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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

RE-INTEGRATE EMT Simulation Software: Graph Convolutional Network for Sparse Matrix Pattern Detection

The increasing complexity of power networks, driven by proliferation of inverters, presents analytical challenges that simplified models often fail to capture, necessitating Electromagnetic Transient (EMT) simulations. EMT models are represented as discretized differential-algebraic equations (DAEs), forming a linear system Ax = b that is computationally intensive to solve. Due to inherent sparsity of adjacency matrix A, distinct patterns emerge that, when accurately identified, enable efficient solver selection to minimize computation time. However, identifying ideal pattern is complicated by numerous reordering algorithms and limited structural insights. To address this, we introduce a Graph Convolutional Network (GCN) model for classifying sparse matrix patterns common in power system analysis. The model, achieving 96% test accuracy, is validated using PV plant models of 125 MW capacities connected to New England 39-bus transmission system (TS), and further scaled to a 4,992-bus network with 384 PV plants, yielding 191, 616 × 191, 616 sized A matrix. For all cases, the GCN model accurately identifies the matrix’s intrinsic sparse pattern, demonstrating its potential to enhance solver performance in EMT analysis.

Hossain, Md Rifat [Florida International Universit↗
DOE OSTI2025

An Optimization-Based Law of Mass Action Precipitation/Dissolution Model

Rare earth elements (REE) and many other critical minerals are necessary for the manufacturing of modern everyday technologies, including microchips, batteries and electric motors. Recovery of these materials typically involves aqueous systems which can be modeled as chemical equilibrium problems. One common method for solving these problems is the law of mass action approach (LMA), where a system of non-linear equations involving the equilibrium constants is solved. However, despite being theoretically simple, these problems are in practice very difficult to solve. Currently, the use of iterative heuristics based on saturation indices to decide on which species and reactions to include in the calculations is the state of the art to arrive at a solution. Here, we present an optimization-based alternative to solve chemical equilibria problems involving precipitation/dissolution reactions without the need for such heuristics. Our approach is first validated against the LMA software MINTEQ and PHREEQC for a number of case studies, and then applied to a novel REE recovery process reported in the literature. Overall, our approach was found to have close agreement with MINTEQ and PHREEQC, and we were able to successfully replicate the reported yield and purity for the published REE process.

42 ENGINEERING↗
DOE OSTI2024

A high-order explicit Runge-Kutta approximation technique for the shallow water equations

Here, we introduce a high-order space–time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP), well-balanced with respect to rest states, and employs a novel explicit Runge–Kutta (ERK) introduced in Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366–A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Influence of wind turbine design parameters on linearized physics-based models in OpenFAST

Abstract. While most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear wind system equations is often important for understanding the system response and exploiting well-established methods and tools for analyzing linear systems. Linearized models are important for eigenanalysis (to derive structural natural frequencies, damping ratios, and mode shapes), controls design (based on linear state-space models), etc. In controls co-design, wherein methods often rely on linearized time-domain models of the physics, the physical structure (often called the plant) and controller are designed and optimized concurrently, so it is important to understand how changes to the physical design affect the linearized system. This work summarizes efforts done to understand the impact of design parameter variations in the physical system (e.g., mass, stiffness, geometry, and aerodynamic and hydrodynamic coefficients) on the linearized system using OpenFAST.

17 WIND ENERGY↗
DOE OSTI2023

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Modeling diffusion and types I-V sorption of water vapor in heterogeneous systems

Here, a sorption and diffusion model is developed using a mobile-immobile decomposition of the vapor concentration. Henry’s mode represents the mobile species which diffuses through the solid, while Langmuir and pooling modes represent possible immobilization processes that cause nonlinearities in sorption capacity. The model can simulate the five classical sorption types and can incorporate additional dynamics compared to models based on thermodynamic equilibrium. Additionally, the framework allows for discontinuities in material properties encountered in multi-material systems. The resulting non-linear coupled equations are solved by employing a finite element method to discretize in space, and a backward Euler method to discretize in time. The discretized system of equations is solved via a Newton-type iteration scheme at each time-step. Four different materials are parameterized for the model, which are then used in examples to demonstrate the model’s ability to capture complex sorption processes in multi-material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂⁡(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂⁡(𝑁⁢log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.

58 GEOSCIENCES↗
DOE OSTI2021

Quasi-linear theory of forced magnetic reconnection for the transition from the linear to the Rutherford regime

Abstract Using the in-viscid two-field reduced magneto-hydrodynamic (MHD) model, a new analytical theory is developed to unify the Hahm–Kulsrud–Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in the Taylor problem. An integral form of an analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient K s ∝ S 8 / 5 ψ c 2 , where S = τ R τ A and ψ c are the Lundquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for the response can be recovered when the index K s → 0. On the other hand, the quasi-linear effect plays a key role in the island growth when K s ~ 1. Our new analytical solution has also been compared with reduced MHD simulations with agreement.

Physics↗
DOE OSTI2023

EUTERPE: A global gyrokinetic code for stellarator geometry

The current state of the EUTERPE code is described with emphasis on the implemented models and their numerical implementation. The code solves the multi-species electromagnetic gyrokinetic equations in the full volume of a three-dimensional domain. Noise reduction of the particle-in-cell method is achieved by using a δf-method and Fourier filters. The field equations are discretized with B-splines and the resulting system of equations is solved iteratively. For linear simulations a phase-factor transformation is applied in order to strongly reduce the necessary grid resolution. Apart from the full gyrokinetic model, other numerically less expensive hybrid models are also implemented. They are mainly tailored for comparison with fluid theory and for studying the interaction of the bulk plasma with fast particles. The code is parallelized for CPUs by particle and domain decomposition. Good scalability up to several thousand nodes is demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Branlard, Emmanuel (ORCID:0000000277506128)↗
DOE OSTI2024

Jacobian-based Model Diagnostics and Application to Equation Oriented Modeling of a Carbon Capture System

Equation-oriented (EO) modeling has the potential to enable the effective design and optimization of the operation of advanced energy systems. However, advanced modeling of energy systems results in a large number of variables and non-linear equations, and it can be difficult to search through these to identify the culprit(s) responsible for convergence issues. The Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES-IP) contains a tool to identify poorly scaled constraints and variables by searching for rows and columns of the Jacobian matrix with small L2-norms so they can be rescaled. A further singular value decomposition can be per-formed to identify degenerate sets of equations and remaining scaling issues. This work presents an EO model of a flowsheet developed for post-combustion carbon capture using a monoethanolamine (MEA) solvent system as a case study. The IDAES diagnostics tools were successfully applied to this flowsheet to identify problems to improve model robustness and enable the optimization of process design and operating conditions of a carbon capture system.

Allan, Douglas↗
DOE OSTI2020

BISON Robustness and Performance Improvements

BISON is a modern finite-element based nuclear fuel performance code that has been under development at the Idaho National Laboratory (USA) since 2009 [1]. The code is applicable to both steady and transient fuel behavior and can be used to analyze 1D (spherically symmetric), 2D (axisymmetric and generalized plane strain) or 3D geometries. BISON is the fuel performance code used within CASL for LWR fuel under both normal operating and accident conditions. BISON is built using the INL Multiphysics ObjectOriented Simulation Environment, or MOOSE [2, 3]. MOOSE is a massively parallel, finite element-based framework to solve systems of coupled non-linear partial differential equations using the Jacobian-Free Newton Krylov (JFNK) method [4]. This enables investigation of computationally large problems, for example a full stack of discrete pellets in a LWR fuel rod, or every rod in a full reactor core. MOOSE supports the use of complex two and three-dimensional meshes and uses implicit time integration, important for the widely varied time scale in nuclear fuel simulation. An object-oriented architecture is employed which greatly minimizes the programming effort required to add new material and behavioral models. The flexibility of the implicit and fully coupled multiphysics approach comes with a need for constructing suitable approximations for the Jacobian matrix of the coupled system used for either preconditioning a Krylov solve or in a direct Newton solve. Preconditioning options for Bison problems need to be revisited with new preconditioning methods becoming available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry

Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain ‘critical’ velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago. A generalization to anisotropic crystals has been attempted for pure screw and edge dislocations only for some special cases. This work aims to fill the gap of deriving a general anisotropic solution for pure screw dislocations applicable to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Finally, further generalizations to arbitrary mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.

42 ENGINEERING↗
DOE OSTI2022

Transport error estimation using residual Monte Carlo

The residual Monte Carlo (RMC) method is also known in the literature as sequential Monte Carlo and reduced-source Monte Carlo. Given a Monte Carlo method for solving a linear equation and an approximate solution to that system, the residual method enables use of essentially the same Monte Carlo algorithm to directly compute the additive error or “defect” associated with the approximate solution. As the size of the defect decreases relative to the size of the solution, the residual Monte Carlo method becomes increasingly efficient relative to the standard Monte Carlo (SMC) method. Here we present a new RMC algorithm for evaluating the space-angle error in S n radiation transport solutions, and provide computational examples demonstrating that it can be far more efficient than SMC for this purpose. Herein we also describe a particular pitfall that must be avoided if RMC is to be efficient, and explain why the performance of RMC can significantly differ between different transport problems and different quantities of interest for the same problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Adaptive Power Flow Approximations With Second-Order Sensitivity Insights

The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these challenges, recent research has proposed adaptive power flow linearizations that aim to achieve accuracy over wide operating ranges. The accuracy of these approximations inherently depends on the curvature of the power flow equations within these ranges, which necessitates considering second-order sensitivities. In this paper, we leverage second-order sensitivities to both analyze and improve power flow approximations. We evaluate the curvature across broad operational ranges and subsequently utilize this information to inform the computation of various sample-based power flow approximation techniques. Additionally, we leverage second-order sensitivities to guide the development of rational approximations that yield linear constraints in optimization problems. In conclusion, this approach is extended to enhance accuracy beyond the limitations of linear functions across varied operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗