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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Simulating Global Terrestrial Carbon and Nitrogen Biogeochemical Cycles With Implicit and Explicit Representations of Soil Microbial Activity

Abstract Nutrient limitation is widespread in terrestrial ecosystems. Accordingly, representations of nitrogen (N) limitation in land models typically dampen rates of terrestrial carbon (C) accrual, compared with C‐only simulations. These previous findings, however, rely on soil biogeochemical models that implicitly represent microbial activity and physiology. Here we present results from a biogeochemical model testbed that allows us to investigate how an explicit versus implicit representation of soil microbial activity, as represented in the MIcrobial‐MIneral Carbon Stabilization (MIMICS) and Carnegie‐Ames‐Stanford Approach (CASA) soil biogeochemical models, respectively, influence plant productivity, and terrestrial C and N fluxes at initialization and over the historical period. When forced with common boundary conditions, larger soil C pools simulated by the MIMICS model reflect longer inferred soil organic matter (SOM) turnover times than those simulated by CASA. At steady state, terrestrial ecosystems experience greater N limitation when using the MIMICS‐CN model, which also increases the inferred SOM turnover time. Over the historical period, however, warming‐induced acceleration of SOM decomposition over high latitude ecosystems increases rates of N mineralization in MIMICS‐CN. This reduces N limitation and results in faster rates of vegetation C accrual. Moreover, as SOM stoichiometry is an emergent property of MIMICS‐CN, we highlight opportunities to deepen understanding of sources of persistent SOM and explore its potential sensitivity to environmental change. Our findings underscore the need to improve understanding and representation of plant and microbial resource allocation and competition in land models that represent coupled biogeochemical cycles under global change scenarios.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗
DOE OSTI2025

Minimal implicit-solvent coarse-grained simulation of Pluronic block copolymers with ionic liquids

Pluronic block copolymers, composed of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) in a triblock structure (PEO–PPO–PEO), are well known for their amphiphilic character and ability to self‐assemble into micelles in aqueous solution. The addition of ionic liquids (ILs) can further modulate the core–shell structures of these copolymers, influencing their stability, critical micellization temperature, and size. However, fully atomistic simulations often become prohibitively expensive due to the size and complexity of these systems. In this work, coarse‐grained simulations using a minimal implicit‐solvent model were performed to examine how two classes of ILs, namely, 1‐alkyl‐3‐methylimidazolium ([C n C 1 im]) and 1‐alkyl‐3‐methylpyrrolidinium ([C n C 1 pyrr]), change the micellization of Pluronic block copolymers in aqueous solution. The effects of IL concentration and alkyl group length were investigated, and the model greatly improved the efficiency of simulating large‐scale micelle systems. Furthermore, the numerical simulations are qualitatively compared with experimental investigations. Our results show that adding ILs expands the micelle core by embedding IL tails among the PPO blocks, thereby increasing overall micelle size. Less polar ILs generally induce more pronounced micellar growth. However, the effect of IL tail length on conformation and micellar packing is non‐monotonic. Up to moderate chain lengths (around C8–C10), the IL tails can extend sufficiently to increase local separation within the micelle; at longer tail lengths, enhanced hydrophobic clustering and steric hindrance cause the tails to bend or fold, capping further expansion. In addition, although block copolymer chains tend to pack more closely in the presence of longer‐tailed ILs, the random coil size of an individual polymer chain does not necessarily shrink. Meanwhile, these insights provide a deeper understanding of how Pluronic/IL systems interact, informing applications in drug delivery, cosmetics, food, and environmental engineering. Finally, our minimal implicit‐solvent model can be applied to larger systems and longer timescales, substantially reducing computational cost while reproducing key structural trends observed experimentally.

Atomistic simulations↗
DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Verification of an energy-conserving semi-implicit electrostatic particle-in-cell scheme for modeling high-density plasma at scale

A verification study of a semi-implicit energy-conserving electrostatic particle-in-cell algorithm is presented. The algorithm relaxes the time-step and mesh-size constraints that require resolution of the plasma period and Debye length associated with traditional explicit momentum-conserving particle-in-cell algorithms. Physical implications and applicability of using the semi-implicit scheme for modeling high-density plasmas are discussed. Where possible, numerical results are compared against analytical solutions. The simulation results indicate that the algorithm is stable at time steps larger than twice the inverse plasma frequency and cell sizes larger than the Debye length. It is found that the algorithm gives adequate results, provided that the distribution function and the spatiotemporal scales dictating the physics of the problem are resolved. As such, the algorithm may provide a robust method for kinetic modeling of high-density plasmas at scale.

Cyclotron resonance↗
DOE OSTI2025

Electromagnetic Transient Simulation of Photovoltaic Inverter Using Implicit-Explicit Solver

This paper introduces the implementation of electromagnetic transient (EMT) simulations of a photovoltaic (PV) inverter module using the Implicit-Explicit (ImEx) solver in the Suite of Nonlinear and Differential/Algebraic Equation Solvers (SUNDIALS). This study demonstrates the effectiveness of the ImEx solver in overcoming the challenges inherent in simulating the complex dynamics of PV inverter modules. Furthermore, using SUNDIALS’ ImEx solver module ARKODE for EMT simulation automates key aspects of the process, such as numerical integration, providing substantial benefits including enhanced consistency, faster implementation, reduced human error, and the capability to handle the complexities of advanced numerical integration. By conducting comparative simulations with an implicit method used in commercial software, the research showcases the ImEx solver’s capability in achieving high accuracy and reliability. Results indicate that leveraging the ImEx approach significantly enhances modeling fidelity and reduces simulation setup times, offering a promising tool for the EMT analysis of PV inverter systems in power electronics-dominated power grids.

Choi, Jongchan [ORNL] (ORCID:000000025952455X)↗
DOE OSTI2026

REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization

Applications of Implicit Neural Representations (INRs) have emerged as a promising deep learning approach for compactly representing large volumetric datasets. These models can act as surrogates for volume data, enabling efficient storage and on-demand reconstruction via model predictions. However, conventional deterministic INRs only provide value predictions without insights into the model’s prediction uncertainty or the impact of inherent noisiness in the data. This limitation can lead to unreliable data interpretation and visualization due to prediction inaccuracies in the reconstructed volume. Identifying erroneous results extracted from model-predicted data may be infeasible, as raw data may be unavailable due to its large size. To address this challenge, we introduce REV-INR, Regularized Evidential Implicit Neural Representation, which learns to predict data values accurately along with the associated coordinate-level data uncertainty and model uncertainty using only a single forward pass of the trained REV-INR during inference. By comprehensively comparing and contrasting REV-INR with existing well-established deep uncertainty estimation methods, we show that REV-INR achieves the best volume reconstruction quality with robust data (aleatoric) and model (epistemic) uncertainty estimates using the fastest inference time. Consequently, we demonstrate that REV-INR facilitates assessment of the reliability and trustworthiness of the extracted isosurfaces and volume visualization results, enabling analyses to be solely driven by model-predicted data.

Saklani, Shanu [Indian Institute of Technology, Ka↗
DOE OSTI2025

Snap-Through Buckling Pressure Prediction of Spherical Caps: A Comparison of Analytical, Implicit, and Explicit Methods

Snap-through buckling is a nonlinear and dynamic instability that occurs in curved shell structures such as domes, pressure vessels, and aerospace panels. Unlike classical linear buckling, it involves a sudden transition between equilibrium states caused by geometric nonlinearity and rapid strain-to-kinetic energy conversion (Timoshenko & Gere, 1961; Budiansky & Roth, 1962). This study investigates the snap-through behavior of thin spherical caps using both implicit and explicit solvers in ANSYS Workbench. While implicit analysis accurately captures quasi-static response, it struggles with convergence near instability. In contrast, explicit LS-DYNA simulation naturally handles the nonlinear dynamic event with minimal tuning and computational cost.

42 ENGINEERING↗
DOE OSTI2025

Planar Collisionless Shock Simulations with the Semi-implicit Particle-in-cell Model FLEKS

This study investigates the applicability of the semi-implicit particle-in-cell code FLexible Exascale Kinetic Simulator (FLEKS) to heliospheric shock simulations. We examine one- and two-dimensional local planar shock simulations, initialized using MHD states with upstream conditions representative of plasmas in the hypersonic, β ∼ 1 regime, for both quasi-perpendicular and quasi-parallel configurations. The refined algorithm in FLEKS proves robust, enabling accurate shock simulations with a grid resolution on the order of the electron inertial length d e . Our simulations successfully capture key shock features, including shock structures (foot, ramp, overshoot, and undershoot), upstream and downstream waves (fast magnetosonic, whistler, Alfvén ion-cyclotron, and mirror modes), and non-Maxwellian particle distributions. Crucially, we find that at least two spatial dimensions are critical for accurately reproducing downstream-wave physics in quasi-perpendicular shocks and capturing the complex dynamics of quasi-parallel shocks, including surface rippling, shocklets, short, large-amplitude magnetic structures, magnetic reconnection, and jets. Furthermore, our parameter studies demonstrate the impact of mass ratio and grid resolution on shock physics. This work provides valuable guidance for selecting appropriate physical and numerical parameters for shock simulations using a semi-implicit PIC method, paving the way for incorporating kinetic shock processes into large-scale collisionless plasma simulations with the MHD-AEPIC model.

plasma astrophysics↗
DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗
NASA NTRS1973

Digital flight control design using implicit model following.

A design procedure for determining the control gains of a discrete-time ('digital') control system is presented. The method is separable into four distinct steps: (1) the definition of closed-loop response criteria, (2) the choice of a discrete-time model which provides the desired response, (3) the determination of control gains which implicitly force the actual system to follow the desired response, and (4) the reduction of the measurement state by the introduction of an 'observer' (a form of integral-differential compensation). It is shown that a single desired response does not completely define the 'ideal' system. The response criterion generally leaves some parameters of the model unspecified, allowing two courses for improving the model: (1) definition of additional response criteria, or (2) redefinition of the discrete-time model for improved implicit model-following with the actual closed-loop system.

Stengel, R. F.↗
NASA NTRS1975

Higher order accurate partial implicitization: An unconditionally stable fourth-order-accurate explicit numerical technique

The previously obtained second-order-accurate partial implicitization numerical technique used in the solution of fluid dynamic problems was modified with little complication to achieve fourth-order accuracy. The Von Neumann stability analysis demonstrated the unconditional linear stability of the technique. The order of the truncation error was deduced from the Taylor series expansions of the linearized difference equations and was verified by numerical solutions to Burger's equation. For comparison, results were also obtained for Burger's equation using a second-order-accurate partial-implicitization scheme, as well as the fourth-order scheme of Kreiss.

Graves, R. A., Jr.↗
NASA NTRS1976

Comments on the role of diagonal dominance in implicit difference methods

Numerical tests were made for a model of the Navier-Stokes equations using a second-order accurate implicit scheme which guarantees diagonal dominance. The results suggest that the failure of implicit methods using large marching steps may not always be attributed to the lack of diagonal dominance in the coefficient matrix. In some cases the failure may be caused by a nonlinear instability associated with the solution method.

Rudy, D. H.↗
NASA NTRS1976

Implicit finite-difference procedures for the computation of vortex wakes

Implicit finite-difference procedures for the primitive form of the incompressible Navier-Stokes and the compressible Euler equations are used to compute vortex wake flows. The partial differential equations in strong conservation-law form are transformed to cluster grid points in regions with large changes in vorticity. In addition to clustering, fourth-order accurate, spatial difference operators are used to help resolve the flow-field gradients. The use of implicit time-differencing permits large time steps to be taken since temporal variations are typically small. Computational efficiency is achieved by approximate factorization. Both two-dimensional and preliminary three-dimensional calculations are described and qualitatively compared with existing experimental data.

Steger, J. L.↗
NASA NTRS1978

Conservative implicit schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) were investigated for the solution of matrix equations resulting from finite difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, was introduced by an upwind bias of the density. Two implicit AF procedures are presented and their convergence performance is compared with that of the standard transonic solution procedure, successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. The results indicate that the AF schemes are substantially faster than SLOR.

Holst, T. L.↗