensurate with the analysis grid to reduce the computational burden. Data are also rejected from the analysis through quality control procedures designed to detect, for example, the presence of cloud. To minimize the spurious periodic perturbations of the analysis, GEOS-5 FP uses the Incremental Analysis Update (IAU) technique developed by Bloom et al. (1996). More details of this procedure are given in Appendix A. The assimilation is performed at a horizontal resolution of 0.3125-degree longitude by 0.25- degree latitude and at 72 levels, extending to 0.01 hPa. All products are generated at the native resolution of the horizontal grid. The majority of data products are time-averaged, but four instantaneous products are also available. Hourly data intervals are used for two-dimensional products, while 3-hourly intervals are used for three-dimensional products. These may be on the model's native 72-layer vertical grid or at 42 pressure surfaces extending to 0.1 hPa. This document describes the gridded output files produced by the GMAO near real-time operational FP, using the most recent version of the GEOS-5 assimilation system. Additional details about variables listed in this file specification can be found in a separate document, the GEOS-5 File Specification Variable Definition Glossary. Documentation about the current access methods for products described in this document can be found on the GMAO products page: http://gmao.gsfc.nasa.gov/products/.

GSI↗

NASA NTRS2017

High-order Accurate Finite-Volume Formulations for the Pressure Gradient Force in Layered Ocean Models

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates andor terrain-following representations.

pressure gradient force↗

NASA NTRS2020

Verification of Anisotropic Mesh Adaptation for Turbulent Simulations over ONERA M6 Wing

Unstructured anisotropic mesh adaptation is known to be an efficient way to control discretization errors in Computational Fluid Dynamics (CFD) simulations. Method verification is required to provide the confidence for routine use in production analysis. The current work aims at verification of anisotropic mesh adaptation for RANS simulations over the ONERA M6 wing. The present verification study is performed using four different flow solvers, three different implementations of the metric field, and three mesh mechanics packages. Two of the flow solvers use stabilized finite-element discretizations (FUN3D-SFE and GGNS), one uses finite-volume discretization (FUN3D-FV), and the last one uses mixed finite-volume and finite element discretizations (Wolf). The mesh adaptation is based on an error estimator that aims to control the quadratic error term in the linear interpolation of Mach number. Two sets of adaptations were performed; the first one controls the interpolation error in L2 norm and the second one controls the interpolation error in L4 norm. Convergence studies were performed on the forces and the pitching moment using all four solvers, and the results are compared with previously verified convergence studies on fixed (nonadapted) meshes. Both forces and pitching moment on adapted meshes are found to be converging to the fine mesh values faster than those on fixed meshes. In addition to forces and moments, convergence of surface pressure and skin friction coefficients at various measurement locations on the wing are also presented. Adapted-mesh surface pressure distributions agree with the fine fixed mesh pressure distributions. Adapted-mesh skin friction distributions contain high frequency noise with mean values approaching the fixed mesh pressure skin friction distributions.

Aravind Balan↗