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At least 271 records · Page 15

Fast model-based scenario optimization in NSTX-U enabled by analytic gradient computation

Model-based optimization offers a systematic approach to advanced scenario planning. In this case, the feedforward-control inputs (actuator trajectories) that are needed to attain and sustain a desired scenario are obtained by solving a nonlinear constrained optimization problem. This class of problems generally minimize a cost function that measures the difference between desired and actual plasma states. Several numerical optimization algorithms, such as sequential quadratic programming, require repeated calculation of the cost function gradients with respect to the input trajectories. Calculating these gradients numerically can be computationally intensive, increasing the time needed to solve the feedforward-control optimization problem. Here, this work introduces a method to analytically calculate these cost function gradients from the current profile evolution model. This can significantly reduce the computational time and allow for fast feedforward-control optimization, which would eventually enable optimal scenario planning between discharges. The performance of the feedforward optimizer with analytical gradients is compared to a traditional optimization algorithm based on numerical gradients for different NSTX-U scenarios. The plasma dynamics in the optimization algorithm are simulated using the Control Oriented Transport SIMulator (COTSIM). Results of the work show that analytical gradients consistently reduce the computation time while achieving trajectories that are comparable to those obtained by traditional optimization algorithms based on numerical gradients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Flutter analysis of a supersonic cascade in time domain using an ADI Euler solver

The aeroelastic stability of a two-dimensional cascade oscillating in supersonic axial flow is analyzed in the time domain. The aeroelastic model consists of a single degree of freedom typical section structural model for each blade of the cascade and an unsteady two-dimensional cascade aerodynamic model based on the Euler equations. The Euler equations are solved using a time accurate Alternating Direction Implicit (ADI) solution scheme. The aeroelastic equations are integrated in time. The effect of interblade phase angle is included in the aeroelastic analysis by an appropriate choice of initial and boundary conditions. Flutter predictions are obtained from the time response of a flat plate cascade in single degree of freedom pitching motion. The results correlate well with those obtained from a separate frequency domain flutter analysis for all values of interblade phase angles considered. Flutter results are then presented for cascades having airfoil sections representative of a supersonic throughflow fan. The validity of the time integration method for a cascade of airfoils at various interblade phase angles is demonstrated.

Reddy, T. S. R.↗

Computations of Axisymmetric Flows in Hypersonic Shock Tubes

A time-accurate two-dimensional fluid code is used to compute test times in shock tubes operated at supersonic speeds. Unlike previous studies, this investigation resolves the finer temporal details of the shock-tube flow by making use of modern supercomputers and state-of-the-art computational fluid dynamic solution techniques. The code, besides solving the time-dependent fluid equations, also accounts for the finite rate chemistry in the hypersonic environment. The flowfield solutions are used to estimate relevant shock-tube parameters for laminar flow, such as test times, and to predict density and velocity profiles. Boundary-layer parameters such as bar-delta(sub u), bar-delta(sup *), and bar-tau(sub w), and test time parameters such as bar-tau and particle time of flight t(sub f), are computed and compared with those evaluated by using Mirels' correlations. This article then discusses in detail the effects of flow nonuniformities on particle time-of-flight behind the normal shock and, consequently, on the interpretation of shock-tube data. This article concludes that for accurate interpretation of shock-tube data, a detailed analysis of flowfield parameters, using a computer code such as used in this study, must be performed.

Sharma, Surendra P.↗

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗

Extended quantitative rescattering model for simulating high-order harmonic streaking spectra by synchronization of an intense IR laser and a time-delayed attosecond XUV pulse

In this work, we theoretically investigate the modulated high-harmonic generation (HHG) driven by an intense few-cycle infrared (IR) laser field and a weak extreme-ultraviolet (XUV) pulse at a delayed time. We establish an extended quantitative rescattering (EQRS) model to simulate the HHG streaking spectra, with the ideas of correcting the IR ionization and the transition from the ground to continuum states in the strong-field approximation. The EQRS model has an accuracy comparable to that from “exactly” solving the time-dependent Schrödinger equation (TDSE). We reveal that the fringes in the streaking spectra are caused by the interference between the attosecond XUV pulse and harmonics resulting from different recombination pathways under the intense IR laser. We then demonstrate that the XUV pulse can be accurately retrieved by treating the single-atom TDSE results or macroscopic propagation results as the “input” data. This work provides with a tool for efficiently simulating and thoroughly analyzing the XUV-assisted HHG, which could also enhance its capability for tracing the electron dynamics involved in the strong-field phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Two-Center Interference in the Photoionization Delays of Kr 2

Herein we present the experimental observation of two-center interference in the ionization time delays of Kr 2 . Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the photoionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a function of the electron kinetic energy, an effect that is traced back to constructive and destructive interference of the photoelectron wave packets that are emitted or scattered from the two atomic centers. Our interpretation of the experimental results is supported by solving the time-independent Schrödinger equation of a 1D double-well potential, as well as coupled-channel multiconfigurational quantum-scattering calculations of Kr 2 . This work opens the door to the study of a broad class of quantum-interference effects in photoionization delays and demonstrates the potential of attosecond coincidence spectroscopy for studying weakly bound systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

Low level coupling scheme between neutronics and thermal-hydraulics based on Anderson acceleration

The simulation of nuclear reactors is a multiphysics problem mixing, amongst other fields, neutron transport and thermal-hydraulics. The simplest and most used approach in multiphysics simulation is based on the coupling of single-physics codes in a black-box fashion. However, in order to reduce the computational time needed for such simulations, case-dependent optimizations are often required. In this paper, we aim at reducing the computational time required to solve a coupled neutronic/thermal-hydraulic steady-state problem on a simplified Pressurized Water Reactor (PWR) core. The idea is to deal simultaneously with the coupling of the energy groups of the deterministic neutronic description of the core and its thermal-hydraulic description with the Anderson acceleration. By doing so, the fission source terms are directly accelerated instead of the power map as done in most cases. The power method used to solve the k-eigenvalue problem inside the neutronic solver is thus accelerated with the Anderson acceleration. The numerical experimentations conducted in this work are performed using APOLLO3 and THEDI, and indicate that such coupling strategy improves the convergence rates in terms of number of iterations required and the total computational time. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Numerical Simulation of Flow Through an Artificial Heart

A solution procedure was developed that solves the unsteady, incompressible Navier-Stokes equations, and was used to numerically simulate viscous incompressible flow through a model of the Pennsylvania State artificial heart. The solution algorithm is based on the artificial compressibility method, and uses flux-difference splitting to upwind the convective terms; a line-relaxation scheme is used to solve the equations. The time-accuracy of the method is obtained by iteratively solving the equations at each physical time step. The artificial heart geometry involves a piston-type action with a moving solid wall. A single H-grid is fit inside the heart chamber. The grid is continuously compressed and expanded with a constant number of grid points to accommodate the moving piston. The computational domain ends at the valve openings where nonreflective boundary conditions based on the method of characteristics are applied. Although a number of simplifing assumptions were made regarding the geometry, the computational results agreed reasonably well with an experimental picture. The computer time requirements for this flow simulation, however, are quite extensive. Computational study of this type of geometry would benefit greatly from improvements in computer hardware speed and algorithm efficiency enhancements.

Rogers, Stuart E.↗

Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

Here we propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in (1+1) dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude E 0 and frequency Ω with a period determined by the Stückelberg phase, (2) the cutoff order of HHG is determined by 2eE 0 ℏΩ 2 , with e being the electron charge, and that (3) noninteger harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter γ = (Δ/2)Ω/eE 0 ,with Δ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

36 MATERIALS SCIENCE↗

An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner in using the method of pseudocompressibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme based on flux-difference splitting is used to compute the convective terms. The upwind differencing is biased based on the sign of the local eigenvalue of the Jacobian matrix. Third-order or fifth-order spatial accuracy is maintained throughout the interior grid points. The equations are solved using an implicit line-relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudotime, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at -90 deg angle-of-attack is also computed.

Rogers, Stuart E.↗

Feasibility of Using Fourier Neural Operators for 3D Elastic Seismic Simulations

Seismic simulations in three-dimensional (3D) Earth models are important in many of the seismological applications related to our lab’s mission, however, accurate high-fidelity simulations are computationally costly. We investigated the capabilities of the newly developed Fourier Neural Operator (FNO) to solve the 3D elastic wave equations for seismic simulations. We generated simulation data for training the FNO model, and analyzed its performance on various test cases, such as the performance with different number of training data, different resolutions, and on more canonical structures. We found the FNO model can reproduce 3D seismic simulations with high accuracy and ~169 times faster on a small spatial grid size of 16 x 16 x16. When applied on higher resolution data, we found that transfer learning with fine-tuning on a small amount of data achieves reasonable results. This feasibility study showed promising results for using FNO’s for 3D seismic simulations and represents the foundation of further research to develop this into a more mature approach for different seismological applications. The potential impact of this project will provide techniques for large-scale or real-time applications of solving PEDs in support of national lab’s programs.

58 GEOSCIENCES↗

A numerical solver for investigating the space charge effect on the electric field in liquid argon time projection chambers

This paper reports the development of a numerical solver aimed to simulate the interaction between the space charge (i.e. ions) distribution and the electric field in liquid argon time projection chamber (LArTPC) detectors. The ion transport equation is solved by a time-accurate, cell-centered finite volume method and the electric potential equation by a continuous finite element method. The electric potential equation updates the electric field which provides the drift velocity to the ion transport equation. The ion transport equation updates the space charge density distribution which appears as the source term in the electric potential equation. The interaction between the space charge distribution and the electric field is numerically simulated within each physical time step. The convective velocity in the ion transport equation can include the background flow velocity in addition to the electric drift velocity. The numerical solver has been parallelized using the Message Passing Interface (MPI) library. Numerical tests show and verify the capability and accuracy of the current numerical solver. It is planned that the developed numerical solver, together with a Computational Fluid Dynamics (CFD) package which provides the flow velocity field, can be used to investigate the space charge effect on the electric field in large-scale particle detectors.

42 ENGINEERING↗

Deterministic modelling of the SPERT IV reactor transients using the multi-physics capability of WIMS

The ANSWERS WIMS reactor physics code is being developed for whole core multi-physics modelling. The established neutronics capability for lattice calculations has recently been extended to be suitable for whole core modelling of Small Modular Reactors (SMRs). A whole core transport, SP3 or diffusion flux solution is combined with fuel assembly resonance shielding. An integrated thermal hydraulic solver permits temperature and density variations to feedback to the neutronics calculation. This capability can be applied to both steady state and time dependent transient problems. Nuclear reactor design and safety case development requires assessment of a range of reactor transients, to inform both normal operation limitations and accident scenario analysis. This paper presents new methodology developed in WIMS to couple the core neutronics to the integrated core thermal hydraulics solver for the simulation of reactor transients in whole core models. To support the validation of the multi-physics capability of WIMS, this capability has been applied to the reactivity insertion transient experiments performed in the plate fuelled SPERT-IV reactor. This study employs WIMS using the whole core solver MERLIN, which calculates the time-dependent flux distribution and magnitude, coupled to ARTHUR, which solves for the time-dependent thermal hydraulics solution, and provides thermal feedback via the cross sections generated by GEOM, which performs resonance shielding calculations and generates cross section data for the plate geometry. This spatial kinetics model, with dynamic cross section generation, allows for variations in the temperature and neutron flux profile with time.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Boson Star from Repulsive Light Scalars and Gravitational Waves

We study properties of boson stars consisting of ultra-light scalar dark matter with repulsive self-interactions. We investigate the origin of the maximum mass of spherically symmetric stable stars which emerges only when solving the full equations of motion in curved space-time, but not when solving the approximated Schrödinger-Newton equations. When the repulsion is weak, the backreaction of the curvature on the scalars acts as an additional source of attraction and can overcome the repulsion, resulting in a maximum star mass and compactness. We also point out that the potential in a UV completed particle physics model of light scalar dark matter is generally more complicated than the widely used φ 4 interaction. Additional interactions beyond φ 4 in the potential can dramatically change the properties of boson stars as well as modify the prospect of LIGO gravitational wave detection for binary mergers of boson stars.

Djuna Croon↗

Real-time operational planning for the U.S. air traffic system

This paper describes an integrated planning model for the U.S. air traffic system. The approach incorporates the dual objectives of monitoring collision risk while minimizing transportation costs. Specialized solution algorithms exploit the underlying structure of the model - especially for large-scale examples. The proposed formulation is tested with real-world data for the Indianapolis control sector. Additional experiments with a CRAY X-MP/24 supercomputer show that a full-scale model can be solved under real time conditions. Despite these advances, additional work is required in developing a practical system. Suggestions are made for combining advances in computer graphics and mathematical modeling.

Mulvey, John M.↗

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗

Learning Forecasts of Rare Stratospheric Transitions from Short Simulations

Abstract Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, sudden stratospheric warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These optimal forecasts concretely measure the event’s progress. Direct numerical simulation can estimate them in principle but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are short compared to the time scale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in time scales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

Finkel, Justin↗

Implicit and coupled fluid plasma solver with adaptive Cartesian mesh and its applications to non-equilibrium gas discharges

In this work, we present a new fluid plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (nonlinear, implicit) scheme for non-equilibrium gas discharge plasma. The electrons and ions are described using drift-diffusion approximation coupled to Poisson equation for the electric field. The electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperature and could also depend on electron density (important for plasma stratification). The ion and gas temperature are kept constant. The transport equations are discretized using a non-isothermal Scharfetter-Gummel scheme to resolve possible large temperature gradients in the sheaths. We demonstrate the new solver for simulations of direct current (DC) and radiofrequency (RF) discharges. The implicit treatment of the coupled equations allows using large time steps. The full-Newton method (FNM) enables fast nonlinear convergence at each time step, offering significantly improved simulation efficiency. We discuss the selection of time steps for solving different plasma problems. The new solver enables solving several problems we could not solve before with existing software: two- and three-dimensional structures of the entire DC discharges including cathode and anode regions, electric field reversals and double-layer formation, the normal cathode spot and an anode ring, moving striations in diffuse and constricted DC discharges, and standing striations in RF discharges. The developed FNM-ACM technique offers many benefits for tackling the disparity of gas discharge plasma systems' time scales and nonlinearity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗