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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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

An efficient high-order numerical solver for diffusion equations with strong anisotropy

In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. Additionally, we demonstrate the accuracy produced by the high-order scheme and develop an efficient preconditioning technique to solve the corresponding linear system, which is robust to the mesh size and anisotropy of the problem. Several numerical tests are provided to validate the accuracy and efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Beam Envelope Variation due to Space-Charge Neutralization

Our non-invasive, time-resolved diamagnetic loop measurements of beam size during the electron current-pulse flattop at the exit of our 20-MeV linear induction accelerator revealed that the beam size varied by about 13% during the current flattop. This was an unexpected result, since both current and energy were constant during the interval of radius variation. One possible cause, poor vacuum, was investigated using a time resolved envelope equation. It was found that sufficiently high residual-gas pressure in the downstream transport region could result in the observed variation.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the prediction of pressure effects for the combination kinetics of two alkyl radicals with the geometric mean rule

Here, alkyl combination reactions, along with their reverse alkane unimolecular decomposition reactions, are widely present in pyrolysis and combustion systems. These reactions occur mainly at temperatures at which their rate coefficients depend on pressure, and only a few studies have explored this dependence for large size alkyls. The accurate calculation of these kinetic data is limited by the size of the alkyl fragments involved, since the theoretical methods used are computationally expensive. Therefore, little reliable data is available for the modeling of real fuels alkane decomposition kinetics. In this paper, we propose an alternative approach that allows an accurate estimation of pressure-dependent kinetic rates for the combination of long-chain alkyl radicals, based on tabulated reaction models. The rates of combination of linear alkyls radicals forming ethane to pentane were calculated using the CASPT2-F12/cc-pVDZ-F12 level within VRC-TST theory combined with master-equation simulations. The computed high-pressure limit rate coefficients showed that n-propyl could be a minimum-size representative structure for larger n-alkyl chain, but this approach fails to capture the pressure dependence of the reaction that remains size-dependent for larger alkyls. The Geometric Mean Rule (GMR), a simple rule that links the self and cross-reactions of three alkyl radicals, is used to address this issue. Our theoretical calculations show for the first time that the GMR applies not only at the high-pressure limit, but also for every pressure explored. The GMR is shown to be accurate, with a maximum 22 % deviation in the falloff region for the estimation of rates for small alkyl combinations. Using this method, we propose a tabulated reaction rate rule for the combination of alkyl radicals up to C5+C5. The use of computed rate coefficients with the GMR approximation opens ways to develop pressure-dependent reaction rate rules for large n-alkyl combinations, based on accurate and computationally expensive theoretical calculations on smaller alkyl fragments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations

In this work, we propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Adiabatic behavior of an elliptical vortex in a time-dependent external strain flow

The adiabatic behavior of two-dimensional (2D) fluid vortices subject to slowly varying, time-dependent external strain flows is studied theoretically, and experimentally using magnetized non-neutral electron plasmas. Here the E × B drift dynamics of the electrons perpendicular to the magnetic field are analogous to the motion of fluid vorticity under the 2D Euler equations describing ideal fluids. A low-dimensional elliptical vortex patch model is used along with a WKB approximation to derive a formula for the breaking of an adiabatic invariant due to the changing external flow. The invariant is interpreted as the amplitude of a perturbative oscillation about a stable fixed point corresponding to a steady elliptical vortex. Smooth, hyperbolic tangent and piecewise linear ramp functions are considered for the external strain time dependence. Standard exponential breaking is observed in the former case, whereas the latter exhibits a power-law breaking curve with periodic modulation. It is found that a driving term in the equations of motion contributes the majority of the breaking whereas the frequency variation plays a weaker, but significant role. The experimental data agree closely with the theoretical model. The most significant deviation is due to inviscid damping behavior associated with the smooth edges of the experimental vortices, which tends to reduce the amplitude of the oscillation. Finally, the results are compared and contrasted with other related experimental, numerical, and theoretical work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

New linear stability parameter to describe low-β electromagnetic microinstabilities driven by passing electrons in axisymmetric toroidal geometry

In magnetic confinement fusion devices, the ratio of the plasma pressure to the magnetic field energy, β, can become sufficiently large that electromagnetic microinstabilities become unstable, driving turbulence that distorts or reconnects the equilibrium magnetic field. In this paper, a theory is proposed for electromagnetic, electron-driven linear instabilities that have current layers localised to mode-rational surfaces and binormal wavelengths comparable to the ion gyroradius. The model retains axisymmetric toroidal geometry with arbitrary shaping, and consists of orbit-averaged equations for the mode-rational surface layer, with a ballooning space kinetic matching condition for passing electrons. The matching condition connects the current layer to the large scale electromagnetic fluctuations, and is derived in the limit that β is comparable to the square root of the electron-to-ion-mass ratio. Electromagnetic fluctuations only enter through the matching condition, allowing for the identification of an effective β that includes the effects of equilibrium flux surface shaping. The scaling predictions made by the asymptotic theory are tested with comparisons to results from linear simulations of micro-tearing and electrostatic microinstabilities in MAST discharge #6252, showing excellent agreement. In particular, it is demonstrated that the effective β can explain the dependence of the local micro-tearing mode (MTM) growth rate on the ballooning parameter θ 0 – possibly providing a route to optimise local flux surfaces for reduced MTM-driven transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Derivative-based SINDy (DSINDy): Addressing the challenge of discovering governing equations from noisy data

Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a predetermined basis in the states and finds the expansion coefficients through linear regression with sparsity constraints. This approach requires an accurate estimation of the state time derivatives, which is not necessarily possible in the high-noise regime without additional constraints. We present an approach called Derivative-based SINDy (DSINDy) that combines two novel methods to improve ODE recovery at high-noise levels. First, we denoise the state variables by applying a projection operator that leverages the assumed basis for the system dynamics. Second, we use a second order cone program (SOCP) to find the derivative and governing equations simultaneously. We derive theoretical results for the projection-based denoising step, which allow us to estimate the values of hyperparameters used in the SOCP formulation. This underlying theory helps limit the number of required user-specified parameters. Finally, we present results demonstrating that our approach leads to improved system recovery for the Van der Pol oscillator, the Duffing oscillator, the Rössler attractor, and the Lorenz 96 model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Impact of impurities on peeling–ballooning modes and turbulence in tokamak plasmas

This study investigates the impact of various impurity species on peeling–ballooning (PB) modes and microturbulence in tokamak plasmas through the extension of traditional two-fluid and gyro-landau-fluid (GLF) models. By incorporating finite Larmor radius (FLR) effects, the analysis provides a comprehensive understanding of impurity-driven impact and its interaction with plasma turbulence. Depending on charge state and local plasma conditions, heavy impurities may exhibit gyro-radii larger than those of main ions, which are captured in the extended GLF model presented. Following the presentation of modified two-fluid equations incorporating impurity effects, we systematically analyze the distinctions between impurity and main ion dynamics and their resultant feedback mechanisms on plasma behavior. Derivation of the linear dispersion relation enables quantification of impurity-mediated modifications to: plasma vorticity, diamagnetic drift and gyroviscous effects, electron Hall physics, and FLR effects. BOUT++ – based linear simulations corroborate this formalism, demonstrating systematic stabilization of PB modes upon impurity seeding. And then operational implications for practical impurity control strategies in tokamak devices are proposed. The results underscore the necessity of impurity management to maintain stability and optimize plasma confinement, with specific focus on how FLR effects contribute to transport dynamics. This work paves the way for enhanced modeling and simulation efforts, supporting the development of strategies to control impurity-induced turbulence and improve overall reactor performance.

BOUT++ simulation↗
DOE OSTI2022

The role of plasma instabilities in relativistic radiation-mediated shocks: stability analysis and particle-in-cell simulations

ABSTRACT Relativistic radiation-mediated shocks are likely formed in prodigious cosmic explosions. The structure and emission of such shocks are regulated by copious production of electron–positron pairs inside the shock-transition layer. It has been pointed out recently that substantial abundance of positrons inside the shock leads to a velocity separation of the different plasma constituents, which is expected to induce a rapid growth of plasma instabilities. In this paper, we study the hierarchy of plasma microinstabilities growing in an electron-ion plasma loaded with pairs and subject to a radiation force. Linear stability analysis indicates that such a system is unstable to the growth of various plasma modes which ultimately become dominated by a current filamentation instability driven by the relative drift between the ions and the pairs. These results are validated by particle-in-cell simulations that further probe the non-linear regime of the instabilities, and the pair-ion coupling in the microturbulent electromagnetic field. Based on this analysis, we derive a reduced-transport equation for the particles via pitch-angle scattering in the microturbulence and demonstrate that it can couple the different species and lead to non-adiabatic compression via a Joule-like heating. The heating of the pairs and, conceivably, the formation of non-thermal distributions, arising from the microturbulence, can affect the observed shock-breakout signal in ways unaccounted for by current single-fluid models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Comprehensive simulation of heavy-ion collisions at nonzero baryon chemical potential

Here, we present results of hydrodynamic modeling of Au-Au collisions from $\sqrt{s_{NN}}$ = 7.7 to 200 GeV. Our simulations have three novel components. First, we use a Linear EXtrapolation of Ultratrelativistic nucleon-nucleon Scattering to nucleus-nucleus collisions (LEXUS) inspired Monte Carlo initial-state model. Second, we use a crossover equation of state at finite baryon densities without a critical point. Finally, we use departure functions derived from the quasiparticle theory of transport coefficients for hadronic matter at nonzero baryon densities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Probabilistic measures for biological adaptation and resilience

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed “ecological resilience through adaptation,” specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. Importantly, the resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Stochastic density functional theory combined with Langevin dynamics for warm dense matter

Here, this study overviews and extends a recently developed stochastic finite-temperature Kohn-Sham density functional theory to study warm dense matter using Langevin dynamics, specifically under periodic boundary conditions. The method's algorithmic complexity exhibits nearly linear scaling with system size and is inversely proportional to the temperature. Additionally, a linear-scaling stochastic approach is introduced to assess the Kubo-Greenwood conductivity, demonstrating exceptional stability for dc conductivity. Utilizing the developed tools, we investigate the equation of state, radial distribution, and electronic conductivity of hydrogen at a temperature of 30 000 K. As for the radial distribution functions, we reveal a transition of hydrogen from gaslike to liquidlike behavior as its density exceeds 4 g/cm 3 . As for the electronic conductivity as a function of the density, we identified a remarkable isosbestic point at frequencies around 7 eV, which may be an additional signature of a gas-liquid transition in hydrogen at 30 000 K.

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

Developing VSC-HVDC Oscillation Damping Control Constraints in Unit Commitment

High-voltage direct current (HVDC) systems within the existing power grids will play a pivotal role in enabling high share of renewable power integration and transportation electrification. There is a need for transmission planning models to accurately capture the impact of VSC-HVDC oscillation damping control on the system planning and model the constraints in the security constrained unit commitment (SCUC) problem. In this paper, the SCUC problem in a hybrid DC-AC grid considering damping on electromechanical inter-area oscillation is studied. An electromechanical oscillation-driven transmission capability constraints are derived from system swing equation and incorporated into the SCUC. Multiple system damping control scenarios are set based on the extracted plausible bounds of damping coefficient and inertia constant to linearize the nonlinear expressions. The SCUC problem with proposed constraints is tested on the Reliability Test System Grid Modernization Lab Consortium (RTS-GMLC) via PLEXOS. The impact of the proposed constraints on regional generation, inertia, power flow, annual system cost, and renewable energy curtailment are fully assessed.

damping control↗
DOE OSTI2020

Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids. LDRD Final Report

This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. In this project, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality. At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5x improvement in accuracy and allows for taking an 8x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method. The report concludes with a brief summary of ongoing projects and collaborations that utilize or extend the products of this work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Developing VSC-HVDC Oscillation Damping Control Constraints in Unit Commitment

High-voltage direct current (HVDC) systems within the existing power grids will play a pivotal role in enabling high share of renewable power integration and transportation electrification. There is a need for transmission planning models to accurately capture the impact of VSC-HVDC oscillation damping control on the system planning and model the constraints in the security constrained unit commitment (SCUC) problem. In this paper, the SCUC problem in a hybrid DC-AC grid considering damping on electromechanical inter-area oscillation is studied. An electromechanical oscillation-driven transmission capability constraints are derived from system swing equation and incorporated into the SCUC. Multiple system damping control scenarios are set based on the extracted plausible bounds of damping coefficient and inertia constant to linearize the nonlinear expressions. The SCUC problem with proposed constraints is tested on the IEEE 73-bus reliability test system (RTS) case via PLEXOS. The impact of the proposed constraints on regional generation, inertia, power flow, annual system cost, and renewable energy curtailment are fully assessed.

damping control↗