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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 379 records · Page 21

A low-rank solver for the stochastic unsteady Navier–Stokes problem

Here we study a low-rank iterative solver for the unsteady Navier–Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once formulation where the algebraic systems at all the time steps are collected and solved simultaneously. The problem is linearized with Picard’s method. To efficiently solve the linear systems at each step, we use low-rank tensor representations within the Krylov subspace method, which leads to significant reductions in storage requirements and computational costs. Combined with effective mean-based preconditioners and the idea of inexact solve, we show that only a small number of linear iterations are needed at each Picard step. The proposed algorithm is tested with a model of flow in a two-dimensional symmetric step domain with different settings to demonstrate the computational efficiency.

97 MATHEMATICS AND COMPUTING↗

Modeling the direct sun component in buildings using matrix algebraic approaches: Methods and validation

Simulation tools that enable annual energy performance analysis of optically-complex fenestration systems have been widely adopted by the building industry for use in building design, code development, and the development of rating and certification programs for commercially-available shading and daylighting products. The tools rely on a three-phase matrix operation to compute solar heat gains, using as input low-resolution bidirectional scattering distribution function (BSDF) data (10–15° angular resolution; BSDF data define the angle-dependent behavior of light-scattering materials and systems). Measurement standards and product libraries for BSDF data are undergoing development to support solar heat gain calculations. Simulation of other metrics such as discomfort glare, annual solar exposure, and potentially thermal discomfort, however, require algorithms and BSDF input data that more accurately model the spatial distribution of transmitted and reflected irradiance or illuminance from the sun (0.5° resolution). This study describes such algorithms and input data, then validates the tools (i.e., an interpolation tool for measured BSDF data and the five-phase method) through comparisons with ray-tracing simulations and field monitored data from a full-scale testbed. Simulations of daylight-redirecting films, a micro-louvered screen, and venetian blinds using variable resolution, tensor tree BSDF input data derived from interpolated scanning goniophotometer measurements were shown to agree with field monitored data to within 20% for greater than 75% of the measurement period for illuminance-based performance parameters. The three-phase method delivered significantly less accurate results. We discuss the ramifications of these findings on industry and provide recommendations to increase end user awareness of the current limitations of existing software tools and BSDF product libraries.

14 SOLAR ENERGY↗

A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

In this work, we introduce a relaxed physical factorization (RPF) preconditioner for the efficient iterative solution of the linearized algebraic system arising from the mixed finite element discretization of coupled poromechanics equations. The preconditioner is obtained by using a proper factorization of the $3\times3$ block matrix and setting a relaxation parameter $\alpha$. The preconditioner is inspired by the relaxed dimensional factorization introduced by Benzi et al. [J. Comput. Phys., 230 (2011), pp. 6185--6202; Comput. Methods Appl. Mech. Engrg., 300 (2016), pp. 129--145]. A stable algorithm is advanced to compute the optimal value of $\alpha$, along with a lower bound to control the possible ill-conditioning of the $\alpha$ dependent inner blocks. Lastly, numerical experiments in both theoretical benchmarks and real-world applications are presented and discussed to investigate the RPF properties, performance, and robustness.

97 MATHEMATICS AND COMPUTING↗

The IDAES process modeling framework and model library—Flexibility for process simulation and optimization

Abstract Energy systems and manufacturing processes of the 21st century are becoming increasingly dynamic and interconnected, which require new capabilities to effectively model and optimize their design and operations. Such next generation computational tools must leverage state‐of‐the‐art techniques in optimization and be able to rapidly incorporate new advances. To address these requirements, we have developed the Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform, which builds on the strengths of both process simulators (model libraries) and algebraic modeling languages (advanced solvers). This paper specifically presents the IDAES Core Modeling Framework (IDAES‐CMF), along with a case study demonstrating the application of the framework to solve process optimization problems. Capabilities provided by this framework include a flexible, modifiable, open‐source platform for optimization of process flowsheets utilizing state‐of‐the‐art solvers and solution techniques, fully open and extensible libraries of dynamic unit operations models and thermophysical property models, and integrated support for superstructure‐based conceptual design and optimization under uncertainty.

42 ENGINEERING↗

Tusas: A fully implicit parallel approach for coupled phase-field equations

In this study, we develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

97 MATHEMATICS AND COMPUTING↗

Fast explicit solutions for neutrino-electron scattering: Explicit asymptotic methods

Here, we present results of explicit asymptotic approximations applied to neutrino-electron scattering in a representative model of neutrino population evolution under conditions characteristic of core-collapse supernova explosions or binary neutron star mergers. It is shown that this approach provides stable solutions of these stiff systems of equations, with accuracy and time stepping comparable to that for standard implicit treatments such as backward Euler, fixed point iteration, and Anderson-accelerated fixed point iteration. Because each time step can be computed more rapidly with the explicit asymptotic approximation than with implicit methods, this suggests that algebraically stabilized explicit integration methods could be used to compute neutrino evolution coupled to hydrodynamics more efficiently in stellar explosions and mergers than the methods currently in use.

79 ASTRONOMY AND ASTROPHYSICS↗

New results on the PLL false lock phenomenon

Conditions, based on the multipliers of a linear differential equation with periodic coefficients, for the occurrence of false lock in a phase lock loop (PLL) are presented. Two new and powerful algorithms are presented for computing the frequency difference between the reference and voltage controlled oscillator when the loop is false locked. The first algorithm expresses omega f sup -1 as a power series in the closed loop gain. The second algorithm expresses omega sup -1 as part of a solution to a nonlinear algebraic system of equations which can be solved by numerical methods. The power of both algorithms is illustrated by application and comparison.

Stensby, J. L.↗

Discrete Fourier Transform in a Complex Vector Space

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Dean, Bruce H.↗

Numerical solution of large scale Hartree–Fock–Bogoliubov equations

The Hartree–Fock–Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree–Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size N b . We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most $\mathcal{O}$(N b 2 ) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with N b up to 2.88 × 10 6 , and the wall clock time is less than 100 s using 17 280 CPU cores. Finally, this enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

97 MATHEMATICS AND COMPUTING↗

Geopotential Error Analysis from Satellite Gradiometer and Global Positioning System Observables on Parallel Architecture

The recovery of a high resolution geopotential from satellite gradiometer observations motivates the examination of high performance computational techniques. The primary subject matter addresses specifically the use of satellite gradiometer and GPS observations to form and invert the normal matrix associated with a large degree and order geopotential solution. Memory resident and out-of-core parallel linear algebra techniques along with data parallel batch algorithms form the foundation of the least squares application structure. A secondary topic includes the adoption of object oriented programming techniques to enhance modularity and reusability of code. Applications implementing the parallel and object oriented methods successfully calculate the degree variance for a degree and order 110 geopotential solution on 32 processors of the Cray T3E. The memory resident gradiometer application exhibits an overall application performance of 5.4 Gflops, and the out-of-core linear solver exhibits an overall performance of 2.4 Gflops. The combination solution derived from a sun synchronous gradiometer orbit produce average geoid height variances of 17 millimeters.

Schutz, Bob E.↗

An Integrated Approach to Scaling Task-Based Runtime Systems for Next Generation Engineering problems

The need to scale next-generation industrial engineering problems to the largest computational platforms presents unique challenges. Such problems may have complex coupled multi-physics models, as well as computationally and communication intensive algorithms not often seen in standard academic problems, while also needing high-demand I/O for analysis purposes. In such cases even codes with good existing scaling properties may need significant changes, addressed in a cross-cutting way to solve such problems at extreme scales. These challenges relate to system components that were not previously problematic on less complex problems and/or at smaller computational scales. This paper illustrates these challenges for Uintah, a highly scalable asynchronous many-task runtime system being applied to the modeling of a 1000 MWe ultra-supercritical coal boiler. In order to model this formidable, production engineering problem, not only was an integrated approach needed that built upon existing scalable components in areas such as complex stencil calculations and linear algebra, but the significant challenges of high demand I/O, complex task graphs, and infrastructure inefficiencies also had to be addressed. This integrated approach allowed this problem to run on 256K CPU cores on Mira, with good weak scaling to 512K CPU cores and similar strong scaling, except for radiation. The need for strong scaling of a new ray tracing-based radiation model required substantial Uintah infrastructure improvements before 119K CPU cores and 7.5K GPUs on Titan could be used, with scaling out to 256K CPU cores and 16K GPUs. The resulting code demonstrates not only excellent overall scalability but a significant improvement in overall performance for the full-scale, production boiler problem.

97 MATHEMATICS AND COMPUTING↗

A parallel strategy for density functional theory computations on accelerated nodes

Using the Löwdin orthonormalization of tall-skinny matrices as a proxy-app for wavefunction-based Density Functional Theory solvers, we investigate a distributed memory parallel strategy focusing on Graphics Processing Unit (GPU)-accelerated nodes as available on some of the top ranked supercomputers at the present time. Here we present numerical results in the strong limit regime, as it is particularly relevant for First-Principles Molecular Dynamics. We also examine how matrix product-based iterative solvers provide a competitive alternative to dense eigensolvers on GPUs, allowing to push the strong scaling limit of these computations to a larger number of distributed tasks. Our strategy, which relies on replicated Gram matrices and efficient collective communications using the NCCL library, leads to a time-to-solution under 0.5 s for the Löwdin orthonormalization of a tall-skinny matrix of 3000 columns on Summit at Oak Ridge Leadership Facility (OLCF). Given the similarity in computational operations between one iteration of a DFT solver and this proxy-app, this shows the possibility of solving accurately the DFT equations well under a minute for 3000 electronic wave functions, and thus perform First-Principles molecular dynamics of physical systems much larger than traditionally solved on CPU systems.

97 MATHEMATICS AND COMPUTING↗

Scalable Knowledge Graph Analytics at 136 Petaflop/s

We are motivated by newly proposed methods for data mining large-scale corpora of scholarly publications, such as the full biomedical literature, which may consist of tens of millions of papers spanning decades of research. In this setting, analysts seek to discover how concepts relate to one another. They construct graph representations from annotated text databases and then formulate the relationship-mining problem as one of computing all-pairs shortest paths (APSP), which becomes a significant bottleneck. In this context, we present a new high-performance algorithm and implementation of the Floyd-Warshall algorithm for distributed-memory parallel computers accelerated by GPUs, which we call DSNAPSHOT (Distributed Accelerated Semiring All-Pairs Shortest Path). For our largest experiments, we ran DSNAPSHOT on a connected input graph with millions of vertices using 4, 096nodes (24,576GPUs) of the Oak Ridge National Laboratory's Summit supercomputer system. We find DSNAPSHOT achieves a sustained performance of 136×1015 floating-point operations per second (136petaflop/s) at a parallel efficiency of 90% under weak scaling and, in absolute speed, 70% of the best possible performance given our computation (in the single-precision tropical semiring or “min-plus” algebra). Looking forward, we believe this novel capability will enable the mining of scholarly knowledge corpora when embedded and integrated into artificial intelligence-driven natural language processing workflows at scale.

Kannan, Ramakrishnan {ramki}↗

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reynolds-Averaged Turbulence Model Assessment for a Highly Back-Pressured Isolator Flowfield

The use of computational fluid dynamics in scramjet engine component development is widespread in the existing literature. Unfortunately, the quantification of model-form uncertainties is rarely addressed with anything other than sensitivity studies, requiring that the computational results be intimately tied to and calibrated against existing test data. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Due to ground test facility limitations, this expanded role is believed to be a requirement by some in the test and evaluation community if scramjet engines are to be given serious consideration as a viable propulsion device. An effort has been initiated at the NASA Langley Research Center to validate several turbulence closure models used for Reynolds-averaged simulations of scramjet isolator flows. The turbulence models considered were the Menter BSL, Menter SST, Wilcox 1998, Wilcox 2006, and the Gatski-Speziale explicit algebraic Reynolds stress models. The simulations were carried out using the VULCAN computational fluid dynamics package developed at the NASA Langley Research Center. A procedure to quantify the numerical errors was developed to account for discretization errors in the validation process. This procedure utilized the grid convergence index defined by Roache as a bounding estimate for the numerical error. The validation data was collected from a mechanically back-pressured constant area (1 2 inch) isolator model with an isolator entrance Mach number of 2.5. As expected, the model-form uncertainty was substantial for the shock-dominated, massively separated flowfield within the isolator as evidenced by a 6 duct height variation in shock train length depending on the turbulence model employed. Generally speaking, the turbulence models that did not include an explicit stress limiter more closely matched the measured surface pressures. This observation is somewhat surprising, given that stress-limiting models have generally been developed to better predict shock-separated flows. All of the models considered also failed to properly predict the shape and extent of the separated flow region caused by the shock boundary layer interactions. However, the best performing models were able to predict the isolator shock train length (an important metric for isolator operability margin) to within 1 isolator duct height.

Baurle, Robert A.↗

Tempus v. 1.0

Tempus is a software framework for the time integration of ordinary differential equations (ODEs), partial differential equations (PDEs), and differential-algebraic equations (DAEs). Examples of time-integration methods available are Forward Euler, Backward Euler, Explicit Runge-Kutta and Implicit Runge-Kutta methods. Tempus can be used from small systems of equations (e.g., single ODEs for the time evolution of plasticity models) to large-scale transient simulations requiring exascale computing (e.g., flow fields around reentry vehicles and magneto-hydrodynamics). Tempus will be released as part of Trilinos under a BSD open source license.

Obert, CurtisC.↗

Multi-physics Preconditioning for Thermally Activated Batteries

Thermal batteries, also known as molten-salt batteries, are single-use reserve power systems activated by pyrotechnic heat generation, which transitions the solid electrolyte into a molten state. The simulation of these batteries relies on multiphysics modeling to evaluate performance and behavior under various conditions. This paper presents advancements in scalable preconditioning strategies for the Thermally Activated Battery Simulator (TABS) tool, enabling efficient solutions to the coupled electrochemical systems that dominate computational costs in thermal battery simulations. We propose a hierarchical block Gauss-Seidel preconditioner implemented through the Teko package in Trilinos, which effectively addresses the challenges posed by tightly coupled physics, including charge transport, porous flow, and species diffusion. The preconditioner leverages scalable subblock solvers, including smoothed aggregation algebraic multigrid (SA-AMG) methods and domain-decomposition techniques, to achieve robust convergence and parallel scalability. Strong and weak scaling studies demonstrate the solver’s ability to handle problem sizes up to 51.3 million degrees of freedom on 2048 processors, achieving near sub-second setup and solve times for the end-to-end electrochemical solve. These advancements significantly improve the computational efficiency and turnaround time of thermal battery simulations, paving the way for higher-resolution models and enabling the transition from 2D axisymmetric to full 3D simulations.

25 ENERGY STORAGE↗

On recent advances and future research directions for computational fluid dynamics

This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.

Baker, A. J.↗