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At least 1,639 records · Page 91

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NASA NTRS1985

A fully implicit scheme for global numerical weather prediction

A fast-slow factored scheme is presented for use with shallow-water primitive equation numerical weather prediction models. The technique was developed to reduce the rotational mode errors which arise when the fast and slow terms of the governing differential equations are treated simultaneously. The method factors out the fast and slow terms along the coordinate directions by means of a modified Crank-Nicolson scheme. A finite-difference spatial discretization is carried out in the zonal and meridional directions to reduce the factorization error to near-zero, and that time steps of 60-90 min can be used to obtain acceptably accurate results, even in the presence of fine spatial structures in the flow.

Augenbaum, J. M.↗

NASA NTRSDate not supplied

A Parallel Symmetric Successive Overrelaxation Method for OVERFLOW

The block Jacobi symmetric successive overrelaxation (SSOR) algorithm has been reformulated as a parallelized algorithm for the OVERFLOWstructured, overset grid, computational fluid dynamics flow solver. Simple changes to the flow solver required to implement the algorithm are discussed. A series of test cases are presented that demonstrate how the addition of implicit overset boundaries has improved the robustness and nonlinear convergence characteristics of the flow solver.

Computational Fluid Dynamics↗

DOE OSTI2016

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Fast Real-Time Time-Dependent Density Functional Theory Calculations with the Parallel Transport Gauge

Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation, because of the fast oscillation of electron wave functions, which significantly limits its range of applicability for the study of ultrafast dynamics. In this paper, we demonstrate that such oscillation can be considerably reduced by optimizing the gauge choice using the parallel transport formalism. RT-TDDFT calculations can thus be significantly accelerated using a combination of the parallel transport gauge and implicit integrators, and the resulting scheme can be used to accelerate any electronic structure software that uses a Schrödinger representation. Here, using absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations for example, we show that the new method can utilize a time step that is on the order of 10–100 attoseconds using a planewave basis set. Thanks to the significant increase of the size of the time step, we also demonstrate that the new method is more than 10 times faster, in terms of the wall clock time, when compared to the standard explicit fourth-order Runge–Kutta time integrator for silicon systems ranging from 32 to 1024 atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Efficient 3D Molecular Design with an E(3) Invariant Transformer VAE

This work introduces a three-dimensional (3D) invariant graph-to-string transformer variational autoencoders (VAE) (Vagrant) for generating molecules with accurate density functional theory (DFT)-level properties. Vagrant learns to model the joint probability distribution of a 3D molecular structure and its properties by encoding molecular structures into a 3D-aware latent space. Directed navigation through this latent space implicitly optimizes the 3D structure of a molecule, and the latent embedding can be used to condition a generative transformer to predict the candidate structure as a one-dimensional (1D) sequence. Additionally, we introduce two novel sampling methods that exploit the latent characteristics of a VAE to improve performance. Here, we show that our method outperforms comparable 3D autoregressive and diffusion methods for predicting quantum chemical property values of novel molecules in terms of both sample quality and computational efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1975

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Anderson, E. C.↗

NASA NTRS1985

The design and implementation of cost-effective algorithms for direct solution of banded linear systems on the vector processor system 32 supercomputer

The problem of solving banded linear systems by direct (non-iterative) techniques on the Vector Processor System (VPS) 32 supercomputer is considered. Two efficient direct methods for solving banded linear systems on the VPS 32 are described. The vector cyclic reduction (VCR) algorithm is discussed in detail. The performance of the VCR on a three parameter model problem is also illustrated. The VCR is an adaptation of the conventional point cyclic reduction algorithm. The second direct method is the Customized Reduction of Augmented Triangles' (CRAT). CRAT has the dominant characteristics of an efficient VPS 32 algorithm. CRAT is tailored to the pipeline architecture of the VPS 32 and as a consequence the algorithm is implicitly vectorizable.

Samba, A. S.↗

NASA NTRS1989

Multibody dynamics model building using graphical interfaces

In recent years, the extremely laborious task of manually deriving equations of motion for the simulation of multibody spacecraft dynamics has largely been eliminated. Instead, the dynamicist now works with commonly available general purpose dynamics simulation programs which generate the equations of motion either explicitly or implicitly via computer codes. The user interface to these programs has predominantly been via input data files, each with its own required format and peculiarities, causing errors and frustrations during program setup. Recent progress in a more natural method of data input for dynamics programs: the graphical interface, is described.

Macala, Glenn A.↗

NASA NTRS1991

An effective multigrid method for high-speed flows

The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for 2-D laminar flow over a circular cylinder and a 15 deg compression ramp.

Swanson, R. C.↗

NASA NTRS1992

Combustion instability analysis for liquid propellant rocket engines

The multi-dimensional numerical model has been developed to analyze the nonlinear combustion instabilities in liquid-fueled engines. The present pressure-based approach can handle the implicit pressure-velocity coupling in a non-iterative way. The additional scalar conservation equations for the chemical species, the energy, and the turbulent transport quantities can be handled by the same predictor-corrector sequences. This method is time-accurate and it can be applicable to the all-speed, transient, multi-phase, and reacting flows. Special emphasis is given to the acoustic/vaporization interaction which may act as the crucial rate-controlling mechanism in the liquid-fueled rocket engines. The subcritical vaporization is modeled to account for the effects of variable thermophysical properties, non-unitary Lewis number in the gas-film, the Stefan flow effect, and the effect of transient liquid heating. The test cases include the one-dimenisonal fast transient non-reacting and reacting flows, and the multi-dimensional combustion instabilities encountered in the liquid-fueled rocket thrust chamber. The present numerical model successfully demonstrated the capability to simulate the fast transient spray-combusting flows in terms of the limiting-cycle amplitude phenomena, correspondence between combustion and acoustics, and the steep-fronted wave and flame propagation. The investigated parameters include the spray initial conditions, air-fuel mixture ratios, and the engine geometry. Stable and unstable operating conditions are found for the liquid-fueled combustors. Under certain conditions, the limiting cycle behavior of the combusting flowfields is obtained. The numerical results indicate that the spray vaporization processes play an important role in releasing thermal energy and driving the combustion instability.

Kim, Y. M.↗

NASA NTRS1992

An effective multigrid method for high-speed flows

Swanson, R. C.↗

NASA NTRS1995

Excursion-Set-Mediated Genetic Algorithm

Excursion-set-mediated genetic algorithm (ESMGA) is embodiment of method of searching for and optimizing computerized mathematical models. Incorporates powerful search and optimization techniques based on concepts analogous to natural selection and laws of genetics. In comparison with other genetic algorithms, this one achieves stronger condition for implicit parallelism. Includes three stages of operations in each cycle, analogous to biological generation.

Noever, David↗

DOE OSTI2020

Regular sensitivity computation avoiding chaotic effects in particle-in-cell plasma methods

Particle-in-cell (PIC) simulation methods are attractive for representing species distribution functions in plasmas. However, as a model, they introduce uncertain parameters, and for quantifying their prediction uncertainty it is useful to be able to assess the sensitivity of a quantity-of-interest (QoI) to these parameters. Such sensitivity information is likewise useful for optimization. However, computing sensitivity for PIC methods is challenging due to the chaotic particle dynamics, and sensitivity techniques remain underdeveloped compared to those for Eulerian discretizations. This challenge is examined from a dual particle–continuum perspective that motivates a new sensitivity discretization. Two routes to sensitivity computation are presented and compared: a direct fully-Lagrangian particle-exact approach provides sensitivities of each particle trajectory, and a new particle-pdf discretization, which is formulated from a continuum perspective but discretized by particles to take the advantages of the same type of Lagrangian particle description leveraged by PIC methods. Since the sensitivity particles in this approach are only indirectly linked to the plasma-PIC particles, they can be positioned and weighted independently for efficiency and accuracy. The corresponding numerical algorithms are presented here in mathematical detail. The advantage of the particle-pdf approach in avoiding the spurious chaotic sensitivity of the particle-exact approach is demonstrated for Debye shielding and sheath configurations. In essence, the continuum perspective makes implicit the distinctness of the particles, which circumvents the Lyapunov instability of the N -body PIC system. The cost of the particle-pdf approach is comparable to the baseline PIC simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery

The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, and pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model on electrostatic interaction, the nonpolar interaction contribution of solvent and the conformational entropy of solute in solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of conformational entropy of solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal/mol for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.

25 ENERGY STORAGE↗

DOE OSTI2015

A HYDROCHEMICAL HYBRID CODE FOR ASTROPHYSICAL PROBLEMS. I. CODE VERIFICATION AND BENCHMARKS FOR A PHOTON-DOMINATED REGION (PDR)

A two-dimensional hydrochemical hybrid code, KM2, is constructed to deal with astrophysical problems that would require coupled hydrodynamical and chemical evolution. The code assumes axisymmetry in a cylindrical coordinate system and consists of two modules: a hydrodynamics module and a chemistry module. The hydrodynamics module solves hydrodynamics using a Godunov-type finite volume scheme and treats included chemical species as passively advected scalars. The chemistry module implicitly solves nonequilibrium chemistry and change of energy due to thermal processes with transfer of external ultraviolet radiation. Self-shielding effects on photodissociation of CO and H{sub 2} are included. In this introductory paper, the adopted numerical method is presented, along with code verifications using the hydrodynamics module and a benchmark on the chemistry module with reactions specific to a photon-dominated region (PDR). Finally, as an example of the expected capability, the hydrochemical evolution of a PDR is presented based on the PDR benchmark.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Neural posterior unfolding

Differential cross section measurements are the currency of scientific exchange in particle and nuclear physics. A key challenge for these analyses is the correction for detector distortions, known as deconvolution or unfolding. Binned unfolding of cross section measurements traditionally rely on the regularized inversion of the response matrix that represents the detector response, mapping pre-detector (`particle level') observables to post-detector (`detector level') observables. In this paper we introduce Neural Posterior Unfolding, a modern, Bayesian approach that leverages normalizing flows for unfolding. By using normalizing flows for neural posterior estimation, NPU offers several key advantages including implicit regularization through the neural network architecture, fast amortized inference that eliminates the need for repeated retraining, and direct access to the full uncertainty in the unfolded result. In addition to introducing NPU, we implement a classical Bayesian unfolding method called Fully Bayesian Unfolding (FBU) in modern Python so it can also be studied. These tools are validated on simple Gaussian examples and then tested on simulated jet substructure examples from the Large Hadron Collider (LHC). We find that the Bayesian methods are effective and worth additional development to be analysis ready for cross section measurements at the LHC and beyond.

Analysis and statistical methods↗

NASA NTRS1978

A view toward future fluid dynamics computing

Advances in computational fluid dynamics are paced by simulation methodology and computer resources. Examples of three-dimensional fluid dynamic simulations are presented to illustrate recent developments in equation modeling and numerical methods and to point out the need for increased computer power. Electronic technology dictates that to fill this need, computers will be based on parallel processing principles. The identification of parallelism in three dimensions is illustrated by examining an implicit, approximate-factorization approach to the Navier-Stokes equations. Finally, two computer concepts aimed at satisfying the demands of the three-dimensional Reynolds averaged Navier-Stokes simulations are discussed.

Bailey, F. R.↗