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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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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Implementing abstract multigrid or multilevel methods

Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult.

Douglas, Craig C.↗
NASA NTRS1994

Nonlinear hydrodynamics of cosmological sheets. 1: Numerical techniques and tests

We present the numerical techniques and tests used to construct and validate a computer code designed to study the multidimensional nonlinear hydrodynamics of large-scale sheet structures in the universe, especially the fragmentation of such structures under various instabilities. This code is composed of two codes, the hydrodynamical code ZEUS-2D and a particle-mesh code. The ZEUS-2D code solves the hydrodynamical equations in two dimensions using explicit Eulerian finite-difference techniques, with modifications made to incorporate the expansion of the universe and the gas cooling due to Compton scattering, bremsstrahlung, and hydrogen and helium cooling. The particle-mesh code solves the equation of motion for the collisionless dark matter. The code uses two-dimensional Cartesian coordinates with a nonuniform grid in one direction to provide high resolution for the sheet structures. A series of one-dimensional and two-dimensional linear perturbation tests are presented which are designed to test the hydro solver and the Poisson solver with and without the expansion of the universe. We also present a radiative shock wave test which is designed to ensure the code's capability to handle radiative cooling properly. And finally a series of one-dimensional Zel'dovich pancake tests used to test the dark matter code and the hydro solver in the nonlinear regime are discussed and compared with the results of Bond et al. (1984) and Shapiro & Struck-Marcell (1985). Overall, the code is shown to produce accurate and stable results, which provide us a powerful tool to further our studies.

Anninos, Wenbo Y.↗
NASA NTRS2023

Developing a Radar Signal Simulator for the Community Radiative Transfer Model

Active radar instruments provide vertically resolved clouds and precipitation measurements that cannot be provided by the passive instruments. These active measurements are not conventionally assimilated into the data assimilation systems because of the lack of fast forward radiative transfer models and also difficulties in the error modelling of the measurements. This paper describes the development, evaluation, and sensitivity analysis for a forward radar model implemented in the Community Radiative Transfer Model (CRTM). The scattering properties required by the forward model are provided by the hydrometeor lookup tables that were generated using the discrete dipole approximation. The model is able to calculate both the reflectivity and the attenuated reflectivity for any given radar instrument at any given zenith angles as long as CRTM instrument specific coefficients are available. The evaluation using CloudSat measurements shows a very good agreement between the simulations and measurements as long as the input profiles of hydrometeors are consistent with the measured reflectivity profiles. Major sources contributing to the differences between the measured and simulated reflectivities are input hydrometeor profiles, scattering lookup tables, lack of melting layer in the forward model, CRTM scattering solvers, and attenuation calculations. In addition to the forward model, both Tangent Linear and Adjoint of the model are also implemented and tested within CRTM. These components may be required by some data assimilation systems for the assimilation of radar measurements.

radar↗
DOE OSTI2018

Adaptive Model Reduction for Parareal in Time Method for Transient Stability Simulations

Real time or faster than real time simulation can enable system operators to foresee the effect of crucial contingencies on the power system dynamics and take timely actions to prevent system instability. Parareal in time method uses concurrent computations on different segments of the time domain of interest to speed up the dynamic simulations. This paper describes the application of an adaptive nonlinear model reduction method in improving computational speed of the Parareal solver. The proposed method adaptively switches between a hybrid system with selective linearization and a completely linear system based on the size of a disturbance. The functions in the hybrid system are linearized based on the electrical distance between specific generators and the area where disturbances originated. The proposed method is tested on the 327-machine 2383-bus Polish system.

Osipov, Denis↗
DOE OSTI2019

IMPLEMENTATION OF DETAILED CHEMISTRY MECHANISMS IN ENGINE SIMULATIONS

The stiffness of large chemistry mechanisms has been proved to be a major hurdle toward predictive engine simulations. As a result, detailed chemistry mechanisms with a few thousand species need to be reduced based on target conditions so that they can be accommodated within the available computational resources. The computational cost of simulations typically increases super-linearly with the number of species and reactions. This work aims to bring detailed chemistry mechanisms within the realm of engine simulations by coupling the framework of unsteady flamelets and fast chemistry solvers. A previously developed tabulated flamelet model (TFM) framework for nonpremixed combustion was used in this study. The flamelet solver consists of the traditional operator-splitting scheme with variable coefficient ordinary differential equation (ODE) solver (VODE) and a numerical Jacobian for solving the chemistry. In order to use detailed mechanisms with thousands of species, a new framework with the Livermore solver for ODEs in sparse form (LSODES) chemistry solver and an analytical Jacobian was implemented in this work. Results from 1D simulations show that with the new framework, the computational cost is linearly proportional to the number of species in a given chemistry mechanism. As a result, the new framework is 2-3 orders of magnitude faster than the conventional variable coefficient ODE (VODE) solver for large chemistry mechanisms. This new framework was used to generate unsteady flamelet libraries for ndodecane using a detailed chemistry mechanism with 2755 species and 11,173 reactions. The engine combustion network (ECN) spray A experiments, which consist of an igniting n-dodecane spray in turbulent, high-pressure engine conditions are simulated using large eddy simulations (LES) coupled with detailed mechanisms. A grid with 0.06 mm minimum cell size and 22 x 10(6) peak cell count was implemented. The framework is validated across a range of ambient temperatures against ignition delay and liftoff lengths (LOLs). Qualitative results from the simulations were compared against experimental OH and CH2O planar laser-induced fluorescence (PLIF) data. The models are able to capture the spatial and temporal trends in species compared to those observed in the experiments. Quantitative and qualitative comparisons between the predictions of the reduced and detailed mechanisms are presented in detail. The main goal of this study is to demonstrate that detailed reaction mechanisms (similar to 1000 species) can now be used in engine simulations with a linear increase in computation cost with number of species during the tabulation process and a small increase in the 3D simulation cost.

Kundu, Prithwish↗
DOE OSTI2018

A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad–Shafranov equation, the solution of which determines the poloidal component of the magnetic field. When the geometry of the confinement region is known, the problem becomes an interior Dirichlet boundary value problem. We propose a high order solver based on the Hybridizable Discontinuous Galerkin method. The resulting algorithm (1) provides high order of convergence for the flux function and its gradient, (2) incorporates a novel method for handling piecewise smooth geometries by extension from polygonal meshes, (3) can handle geometries with non-smooth boundaries and x-points, and (4) deals with the semi-linearity through an accelerated two-grid fixed-point iteration. The effectiveness of the algorithm is verified with computations for cases where analytic solutions are known on configurations similar to those of actual devices (ITER with single null and double null divertor, NSTX, ASDEX upgrade, and Field Reversed Configurations).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Precise 2D electric field density simulations for superconducting quantum devices

Dielectric loss due to two-level systems is a limiting factor for superconducting qubit relaxation times. These losses arise mostly from nanometer-scale interfacial defect regions in superconducting devices with planar dimensions of microns to millimeters, thus making it resource intensive to accurately simulate the electric field density in these regions with traditional electromagnetic solvers. In this work, we demonstrate a fast boundary integral equation solver that allows precise simulation of electric field density in these thin regions, showing a speedup of around two orders of magnitude over traditional solvers, with relative errors around $10^{-7}$ for a ten-minute solution runtime. By computing participation ratios through Green's first identity without squaring the electric field, our approach is less susceptible to the field singularities near conductor corners. We apply this solver to a basic untrenched coplanar waveguide cross-section, showing that the common assumption of participation ratio linearity with dielectric constant holds well for some interfaces and not others; in particular, while the metal-air (MA) top and corner follow this linear relationship strongly, the MA sidewall does not. We then compare isotropic and anisotropic etching, showing that the MA sidewall and the metal-air-substrate triple junction are the most strongly affected. We are currently leveraging this solver to explore geometries that will uniquely isolate the participation ratios of the different dielectrics. Finally, we are working to combine this solver framework with a full 3D microwave solver to accurately calculate participation ratios for the thin dielectrics that are known sources of loss in superconducting qubits.

Gimbutas, Z. [NIST, Boulder] (ORCID:00000003320982↗
NASA NTRS1999

A Computational/Experimental Study of Two Optimized Supersonic Transport Designs and the Reference H Baseline

Two supersonic transport configurations designed by use of non-linear aerodynamic optimization methods are compared with a linearly designed baseline configuration. One optimized configuration, designated Ames 7-04, was designed at NASA Ames Research Center using an Euler flow solver, and the other, designated Boeing W27, was designed at Boeing using a full-potential method. The two optimized configurations and the baseline were tested in the NASA Langley Unitary Plan Supersonic Wind Tunnel to evaluate the non-linear design optimization methodologies. In addition, the experimental results are compared with computational predictions for each of the three configurations from the Enter flow solver, AIRPLANE. The computational and experimental results both indicate moderate to substantial performance gains for the optimized configurations over the baseline configuration. The computed performance changes with and without diverters and nacelles were in excellent agreement with experiment for all three models. Comparisons of the computational and experimental cruise drag increments for the optimized configurations relative to the baseline show excellent agreement for the model designed by the Euler method, but poorer comparisons were found for the configuration designed by the full-potential code.

Cliff, Susan E.↗
DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2022

Foraging with MUSHROOMS: A Mixed-integer Linear Programming Scheduler for Multimessenger Target of Opportunity Searches with the Zwicky Transient Facility

Electromagnetic follow-up of gravitational-wave detections is very resource intensive, taking up hours of limited observation time on dozens of telescopes. Creating more efficient schedules for follow-up will lead to a commensurate increase in counterpart location efficiency without using more telescope time. Widely used in operations research and telescope scheduling, mixed-integer linear programming is a strong candidate to produce these higher-efficiency schedules, as it can make use of powerful commercial solvers that find globally optimal solutions to provided problems. We detail a new target-of-opportunity scheduling algorithm designed with Zwicky Transient Facility in mind that uses mixed-integer linear programming. We compare its performance to gwemopt, the tuned heuristic scheduler used by the Zwicky Transient Facility and other facilities during the third LIGO–Virgo gravitational-wave observing run. This new algorithm uses variable-length observing blocks to enforce cadence requirements and to ensure field observability, along with having a secondary optimization step to minimize slew time. We show that by employing a hybrid method utilizing both this scheduler and gwemopt, the previous scheduler used, in concert, we can achieve an average improvement in detection efficiency of 3%–11% over gwemopt alone for a simulated binary neutron star merger data set consistent with LIGO–Virgo's third observing run, highlighting the potential of mixed-integer target of opportunity schedulers for future multimessenger follow-up surveys.

B Parazin↗
DOE OSTI2018

A multigrid waveform relaxation method for solving the poroelasticity equations

In this work, a multigrid waveform relaxation method is proposed for solving a collocated finite difference discretization of the linear Biot’s model. This gives rise to the first space–time multigrid solver for poroelasticity equations in the literature. The waveform relaxation iteration is based on a point-wise Vanka smoother that couples the pressure variable at a grid-point with the displacements around it. A semi-algebraic mode analysis is proposed to theoretically analyze the convergence of the multigrid waveform relaxation algorithm. This analysis is novel since it combines the semi-algebraic analysis, suitable for parabolic problems, with the non-standard analysis for overlapping smoothers. The practical utility of the method is illustrated through several numerical experiments in one and two dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

All-electron APW+ lo calculation of magnetic molecules with the SIRIUS domain-specific package

We report APW+lo (augmented plane wave plus local orbital) density functional theory (DFT) calculations of large molecular systems using the domain specific SIRIUS multi-functional DFT package. The APW and FLAPW (full potential linearized APW) task and data parallelism options and the advanced eigen-system solver provided by SIRIUS can be exploited for performance gains in ground state Kohn–Sham calculations on large systems. This approach is distinct from our prior use of SIRIUS as a library backend to another APW+lo or FLAPW code. We benchmark the code and demonstrate performance on several magnetic molecule and metal organic framework systems. We show that the SIRIUS package in itself is capable of handling systems as large as a several hundred atoms in the unit cell without having to make technical choices that result in the loss of accuracy with respect to that needed for the study of magnetic systems.

Chemistry↗
DOE OSTI2020

An investigation of Newton-Sketch and subsampled Newton methods

Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. In this work, we study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not been investigated in the optimization literature. Additionally, our study focuses on practical versions of the two methods in which the resulting linear systems of equations are solved approximately, at every iteration, using an iterative solver. The advantages of using the conjugate gradient method vs. a stochastic gradient iteration are revealed through a set of numerical experiments, and a complexity analysis of the Hessian subsampling method is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Generating Euler Diagrams Through Combinatorial Optimization

Abstract Can a given set system be drawn as an Euler diagram? We present the first method that correctly decides this question for arbitrary set systems if the Euler diagram is required to represent each set with a single connected region. If the answer is yes, our method constructs an Euler diagram. If the answer is no, our method yields an Euler diagram for a simplified version of the set system, where a minimum number of set elements have been removed. Further, we integrate known wellformedness criteria for Euler diagrams as additional optimization objectives into our method. Our focus lies on the computation of a planar graph that is embedded in the plane to serve as the dual graph of the Euler diagram. Since even a basic version of this problem is known to be NP‐hard, we choose an approach based on integer linear programming (ILP), which allows us to compute optimal solutions with existing mathematical solvers. For this, we draw upon previous research on computing planar supports of hypergraphs and adapt existing ILP building blocks for contiguity‐constrained spatial unit allocation and the maximum planar subgraph problem. To generate Euler diagrams for large set systems, for which the proposed simplification through element removal becomes indispensable, we also present an efficient heuristic. We report on experiments with data from MovieDB and Twitter. Over all examples, including 850 non‐trivial instances, our exact optimization method failed only for one set system to find a solution without removing a set element. However, with the removal of only a few set elements, the Euler diagrams can be substantially improved with respect to our wellformedness criteria.

Computer Science↗
DOE OSTI2018

Millstone

Millstone is a mechanics solver for geological processes, focusing on coupling to reservoir simulators. It solves the linear balance of momentum with incremental poroelastic stress rate formulations under quasistatic assumptions.

Queiruga, Alejandro↗
NASA NTRS1990

Numerical investigation of laminar-turbulent transition in a flat plate wake

Lamina-turbulent transition of high-deficit flat plate wakes is investigated by direct numerical simulations using the complete Navier Stokes equations. The simulations are based on a spatial model so that both the base flow and the disturbance flow can develop in the downstream direction. The Navier Stokes equations are used in a vorticity-velocity form and are solved using a combination of finite difference and spectral approximations. Fourier series are used in the spanwise direction. Second-order finite-differences are used to approximate the spatial derivatives in the streamwise and transverse directions. For the temporal discretion, a combination of ADI, Crank-Nicolson, and Adams-Bashforth methods is employed. The discretized velocity equations are solved using fast Helmholtz solvers. Code validation is accomplished by comparison of the numerical results to both linear stability and to experiments. Calculations of two- and/or three-dimensional sinuous and mode disturbances in the wake of flat plate are undertaken. For calculations of two-dimensional disturbances, the wake is forced at an amplitude level so that nonlinear disturbance development may be observed. In addition, the forcing amplitude is varied in order to determine its effect on the disturbance behavior. To investigate the onset of three-dimensionality, the wake is forced with a small-amplitude three-dimensional disturbance and a larger amplitude two-dimensional disturbance. The two-dimensional forcing amplitude is varied in order to determine its influence on the three-dimensional flow field.

Fasel, Hermann F.↗
NASA NTRS1991

Parallel Methods on Large-Scale Structural Analysis and Physics Applications; Symposium, Hampton, VA, Feb. 5, 6, 1991, Selected Papers

Recent advances in parallel methods and algorithms integrated into large-scale codes are presented. Consideration is given to problem decomposition (substructuring), efficient matrix solution algorithms for shared memory architectures, dynamic and transient analysis algorithms for shared memory architectures, and algorithms for distributed and massively parallel architectures. Particular attention is given to partitioning of unstructured problems for parallel processing, parallel-vector computation for linear-structural analysis and nonlinear unconstraint optimization problems, a parallel-vector equation solver for unsymmetric matrices on supercomputers, parallel nonlinear finite element dynamic response, multigrid algorithms for solving structural mechanics problems on supercomputers, structural analysis on massively parallel computers, explicit finite element methods with contact-impact on SIMD computers, and the impact of mapping and sparsity on parallelized finite element method modules.

Storaasli, Olaf O.↗
NASA NTRS2013

An Extension of the Time-Spectral Method to Overset Solvers

Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

Leffell, Joshua Isaac↗