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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗
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 OSTI2024

Virtual Time III, Part 3: Throttling and Message Cancellation

This is Part 3 of a trio of papers that unify in a natural way the two historically distinct parallel discrete event synchronization paradigms, optimistic and conservative, combining the best properties of both into a single framework called Unified Virtual Time (UVT). In this part, we survey the synchronization effects that can be achieved by restricting to corner cases the relationships permitted among the control variables, GVT, CVT, TVT, and LVT, which were defined in Part 1. Here we also survey various throttling policies from the literature and describe how they can be implemented in UVT by controlling the value of TVT, including policies that can take advantage of rollback in addition to LP blocking. A significant result is a new category of efficient and higher precision throttling algorithms for optimistic execution that are based on optimistic lookahead, defined in a way that is symmetric to what we now call the conservative lookahead information that is traditionally used for conservative synchronization. Finally, we present a novel algorithm allowing the choice between lazy and aggressive cancellation to be made on a message-by-message basis using either external logic expressed in the model code, or policy code internal to the simulator, or a mixture of both.

throttling↗
DOE OSTI2020

Continuous and discrete modeling of HIV-1 decline on therapy

Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582–1586, 1996) and Perelson and Nelson (SIAM Rev 41:3–44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. Here, one of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Automatic Time Step Control to Resolve Hydromechanically Driven Fault Reactivation, Spontaneous Nucleation, and Seismic Arrest

Abstract A physical understanding of the progression from flow‐driven (quasi‐static) poromechanical deformation to dynamic fault rupture is critical to the resilient operations of several engineering systems. These processes are bridged by a progression from fault reactivation to the spontaneous nucleation of unstable sliding. Toward addressing this challenge, novel automatic time step size control methods are developed to enable accurate and efficient simulation of these dynamics and transitions from the first principles. The controllers combine local models for discretization error and Coulomb failure conditions to automatically adjust the time step size across several orders of magnitude. The methods do not require additional empirical or theoretical input and can resolve the pre‐rupture, interseismic, and seismic periods to the allowed accuracy. The computational results reveal that the proposed methods automatically capture the onset of reactivation and nucleation for homogeneous and heterogeneous fields. Hydrodynamic and structural heterogeneity lead to disparate critical nucleation sizes compared to those predicted by theory. The results highlight its potential in predicting induced seismicity in realistic subsurface engineering systems and at practical scales.

Environmental Sciences & Ecology↗
DOE OSTI2023

Discrete element simulation of Pebble Bed Reactors on graphics processing units

Prediction of pebble positions in a Pebble Bed Reactor (PBR) is necessary for both reactor physics and thermal hydraulics simulations as the arrangement of pebbles has a significant impact on the resulting core power, coolant flow, and fuel temperature. Knowledge of pebble movement as the fuel is cycled through the core is also critical for predicting the fuel residence time and subsequently, the fuel burnup. Simulation with the Discrete Element Method (DEM) can provide knowledge of both the fuel packing and the fuel movement during cycling. Previous works that have performed 3D full-core DEM simulation of PBRs have used simplified models that neglect reflector wall features. This work employs a graphics processing unit (GPU)-enabled DEM code, Project Chrono, to analyze the differences in pebble packing and pebble velocities between a simplified smooth PBR reflector and a more realistic reflector that includes circular wall features. Additionally, a sensitivity study is performed on the depth of the wall features to ensure that crystallization is prevented. Project Chrono is also validated for PBR cycling applications using experimental data. It is found that wall features with a depth of at least 0.5 pebble diameters significantly reduce crystallization in the near-wall region, leading to discrepancies in both packing fraction and pebble velocity in this region compared to the simplified reflector models. These discrepancies are found to lead to roughly a 5–10% difference in the prediction of the near-wall porosity and a 10% difference in the prediction of the velocity of pebbles near the wall. As a result of these discrepancies, it is suggested that future DEM simulations of PBRs include wall features to reduce modeling errors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

An error-controlled adaptive time-stepping method for particle advancement in coupled CFD-DEM simulations

Coupled Computational-Fluid-Dynamics (CFD) and Discrete-Element-Method (DEM) models provide an accurate description of multiphase physical systems where a solid granular particle phase exists in an underlying gaseous continuous medium. The time integration of the granular phase in these simulations is typically handled using an explicit scheme with a constant time-step among all particles that is invariant in time to resolve inter-particle collisions. A locally third-order accurate adaptive time integration technique for particles that employs an embedded locally second-order scheme for error determination is presented in this work. The particle time-step size is dynamically adapted based on solution error, thus leading to significant savings in computational time. The efficacy of our scheme is quantified using four test cases of varying complexity (binary collision, homogeneous cooling system, fluidized bed and hopper discharge). The adaptive time-stepping method exhibits improved performance (~ 2–3 times in most of the cases studied) compared to three commonly used non-adaptive time-step methods (first-order Euler-explicit, second-order Adams-Bashforth and third-order Runge-Kutta schemes), while maintaining the same level of accuracy and parallel scalability.

42 ENGINEERING↗
DOE OSTI2024

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Non-orientable AdS 3 and its holography

Known solutions to three-dimensional gravity with negative cosmological constant consist of either AdS 3 or its orbifolds (or orientifolds). We geometrically derive a novel non-orientable AdS 3 spacetime that is an orientifold of a spinor double cover of AdS 3 . This spacetime’s universal cover contains a lightlike compact direction instead of AdS 3 ’s spacelike compact direction. We show that its gravity theory possesses a simpler excited state spectrum and a Chern-Simons/Wess-Zumino-Witt (CS/WZW) correspondence between a single independent CS term and boundary chiral WZW term. This leads us to suggest that CS theory is able to more fully describe non-orientable pure gravity theory compared to orientable gravity.

AdS-CFT Correspondence↗
DOE OSTI2021

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

GX: a GPU-native gyrokinetic turbulence code for tokamak and stellarator design

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. Here, this has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Prediction of hemiwicking dynamics in micropillar arrays

Dynamic hemiwicking behavior is observable in both nature and a wide range of industrial applications ranging from biomedical devices to thermal management. We present a semi-analytical modeling framework (without empirical fitting coefficients) to predict transient capillary-driven hemiwicking behavior of a liquid through a nano/microstructured surface, specifically a micropillar array. In our model framework, the liquid domain is discretized into micropillar unit cells to enable the time marching of the hemiwicking front. A simplified linear pressure drop is assumed along the hemiwicking length such that the local meniscus curvature, contact angle, and effective liquid height are determined at each time step in our transient model. This semi-analytical model is validated with experimental data from our own experiments and from published literature for different fluids. Our model predicts hemiwicking dynamics with <20% error over a broad range of micropillar geometries with height-to-pitch ratio ranging between ≈0.34 and 6.7 and diameter-to-pitch ratio in the range of ≈0.25–0.7 and without any fitting parameters. For lower diameter-to-pitch ratio data points related to sparse micropillar array arrangements, we suggest modifications to the semi-analytical model. This work sheds light on complex and dynamic solid–liquid–vapor interfacial interactions which could serve as a guide for the design of textured surfaces for wicking enhancement in multi-phase thermal and mass transport technologies and applications.

Mechanics↗
DOE OSTI2020

Interpenetrating Plasma Simulations

This project investigated multifluid models for simulating interpenetrating plasmas. These models solve the Euler equations for each plasma stream along with an appropriate model for electron dynamics. The project developed a novel code, Euclid, that simulates these models using high-order conservative spatial discretization methods and explicit and semi-implicit time integration methods. Euclid was used to solve several multifluid test cases representative of plasma dynamics in high-energy density physics experiments. Kinetic simulations of interpenetrating flows using the LOKI code revealed novel physical effects of the ion-ion streaming instability. A new multi-flow collision operator was developed for the LOKI code. A simple model of the ion-ion streaming instability was also developed. Several presentations were given on the project results; three journal articles have been published, one has been submitted, and two are planned.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Here, we explore the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing with explicit time stepping of the same order accuracy in time, the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomain problems of smaller sizes and solving them locally, the proposed approach could speed up the calculation of matrix exponential vector products. Several standard test cases for shallow water equations of one or multiple layers are considered. The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

58 GEOSCIENCES↗
DOE OSTI2022

Electromagnetic Transient (EMT) Simulation Algorithms for Evaluation of Large-Scale Extreme Fast Charging Systems (T&D Models)

Simulation of high-fidelity models of extreme fast charging (XFC) systems and large-area power grids with many XFCs can be time consuming in traditional simulators. Traditional simulators use a single method of discretization for all the components that results in imposing a large computational burden of inverting a large matrix as well as increased computations related to single method of discretization (that is typically a trapezoidal method). To overcome the problem of simulating large-area power grids with many XFCs, in this paper, advanced numerical simulation algorithms are applied for the first time together to reduce the dimension of matrix inversion. Here, the algorithms include numerical stiffness-based segregation, time constant-based segregation, clustering and aggregation on differential algebraic equations (DAEs), and multi-order integration approaches. These algorithms apply multiple discretization algorithms rather than a single discretization algorithm that further reduces the computational burden. The approaches mentioned here have resulted in speed-up of up to 18x in the simulation of a single distribution system with 15 XFCs and of up to 271x in the simulation of a transmission-distribution system with 300 XFCs in multiple distribution feeders with respect to conventional simulators (like power systems computer aided design [PSCAD]).

42 ENGINEERING↗
DOE OSTI2024

Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds

Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analysis of the performance of a hybrid CPU/GPU 1D2D coupled model for real flood cases

Coupled 1D2D models emerged as an efficient solution for a two-dimensional (2D) representation of the floodplain combined with a fast one-dimensional (1D) schematization of the main channel. At the same time, high-performance computing (HPC) has appeared as an efficient tool for model acceleration. In this work, a previously validated 1D2D Central Processing Unit (CPU) model is combined with an HPC technique for fast and accurate flood simulation. Due to the speed of 1D schemes, a hybrid CPU/GPU model that runs the 1D main channel on CPU and accelerates the 2D floodplain with a Graphics Processing Unit (GPU) is presented. Since the data transfer between sub-domains and devices (CPU/GPU) may be the main potential drawback of this architecture, the test cases are selected to carry out a careful time analysis. Here, the results reveal the speed-up dependency on the 2D mesh, the event to be solved and the 1D discretization of the main channel. Additionally, special attention must be paid to the time step size computation shared between sub-models. In spite of the use of a hybrid CPU/GPU implementation, high speed-ups are accomplished in some cases.

54 ENVIRONMENTAL SCIENCES↗