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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Parameter Reduction of Composite Load Model Using Active Subspace Method

Over the past decades, the increasing penetration of distributed energy resources (DERs) has dramatically changed the power load composition in the distribution networks. The traditional static and dynamic load models can hardly capture the dynamic behavior of modern loads especially for fault-induced delayed voltage recovery (FIDVR) events. Thus, a more comprehensive composite load model with combination of static load, different types of induction motors, single-phase A/C motor, electronic load and DERs has been proposed by Western Electricity Coordinating Council (WECC). However, due to the large number of parameters and model complexity, the WECC composite load model (WECC CMLD) raises new challenges to power system studies. To overcome these challenges, in this paper, a cutting-edge parameter reduction (PR) approach for WECC CMLD based on active subspace method (ASM) is proposed. Firstly, the WECC CMLD is parameterized in a discrete-time manner for the application of the proposed method. Then, parameter sensitivities are calculated by discovering the active subspace, which is a lower-dimensional linear subspace of the parameter space of WECC CMLD in which the dynamic response is most sensitive. The interdependency among parameters can be taken into consideration by our approach. Finally, the numerical experiments validate the effectiveness and advantages of the proposed approach for WECC CMLD model.

active subspace↗
DOE OSTI2026

Second Order System Study

During my education in mathematics, engineering and physics, I learned transform pairs and their usage mechanics but I never remember seeing the derivations of the solutions to second order ordinary differential equations (ODE) and difference equations. A solution to a question posed in a potential funder meeting put me on a path to solving second order systems using the five principal Fourier based methods: Fourier transform (FT), Z-transform (ZT), discrete time Fourier transform (DTFT), discrete Fourier transform (DFT) and Laplace transform (LT).

42 ENGINEERING↗
DOE OSTI2023

Diagonally implicit Runge–Kutta schemes: Discrete energy-balance laws and compactness properties

Abstract We study diagonally implicit Runge–Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.

Mathematics↗
DOE OSTI2021

Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Windowed least-squares model reduction for dynamical systems

Here we propose a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space–time trial subspace over time windows. The approach comprises a generalization of existing model reduction approaches, as particular instances of the methodology recover Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG projection. In addition, the approach addresses key deficiencies in existing model reduction techniques, e.g., the dependence of LSPG and space–time LSPG projection on the time discretization and the exponential growth in time exhibited by a posteriori error bounds for both Galerkin and LSPG projection. We consider two types of space–time trial subspaces within the proposed approach: one that reduces only the spatial dimension of the full-order model, and one that reduces both the spatial and temporal dimensions of the full-order model. For each type of trial subspace, we consider two different solution techniques: direct (i.e., discretize then optimize) and indirect (i.e., optimize then discretize). Numerical experiments conducted using trial subspaces characterized by spatial dimension reduction demonstrate that the WLS approach can yield more accurate solutions with lower space–time residuals than Galerkin and LSPG projection.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ∼1/Np with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly non-equilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ~1/$\sqrt{N_p}$ with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly nonequilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

On the discretization error of the discrete generalized quantum master equation

The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 112 , 110401 (2014)] can be considered a discrete-time formulation of the Nakajima–Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 21 , 5037 (2025)] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time t = 0. Here, this work presents a detailed analysis of the discretization structure of the TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel K N and the continuous-time NZ-QME kernel $\mathscr{K}$( N Δ t ). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as Δ t → 0. While the TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri’s work. The relative performance of various schemes for either computing accurate $\mathscr{K}$( N Δ t ) from exact dynamics or obtaining accurate dynamics from exact $\mathscr{K}$( N Δ t ) warrants further investigation.

Density-matrix↗
DOE OSTI2020

Slow manifold reduction for plasma science

The classical Chapman–Enskog procedure admits a substantial geometrical generalization known as slow manifold reduction. This generalization provides a paradigm for deriving and understanding most reduced models in plasma physics that are based on controlled approximations applied to problems with multiple timescales. In this Review we develop the theory of slow manifold reduction with a plasma physics audience in mind. In particular we illustrate (a) how the slow manifold concept may be used to understand breakdown of a reduced model over sufficiently-long time intervals, and (b) how a discrete-time analogue of slow manifold theory provides a useful framework for developing implicit integrators for temporally-stiff plasma models. For readers with more advanced mathematical training we also use slow manifold reduction to explain the phenomenon of inheritance of Hamiltonian structure in dissipation-free reduced plasma models. Various facets of the theory are illustrated in the context of the Abraham–Lorentz model of a single charged particle experiencing its own radiation drag. As a culminating example we derive the slow manifold underlying kinetic quasineutral plasma dynamics up to first-order in perturbation theory. This first-order result incorporates several physical effects associated with small deviations from exact charge neutrality that lead to slow drift away from predictions based on the leading-order approximation n e = Z i n i .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Machine learning a molecular Hamiltonian for predicting electron dynamics

We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density evolution, producing highly accurate results even when propagating 1,000 time steps beyond the training data. As a more rigorous test, we use the learned Hamiltonians to simulate electron dynamics in the presence of an applied electric field, extrapolating to a problem that is beyond the field-free training data. We find that the resulting electron dynamics predicted by our learned Hamiltonian are in close quantitative agreement with the ground truth. Our method relies on combining a reduced-dimensional, linear statistical model of the Hamiltonian with a time-discretization of the quantum Liouville equation within time-dependent Hartree Fock theory. In conclusion, we train the model using a least-squares solver, avoiding numerous, CPU-intensive optimization steps. For both field-free and field-on problems, we quantify training and propagation errors, highlighting areas for future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

Efficient solution of the Vlasov equation, which can be up to six-dimensional, is key to the simulation of many difficult problems in plasma physics. The discontinuous Petrov-Galerkin (DPG) finite element methodology provides a framework for the development of stable (in the sense of Ladyzhenskaya–Babuška–Brezzi conditions) finite element formulations, with built-in mechanisms for adaptivity. While DPG has been studied extensively in the context of steady-state problems and to a lesser extent with space-time discretizations of transient problems, relatively little attention has been paid to time-marching approaches. In the present work, we study a first application of time-marching DPG to the Vlasov equation, using backward Euler for a Vlasov-Poisson discretization. We demonstrate adaptive mesh refinement for two problems: the two-stream instability problem, and a cold diode problem. Furthermore, we believe the present work is novel both in its application of unstructured adaptive mesh refinement (as opposed to block-structured adaptivity, which has been studied previously) in the context of Vlasov-Poisson, as well as in its application of DPG to the Vlasov-Poisson system. We also discuss extensive additions to the Camellia library in support of both the present formulation as well as extensions to higher dimensions, Maxwell equations, and space-time formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗
DOE OSTI2023

Simulating Heisenberg interactions in the Ising model with strong drive fields

The time evolution of an Ising model with large driving fields over discrete time intervals is shown to be reproduced by an effective XXZ-Heisenberg model at leading order in the inverse field strength. For specific orientations of the drive field, the dynamics of the XXX-Heisenberg model is reproduced. Finally, these approximate equivalences, valid above a critical driving field strength set by dynamical phase transitions in the Ising model, are expected to enable quantum devices that natively evolve qubits according to the Ising model to simulate more complex systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Transport @ LANL: An Overview [Slides]

Deterministic neutron transport requires discretization of the Boltzmann transport equation in space, angle, energy, and time. Discretization in energy is typically performed with the multigroup approximation, which tries to preserve continuous energy cross section information by using a weighted average over discrete energy groups. There are two important requirements for accurate multigroup cross sections: appropriate energy group boundaries and an accurate weight function. The former can be selected with appropriate optimizers; the latter either requires flux solutions from comparable simulations or expert knowledge.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Co-Optimization of Velocity and Charge-Depletion for Plug-In Hybrid Electric Vehicles: Accounting for Acceleration and Jerk Constraints

Abstract Recent advances in vehicle connectivity and automation technologies promote advanced control algorithms that co-optimize the longitudinal dynamics and powertrain operation of hybrid electric vehicles. Typically, a sequential optimization with the vehicle dynamics optimized followed by powertrain optimization is adopted to manage a number of complexities such as the inherent mixed-integer nature of the hybrid powertrain, the numerous state and control variables, the differing time scales of vehicle and powertrain subsystems, time-varying state constraints, and large horizon lengths. Instead, we solve the offline optimization problem in a centralize manner assuming exact knowledge of the lead vehicle's position over the entire trip by applying a discrete-time single shooting-based numerical approach, Discrete Mixed-Integer Shooting (DMIS), including a linearly increasing computational complexity to the problem horizon. In particular, the hierarchical problem structure is exploited to decompose the computationally intensive Hamiltonian minimization step into a set of low-dimensional optimizations. DMIS allows us to compute the direct fuel minimization problem including the vehicle and powertrain dynamics in a centralized manner to its full horizon while systematically tuning weighting factors that penalize passenger discomfort. For the first time, this study reveals that practically implemented sequential optimization exhibits similar fuel optimality as co-optimization when a certain level of passenger comfort is required.

Automation & Control Systems↗
DOE OSTI2020

Sequentially coupled flow and geomechanical simulation with a discrete fracture model for analyzing fracturing fluid recovery and distribution in fractured ultra-low permeability gas reservoirs

More accurate characterization and prediction of the in-situ distribution of fracturing fluid in fractured reservoirs are needed for enhancing well productivity. In this study, an implicit-sequentially coupled flow/geomechanics simulator incorporating an efficient discrete fracture model is developed to model fluid distribution and recovery performance of ultra-low permeability gas reservoirs. The finite-volume and finite-element methods are used for space discretization of the flow and geomechanics equations, respectively, while the backward Euler method is employed for time discretization. The flow and geomechanics equations are solved sequentially based on fixed-stress splitting. An efficient discrete-fracture model is used to explicitly model the fractured system. Flexible unstructured gridding is employed to model arbitrarily-oriented fractures. The interrelations among pore volume, permeability and geomechanical conditions are considered dynamically using two-way coupled flow and geomechanics computations. The geometry of fracture (networks) due to hydraulic fracturing has significant impacts on the fracturing fluid recovery efficiency and ensuing fluid distribution. Under the same injection volume, the fracturing fluid recovery is higher when the fracture geometry is planar. Fluid recovery is relatively lower whenever natural fractures are activated during fracturing treatments; flowback time is also shortened when complex fracture network with enlarged fracture interface is present. Fracturing fluid in hydraulic fractures may leak off into the natural fractures and subsequently imbibes into the surrounding matrix due to capillarity effects. The fracturing fluid recovery and in-situ fluid distribution are sensitive to the shut-in duration and fracture closure behavior. This study analyzes the coupled flow-geomechanical responses of fractured gas reservoirs during the post-fracturing periods. Understanding the fate of the fracturing fluid can provide insights on, to some extent, the stimulated fracture volume, size of the water invasion zone, and efficiency of the fracturing design. The simulation predictions can also provide more accurate initial reservoir conditions (e.g. distributions of different phases and pressure) for long-term well performance estimation.

42 ENGINEERING↗
DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A review of high order strong stability preserving two-derivative explicit, implicit, and IMEX methods

High order strong stability preserving time discretizations ensure the nonlinear non-inner-product strong stability properties of spatial discretizations suited for the stable simulation of hyperbolic PDEs in a wide variety of application areas including fluid dynamics, magnetohydrodynamics, semiconductor devices, electromagnetics, and astrophysics. Over the past decade multiderivative time-stepping have been increasingly used for the time-evolution hyperbolic PDEs, so that the strong stability properties of these methods have become important. In this work we review sufficient conditions for a two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and different conditions on the second derivative. In particular we present the strong stability preserving theory for explicit and implicit two-derivative Runge–Kutta schemes, including a special condition on the second derivative under which these implicit methods may be unconditionally strong stability preserving. This special condition is natural for the stiff component of wide range of plasma physics problems, and can be useful in the context of strong stability preserving implicit-explicit multi-derivative Runge–Kutta schemes, where the time-step restriction is then independent of the stiff term. Lastly, we present the strong stability preserving theory for implicit-explicit multi-derivative general linear methods, and some novel second and third order methods where the time-step restriction is independent of the stiff term.

97 MATHEMATICS AND COMPUTING↗