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All sources NASA NTRS DOE OSTI

DOE OSTI2017

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Enhanced nearfield acoustic holography for larger distances of reconstructions using fixed parameter Tikhonov regularization

This paper evaluates the performance of various regularization parameter choice methods applied to different approaches of nearfield acoustic holography when a very nearfield measurement is not possible. For a fixed grid resolution, the larger the hologram distance, the larger the error in the naive nearfield acoustic holography reconstructions. These errors can be smoothed out by using an appropriate order of regularization. In conclusion, this study shows that by using a fixed/manual choice of regularization parameter, instead of automated parameter choice methods, reasonably accurate reconstructions can be obtained even when the hologram distance is 16 times larger than the grid resolution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

THREE-DIMENSIONAL BOLTZMANN HYDRO CODE FOR CORE COLLAPSE IN MASSIVE STARS. I. SPECIAL RELATIVISTIC TREATMENTS

We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled with hydrodynamics equations. This method is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of the advection and collision terms in the Boltzmann equations has been a challenge, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce, and shock-stall for a 15 M {sub ☉} progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects into our method.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Energy Exascale Earth System Model v2.0.1

First patch release of v2.0.0 Changes since v2.0.0 [Important change] Fix ocean threading bug seen in debug cases on Chrysalis with Intel 20.0.4. Was introduced around time of v2.0.0 tag. Does not change v2.0.0 answers on Chrysalis because those didn't use threading or debugging. [EAM] Add semi-lagrangian tracer transport for theta-l (F90 and C++), add new algorithm for finding tropopause, add DSCREAM to allow v2 and SCREAM settings in same code such as adjust_ps [EAM-MMF] 60L default, allow C++ back end of RRTMGP (EAM too). [EAMxx] add nu-top functionality, fix forcing functor, add ttype9 and dcmip2012 tests 2.1, 2.2, and 3 HOMME: remove obsolete remap algs, option to specify dynamics alg indep of tracer, new sponge layer, add imex tests [ELM] Add topography-based subgrid (topounits), add FATES-ELM Nitro., Phos. and CH4 coupling, add land-use ts for NARRM, add lulc for SSP3 RCP7, Fix nutrient fertilization exp test and carbon isotope flux, Fix xactive lnd dry deposition, add lake water storage option, fix plant hydraulics 2d params, fix carbon budget calc, fix soil nutrient conc. bug, fix mosart dam bug, add test for new ELM, MOSART features, fix bug in O3 dry dep stomatal resistances, fix plant hydraulics restart BFB error, update mkmapdata. [MOSART] fix bug for reading the latitude from an unstructured input file, fix oversat in bubble test. [MPAS-ocean] Add CFC11, CFC12 tracers, add 2D spherical transport tests, fix del4 tracer mixing, add MARBL ocean tracer mixing, modify harmonic analysis options, add GPU port of vmix routines, fix calc of ML-averaged BV freq. [MPAS-seaice] Change extents of initial polar disks for oRRS18to6v3 grid, fix ice BGC with MARBL, update spherical test cases, fix DON coupling, Remove Cf from sea ice constants. [MPAS-landice] add CRYO1850-4xCO2 compset [CIME] add GCP, ANL GCE, Spock, Perlmutter, deprecate config_compilers.xml, fix and clean-up cmake macros, fix slurm bindings, refactor CIME internal testing, cleanup SCORPIO perf data, allow position independent compset naming, [also] update v2 benchmarking suite, extend e3sm_prod with throughput and memory checks

E3SM Project, DOE↗

DOE OSTI2022

Numerical and experimental investigation of the flame kernel growth in a methane/air mixture near the lean flammability limit

Lean combustion has the potential to improve the thermal efficiency of spark-ignition engines, but it faces the significant challenge of increased cycle-to-cycle variation due to low mixture reactivity and unstable flame dynamics. Computational fluid dynamics (CFD) employing predictive models can guide engine design and optimize operating strategies for lean combustion. However, ignition and combustion models have rarely been validated at fuel-lean conditions, and a fundamental understanding of the early flame kernel growth process is also lacking for a successful sub-model development. Here, the present study develops a numerical simulation framework used to investigate early flame kernel growth in methane/air mixtures. A nanosecond-pulsed discharge (NPD) approach is employed to effectively decouple the flame kernel growth from the electrical discharge due to their difference in timescales, and equivalence ratios near the experimentally measured lean flammability limit (LFL) are selected to focus on challenging mixture conditions. Three numerical investigations, such as the choice of turbulence modeling, grid size, and grid control strategies, are examined to match both LFL and flame kernel structure measured from experiments. It is demonstrated that a quasi-direct numerical simulation (QDNS) with a fixed grid embedding of 10 μm can predict the LFL as φ CFD =0.61 and match the displacement speed of the kernel’s boundary marked in schlieren images. To predict the LFL and flame kernel shape, a fine grid (Δ≤12.5 μm) is needed to capture the consumption of formaldehyde (CH 2 O) in kernel’s reaction branches attached to the anode, and adaptive mesh refinement is replaced with the fixed embedding due to loss of simulation accuracy. Also, it is found that a large-eddy simulation (LES) using the Dynamic Structure model is not suitable for the NPD-induced flame kernel simulation because artificial sub-grid turbulent kinetic energy induced by shock dynamics alters the flow velocity calculation, resulting in divergence of LES from QDNS. Lastly, the simulation well matches the experimental data for the flame kernel evolution in three mixture conditions (φ = 0.7, 0.61, 0.55), showing toroidal flame kernel expansion and flame kernel growth/extinction.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

An implicit, sharp numerical treatment of viscous terms at arbitrarily shaped liquid-gas interfaces in evaporative flows

We report a novel methodology for accurate treatment of viscous terms in evaporation problems. The proposed scheme is an extension of the sharp viscous treatment of Kang et al. (2000) [7] to 3D phase change problems. To ensure accuracy and grid converging solutions, a new implicit approach to computing viscous fluxes across the phase interfaces is proposed, which was previously unavailable in fixed grid numerical schemes. Analytical relations were derived for the jump in velocity gradients across the 2D and 3D phase interfaces, an important constituent of the proposed scheme. The relations show a non-vanishing jump in the tangential gradients across the phase interface that are associated with evaporative flux and interfacial curvature. The proposed methodology demonstrated first order accuracy in canonical test cases. It is general and applicable to arbitrarily oriented interfaces, and can be readily implemented in existing evaporation flow solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

AnisWave2D

AnisWave2D is a 2D finite-difference code for simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.

Toomey, Aoife↗

DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Toward Exascale Earthquake Ground Motion Simulations for Near-Fault Engineering Analysis

Modernizing SW4 for massively parallel time-domain simulations of earthquake ground motions in 3D earth models increases resolution and provides ground motion estimates for critical infrastructure risk evaluations. Simulations of ground motions from large (M ≥ 7.0) earthquakes require domains on the order of 100 to500 km and spatial granularity on the order of 1 to5 m resulting in hundreds of billions of grid points. Surface-focused structured mesh refinement (SMR) allows for more constant grid point per wavelength scaling in typical Earth models, where wavespeeds increase with depth. In fact, MR allows for simulations to double the frequency content relative to a fixed grid calculation on a given resource. The authors report improvements to the SW4 algorithm developed while porting the code to the Cori Phase 2 (Intel Xeon Phi) systems at the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory. As a result, investigations of the performance of the innermost loop of the calculations found that reorganizing the order of operations can improve performance for massive problems.

58 GEOSCIENCES↗

DOE OSTI2024

Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors

Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfiability modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.

Physics↗

DOE OSTI2015

An empirical model of electron and ion fluxes derived from observations at geosynchronous orbit

Knowledge of the plasma fluxes at geosynchronous orbit is important to both scientific and operational investigations. We present a new empirical model of the ion flux and the electron flux at geosynchronous orbit (GEO) in the energy range ~1 eV to ~40 keV. The model is based on a total of 82 satellite-years of observations from the Magnetospheric Plasma Analyzer instruments on Los Alamos National Laboratory satellites at GEO. These data are assigned to a fixed grid of 24 local-times and 40 energies, at all possible values of Kp. Bi-linear interpolation is used between grid points to provide the ion flux and the electron flux values at any energy and local-time, and for given values of geomagnetic activity (proxied by the 3-hour Kp index), and also for given values of solar activity (proxied by the daily F10.7 index). Initial comparison of the electron flux from the model with data from a Compact Environmental Anomaly Sensor II (CEASE-II), also located at geosynchronous orbit, indicate a good match during both quiet and disturbed periods. The model is available for distribution as a FORTRAN code that can be modified to suit user-requirements.

58 GEOSCIENCES↗

DOE OSTI2021

Effect of topology changes on the breakup of a periodic liquid jet

Here, the breakup of a periodic jet is examined computationally, using a front-tracking/finite-volume method, where the interface is represented by connected marker points moving with the fluid, while the governing equations are solved on a fixed grid. Tracking the interface allows control of whether topology changes take place or not. The Reynolds and Capillary numbers are kept relatively low ($Re = 150$ and $Ca = 2$) so most of the flow is well resolved. The effect of topology changes is examined by following the jet until it has mostly disintegrated, for different “coalescence criterion,” based on the thickness of thin films and threads. The evolution of both two-dimensional and fully three-dimensional flows is examined. It is found that although there is a significant difference between the evolution when no breakup takes place and when it does, once breakup takes place the evolution is relatively insensitive to exactly how it is triggered for a range of coalescence criterion, and any differences are mostly confined to the smallest scales.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

An Eulerian projection method for quasi-static elastoplasticity

A well-established numerical approach to solve the Navier-Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. Here, we highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

TURBULENCE IN THE INTERGALACTIC MEDIUM: SOLENOIDAL AND DILATATIONAL MOTIONS AND THE IMPACT OF NUMERICAL VISCOSITY

We use a suite of cosmological hydrodynamical simulations, run by two fixed grid codes, to investigate the properties of solenoidal and dilatational motions of the intergalactic medium (IGM) and the impact of numerical viscosity on turbulence in an ΛCDM universe. The codes differ only in the spatial difference discretization. We find that (1) The vortical motion grows rapidly since z = 2 and reaches ∼10 km s{sup –1}-90 km s{sup –1} at z = 0. Meanwhile, the small-scale compressive ratio r{sub CS} drops from 0.84 to 0.47, indicating comparable vortical and compressive motions at z = 0. (2) Power spectra of the solenoidal velocity possess two regimes, ∝k {sup –0.89} and ∝k {sup –2.02}, while the total and dilatational velocity follow the scaling k {sup –1.88} and k {sup –2.20}, respectively, in the turbulent range. The IGM turbulence may contain two distinct phases, the supersonic and post-supersonic phases. (3) The non-thermal pressure support, measured by the vortical kinetic energy, is comparable with the thermal pressure for ρ{sub b} ≅ 10-100, or T < 10{sup 5.5} K at z = 0.0. The deviation of the baryon fraction from the cosmic mean shows a preliminary positive correlation with the turbulence pressure support. (4) A relatively higher numerical viscosity would dissipate both the compressive and vortical motions of the IGM into thermal energy more effectively, resulting in less developed vorticity, remarkably shortened inertial range, and leading to a non-negligible uncertainty in the thermal history of gas accretion. Shocks in regions outside of clusters are significantly suppressed by numerical viscosity since z = 2, which may directly cause the different levels of turbulence between the two codes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Binary black hole accretion from a circumbinary disk: Gas dynamics inside the central cavity

We present the results of two-dimensional (2D) hydrodynamical simulations of circumbinary disk accretion using the finite-volume code DISCO. This code solves the 2D viscous Navier-Stokes equations on a high-resolution moving mesh which shears with the fluid flow, greatly reducing advection errors in comparison with a fixed grid. We perform a series of simulations for binary mass ratios in the range 0.026 ≤ q ≤ 1.0, each lasting longer than a viscous time so that we reach a quasi-steady accretion state. In each case, we find that gas is efficiently stripped from the inner edge of the circumbinary disk and enters the cavity along accretion streams, which feed persistent 'mini disks' surrounding each black hole. We find that for q ≳ 0.1, the binary excites eccentricity in the inner region of the circumbinary disk, creating an overdense lump which gives rise to enhanced periodicity in the accretion rate. The dependence of the periodicity on mass ratio may provide a method for observationally inferring mass ratios from measurements of the accretion rate. We also find that for all mass ratios studied, the magnitude of the accretion onto the secondary is sufficient to drive the binary toward larger mass ratio. This suggests a mechanism for biasing mass-ratio distributions toward equal mass.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗

DOE OSTI2026

ObstacleSense: Low-Power Neuromorphic Vision for Corridor Obstacle Awareness in Low-Level ADAS

The automotive industry’s pursuit of Level 5 autonomy is constrained by substantial perception-compute power requirements, often reaching 1, 000 + watts in full autonomy stacks. Reducing this energy burden requires rethinking perception not only at the high-end autonomy level, but also at the foundational Advanced Driver Assistance Systems (ADAS) level where low-power, safety-critical sensing can have broad impact. Neuromorphic vision provides a promising starting point: HD Dynamic Vision Sensors (DVS) can operate below 100 mW at the sensor level by reporting only asynchronous brightness changes. However, low-power sensing alone is insufficient if downstream perception reintroduces dense, energy-intensive computation. In particular, many event-driven object-detection pipelines still rely on CNN backbones, while purely spiking alternatives often trade away accuracy or ignore deployment constraints. We introduce ObstacleSense, a highly compact, CNN-free hybrid ANN–SNN framework for Level 0–1 forward-corridor obstacle awareness. Instead of performing full-scene object detection with a convolutional feature backbone, ObstacleSense targets the safety-critical question of whether the ego corridor is occupied and how far the nearest obstacle is. The architecture combines polarity-conditioned event encoding, lightweight temporal spiking dynamics, axial spatial mixing, and coarse-to-fine range estimation within a regular fixed-grid compute pattern. This design avoids the dense CNN backbone commonly used in event-based detection while maintaining a small state footprint suitable for eventual small-FPGA deployment. Before hardware mapping, we evaluate the software implementation using a model-side power proxy derived from MACs, weight and activation traffic, and spiking state updates under shared FP16 assumptions. On simulated CARLA event corpora, the deployment-oriented model achieves 0.9464 objectness F1, 0.9978 grid-level mAP, and 0.8987 m distance Mean Absolute Error at an estimated 1.92 mW proxy cost, while maintaining performance on unseen generalization test sequences.

Johnson-Scott, Zac [ORNL]↗

DOE OSTI2024

SDE_quark

This program provides a fixed-grid quadrature algorithm to compute integrals in the self-energy of the quark propagator within the Maris-Tandy model. The quark propagator both on t he spacelike real axis and at complex-valued momenta is determined from its Schwinger-Dyson equation (SDE). We first apply an iterative solver to find the quark propagator on the spacelike real axis. The propagator at complex-valued momenta is then computed from its self-energy based on this solution, where demanding integrals are encountered. In order to compute of these integrals, we apply customized variable transformations for the radial integral after subtracting the asymptotics. We subsequently apply an optional compound of quadrature rules for the angular integral.

Jia, Shaoyang↗