SEARCH · Engineering Papers

Results for “Numerical Methods”

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.

SourceResearch connectionFrom yearThrough year

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

At least 1,153 records · Page 64

All sources NASA NTRS DOE OSTI

NASA NTRS2011

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Solakiewicz, Richard↗

DOE OSTI2013

Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics

Mathematical modeling of ice sheets is complicated by the non-linearity of the governing equations and boundary conditions. Standard grid-based methods require complex front tracking techniques and have limited capability to handle large material deformations and abrupt changes in bottom topography. As a consequence, numerical methods are usually restricted to shallow ice sheet and ice shelf approximations. We propose a new smoothed particle hydrodynamics (SPH) non-Newtonian model for coupled ice sheet and ice shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation, and material fragmentation. In this paper, SPH is used to study 3D ice sheet/ice shelf behavior, and the dynamics of the grounding line. The steady state position of the grounding line obtained from SPH simulations is in good agreement with laboratory observations for a wide range of simulated bedrock slopes, and density ratios, similar to those of ice and sea water. The numerical accuracy of the SPH algorithm is verif;ed by simulating Poiseuille flow, plane shear flow with free surface and the propagation of a blob of ice along a horizontal surface. In the laboratory experiment, the ice was represented with a viscous Newtonian fluid. In the present work, however, the ice is modeled as both viscous Newtonian fluid and non-Newtonian fluid, such that the effect of non-Newtonian rheology on the dynamics of grounding line was examined. The non-Newtonian constitutive relation is prescribed to be Glen’s law for the creep of polycrystalline ice. A V-shaped bedrock ramp is further introduced to model the real geometry of bedrock slope.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Performance of the rigorous renormalization group for first-order phase transitions and topological phases

Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in one-dimensional systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau [Nat. Phys. 11, 566 (2015)1745-247310.1038/nphys3345]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first-order phase transitions and in symmetry-protected topological phases. Our study is motivated by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first-order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near-)degenerate manifolds. Furthermore, the rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines well-ordered, accurate energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

An investigation of the multi-mode Richtmyer-Meshkov instability at a gas/HE interface using Pagosa

Here, in this work, we present a hydrocode Pagosa and explore the Richtmyer-Meshkov Instability (RMI) at an air/high explosive (HE) interface for the first time that is important but has not received much attention yet in the high explosive safety field. Thus, the presented Pagosa can be expected to predict the whole deflagration-to-detonation transition (DDT) process in future. In Pagosa, spatial discretization is implemented on cubic staggered grids by computing different variables at the vertex and the cell center, respectively, a special operator-splitting technique is employed to reduce the computational cost, and an artificial viscosity is added to handle the discontinuous shock waves in our simulations. To quantitatively evaluate the capability of Pagosa to solve these kinds of instabilities, the single mode Rayleigh-Taylor instability (RTI) and the multimode RMI at an air/SF 6 interface are first performed, respectively. The Pagosa results are compared with the related numerical solutions in the existing references and the experimental result. Moreover, a theoretical derivation of growth of RTI is also provided based on our numerical method. Subsequently, we explore the multi-mode RMI at an air/HE interface as well as the effects of several factors using Pagosa. Numerical results show that Pagosa is a powerful toolset to generate the right structures and the amplitude of RTI and RMI at an air/SF 6 interface. The solid HE can be penetrated by a strong shock wave and forms RMI deformations. The RMI at an air/HE interface behaves very different than at an air/SF 6 interface, periodic, decreased oscillation is observed due to material character, and is very sensitive to the initial simulation settings, that is, a tiny change in physical quantities will lead to a remarkable RMI structure, which is also observed in a shock bubble interaction. The findings in this work are significant, and will present a new insight for the high explosive field.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

A consistent approach for the development of a comprehensive data base of time-dependent parameters for concrete engineered barriers

This paper presents a consistent approach for the development of a comprehensive data base of time-dependent hydraulic and transport parameters for concrete engineered barriers of the future Dessel near surface repository for low level waste. The parameter derivation is based on integration of selected data obtained through an extensive literature review, data from experimental studies on cementitious materials specific for the Dessel repository and numerical modelling using physically-based models of water and mass transport. Best estimate parameter values for assessment calculations are derived, together with source and expert range and their probability density function wherever the data was sufficient. We further discuss a numerical method for up-scaling laboratory derived parameter values to the repository scale; the resulting large-scale effective parameters are commensurate with numerical grids used in models for radionuclide migration. To accommodate different levels of conservatism in the various assessment calculations defined by ONDRAF/NIRAS, several sets of parameter values have been derived based on assumptions that introduce different degrees of conservatism. For pertinent parameters, the time evolution of such properties due to the long-term concrete degradation is also addressed. The implementation of the consistent approach is demonstrated by considering the pore water diffusion coefficient as an example. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2014

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

Our two key accomplishments in the first three years were towards the development of, (1) a mathematically rigorous and at the same time computationally flexible framework for parallelization of Kinetic Monte Carlo methods, and its implementation on GPUs, and (2) spatial multilevel coarse-graining methods for Monte Carlo sampling and molecular simulation. A common underlying theme in both these lines of our work is the development of numerical methods which are at the same time both computationally efficient and reliable, the latter in the sense that they provide controlled-error approximations for coarse observables of the simulated molecular systems. Finally, our key accomplishment in the last year of the grant is that we started developing (3) pathwise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of nonequilibrium extended (high-dimensional) systems. We discuss these three research directions in some detail below, along with the related publications.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

The exact solution of the monoenergetic transport equation for critical cylinders

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.

Westfall, R. M.↗

NASA NTRS1990

Numerical simulation of turbulent flows around airfoil and wing

During the last years the simulation of compressible viscous flows has received much attention. While the numerical methods were improved drastically, a satisfactory modeling of the Reynolds stresses is still missing. In this paper, after a short description of the numerical procedure used for solving the Reynolds equations, experiments with a promising simple turbulence model are discussed.

Marx, Yves P.↗

NASA NTRS1992

Ship viscous flow: A report on the 1990 SSPA-IIHR Workshop

To assess the state of the art in ship viscous flow computation a Workshop was organized in 1990 by three organizations: SSPA Maritime Consulting AB, Chalmers University of Technology, and the Iowa Institute of Hydraulic Research. Two test cases were specified by the organizers and sent out to all interested research groups, which were asked to submit results in a prescribed format. In September 1990 a meeting was held at Chalmers University of Technology. All results had then been collected and presented in a common format, and the theories based on responses to a questionnaire sent out earlier. During the meeting, each research group was first given the opportunity to briefly introduce their method and results. Thereafter, a considerable time was spent on general discussions on the performance of the different methods considering the differences in the underlying theories. Specific items that were addressed were grid generation, governing equations, boundary conditions, turbulence modelling, and numerical methods. Practical aspects of the results, for instance from the point of view of propeller design, were also discussed. The Workshop Proceedings contain a description of the participating methods, and the results of both test cases. In the present paper, a summary of the Workshop and its results is presented.

Patel, Virendra C.↗

NASA NTRS1993

Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

Myhill, Elizabeth A.↗

NASA NTRS2001

Sources of Variability in Chlorophyll Analysis by Fluorometry and by High Performance Liquid Chromatography

The need for accurate determination of chlorophyll a (chl a) is of interest for numerous reasons. From the need for ground-truth data for remote sensing to pigment detection for laboratory experimentation, it is essential to know the accuracy of the analyses and the factors potentially contributing to variability and error. Numerous methods and instrument techniques are currently employed in the analyses of chl a. These methods range from spectrophotometric quantification, to fluorometric analysis and determination by high performance liquid chromatography. Even within the application of HPLC techniques, methods vary. Here we provide the results of a comparison among methods and provide some guidance for improving the accuracy of these analyses. These results are based on a round-robin conducted among numerous investigators, including several in the Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) and HyCODE Programs. Our purpose here is not to present the full results of the laboratory intercalibration; those results will be presented elsewhere. Rather, here we highlight some of the major factors that may contribute to the variability observed. Specifically, we aim to assess the comparability of chl a analyses performed by fluorometry and HPLC, and we identify several factors in the analyses which may contribute disproportionately to this variability.

VanHeukelem, Laurie↗

NASA NTRS1997

Numerical Simulation of Unsteady Aerodynamic Models

This report documents the results of the numerical simulations of unsteady aerodynamic models. The results focus on numerical accuracy and efficiency, and the robustness of the numerical methods. The aerodynamic models includes the classical Wagner and Kussner functions and the Leishman-Beddoes dynamic stall model. The simulations includes the numerical approximations of the Duhamel's integrals using both indicial (step) and impulse responses, the numerical integrations of the state-space models, and the exact solutions. The report also presents the conversion among different model representations.

Nguyen, Khanh Q.↗

NASA NTRS2001

Development of a Hybrid RANS/LES Method for Turbulent Mixing Layers

Significant research has been underway for several years in NASA Glenn Research Center's nozzle branch to develop advanced computational methods for simulating turbulent flows in exhaust nozzles. The primary efforts of this research have concentrated on improving our ability to calculate the turbulent mixing layers that dominate flows both in the exhaust systems of modern-day aircraft and in those of hypersonic vehicles under development. As part of these efforts, a hybrid numerical method was recently developed to simulate such turbulent mixing layers. The method developed here is intended for configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. Interest in Large Eddy Simulation (LES) methods have increased in recent years, but applying an LES method to calculate the wide range of turbulent scales from small eddies in the wall-bounded regions to large eddies in the mixing region is not yet possible with current computers. As a result, the hybrid method developed here uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall-bounded regions entering a mixing section and uses a LES procedure to calculate the mixing-dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. With this technique, closure for the RANS equations is obtained by using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The LES equations are closed using the Smagorinsky subgrid scale model. Although the function of the Cebeci-Smith model to replace all of the turbulent stresses is quite different from that of the Smagorinsky subgrid model, which only replaces the small subgrid turbulent stresses, both are eddy viscosity models and both are derived at least in part from mixing-length theory. The similar formulation of these two models enables the RANS and LES equations to be solved with a single solution scheme and computational grid. The hybrid RANS-LES method has been applied to a benchmark compressible mixing layer experiment in which two isolated supersonic streams, separated by a splitter plate, provide the flows to a constant-area mixing section. Although the configuration is largely two dimensional in nature, three-dimensional calculations were found to be necessary to enable disturbances to develop in three spatial directions and to transition to turbulence. The flow in the initial part of the mixing section consists of a periodic vortex shedding downstream of the splitter plate trailing edge. This organized vortex shedding then rapidly transitions to a turbulent structure, which is very similar to the flow development observed in the experiments. Although the qualitative nature of the large-scale turbulent development in the entire mixing section is captured well by the LES part of the current hybrid method, further efforts are planned to directly calculate a greater portion of the turbulence spectrum and to limit the subgrid scale modeling to only the very small scales. This will be accomplished by the use of higher accuracy solution schemes and more powerful computers, measured both in speed and memory capabilities.

Georgiadis, Nicholas J.↗

DOE OSTI2024

A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulations

Modeling strong shock waves in fluids remains a persistent challenge in computational physics. Essential to research efforts in industry and defense, numerous methods have been devised to improve the accuracy and efficiency of shock simulations. A novel, hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach is capable of further improving efficiency and retaining accuracy by exploiting the favorable characteristics of each respective method. This hybrid approach is presented for shock capturing in compressible fluids. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. The performance of the hybrid FVM-SPH scheme, compared to the individual FVM and SPH methods, is assessed in 1 kt and 10 kt blast simulations. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy and characteristics. The hybrid approach had a relative speedup of 11.3x and 22.3x over the FVM and SPH approaches for the 1 kt simulation and a relative speedup of 14.7x and 20.9x over the FVM and SPH approaches for the 10 kt simulation. The hybrid SPH algorithm enables future compressible fluid simulations with more extensive capabilities than grid-based methods alone, presenting potential applications in modeling fluid-structure interactions and solid deformation and fracturing in blast simulations.

Myers, Conner↗

DOE OSTI2025

Overset-Grid Method with Smooth Orbital Partitioning for Molecular Scattering Calculations

To solve molecular photoionization and electron scattering problems, we use an overset-grid representation of electronic continuum functions, which has an extended central spherical grid that overlaps small spherical grids (subgrids) centered on each atom of a polyatomic molecule. Here, in this work, we present an improved algorithm that smoothly partitions the total wave function between the central grid and the atomic subgrids. The smooth partitioning allows one to use approximately one-fourth the number of partial waves on the central grid compared to our previous implementation with switching functions. The resulting numerical method for treating electron scattering and photoionization of polyatomic molecules combines the accuracy and flexibility of pure numerical grid representations with the rapid convergence of hybrid combinations of atom-centered basis-set expansions and grid methods. The overset-grid representation is implemented using the complex Kohn variational principle for scattering and photoionization amplitudes. The faster convergence with respect to the number of central grid partial waves is demonstrated and accuracy is verified by comparisons with the previous implementation and with far more computationally demanding single-center numerical expansions in electron-molecule scattering and photoionization calculations on the neon dimer (Ne 2 ) system, carbon tetrafluoride (CF 4 ) molecule, and the pyridine (C 5 H 5 N) molecule in the static-exchange approximation.

Molecules↗

NASA NTRS1987

Numerical tests of a modified full implicit continuous Eulerian (FICE) scheme with projected normal characteristic boundary conditions for MHD flows

A numerical method has been developed based on a modified full implicit continuous Eulerian (FICE) scheme and projected normal characteristic boundary conditions for simulating MHD flows which undergo a long process of evolution. An astrophysical flow is chosen for illustration of this procedure, and numerical tests are made to verify the computational stability and physically realistic solution. Three computational tests have been accomplished; they are tests of solving methods, characteristic boundary condition, and time steps. The tests show that the program from the modified FICE scheme with proper boundary conditions and time steps can be made numerically stable for a time long enough to obtain physically plausible solutions.

Wu, S. T.↗

NASA NTRS2009

The Capillary Flow Experiments Aboard the International Space Station: Increments 9-15

This report provides a summary of the experimental, analytical, and numerical results of the Capillary Flow Experiment (CFE) performed aboard the International Space Station (ISS). The experiments were conducted in space beginning with Increment 9 through Increment 16, beginning August 2004 and ending December 2007. Both primary and extra science experiments were conducted during 19 operations performed by 7 astronauts including: M. Fincke, W. McArthur, J. Williams, S. Williams, M. Lopez-Alegria, C. Anderson, and P. Whitson. CFE consists of 6 approximately 1 to 2 kg handheld experiment units designed to investigate a selection of capillary phenomena of fundamental and applied importance, such as large length scale contact line dynamics (CFE-Contact Line), critical wetting in discontinuous structures (CFE-Vane Gap), and capillary flows and passive phase separations in complex containers (CFE-Interior Corner Flow). Highly quantitative video from the simply performed flight experiments provide data helpful in benchmarking numerical methods, confirming theoretical models, and guiding new model development. In an extensive executive summary, a brief history of the experiment is reviewed before introducing the science investigated. A selection of experimental results and comparisons with both analytic and numerical predictions is given. The subsequent chapters provide additional details of the experimental and analytical methods developed and employed. These include current presentations of the state of the data reduction which we anticipate will continue throughout the year and culminate in several more publications. An extensive appendix is used to provide support material such as an experiment history, dissemination items to date (CFE publication, etc.), detailed design drawings, and crew procedures. Despite the simple nature of the experiments and procedures, many of the experimental results may be practically employed to enhance the design of spacecraft engineering systems involving capillary interface dynamics.

Jenson, Ryan M.↗

DOE OSTI2019

eSHIVA in IOTA: Experiment on Stochasticity in High Intensity Variable Accelerators

Nonlinear integrable optics, the basis of IOTA, is a very special form of Hamiltonian system, called completely integrable. The consequences are many, most importantly the absence of fixed points that are in one-to-one correspondence with (overlapping) resonances. This, in turn, does not limit the dynamic aperture and allows large amplitude dependent tune shifts without adverse effects. In fact, it helps significantly in alleviating issues with collective instabilities. We developed and tested different numerical methods to give a more complete picture of the dynamics of integrable and near-integrable nonlinear Hamiltonian systems consisting of motion of charged particles in electromagnetic fields. Comparison of the results allowed us to discern real phenomena from numerical artifacts and come up with conclusions that will facilitate pushing the intensity frontier in beam dynamics even further for the benefit of the accelerator community as a whole and society as the consequence of the science and technological advancements it will make possible. We concluded that, while novel structure preserving integrators would be ideal, symplectic methods under mild restrictions offer adequate invariant preservation. We especially highlighted the very good performance of the Stormer-Verlet method at low accuracy and a modified Lobatto method at high accuracy for the Integrable Optics Test Accelerator (IOTA). However, we showed that symplectic integrators are limited by numerically induced resonances, which make interpretation of some simulation results challenging. These limitations and workarounds have been addressed.The nonlinear integrable optics test accelerator IOTA at Fermilab -- a very special experimental accelerator designed to investigate nonlinear optics under severe space-charge conditions – has recently completed its construction and initial commissioning of the ring has begun. We report first, under 2 (a) below: the progress on the nonlinear tune-shift measurements for various values of the nonlinear strength potential and their comparison with theoretical expectations, thus benchmarking the nonlinear characteristics of the ring; then, under 2 (b) below: the progress on simulation and design of a gas-jet monitor to measure beam profile and in particular its diffusive halo, expected to develop during stochastic diffusion of large amplitude particles under nonlinear forces of the magnetic lattice and Coulomb space-charge. Since the development of a proton beam source in IOTA is delayed and to be completed only in the future pending financial support, the gas-jet monitor is planned for testing with real proton beams elsewhere at Fermilab (e.g. in the Main Injector or PIP-II source possibly). Once proton beams are available in IOTA, the understanding of the nonlinear properties of IOTA combined with the developed gas-jet monitor, will enable a thorough experimental analysis of nonlinear stochastic diffusion in IOTA nonlinear ring, and boosted by proper theoretical understanding of the same.

43 PARTICLE ACCELERATORS↗