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DOE OSTI2025

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes

Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of Ren et al. (2018) to admit fracture propagation (FP). The coupled XFEM-EDFM scheme utilizes a separate fracture mesh that is embedded on a static background mesh. The onset and dynamics of fracture propagation are governed by the equivalent stress intensity factor (SIF) criterion. A domain-integral method (J integral) is applied to compute this information. Additionally, an adaptive time-marching scheme is proposed to rapidly restrict and grow temporal resolution to match the underlying time-scales. The proposed model is verified with analytical solutions, and shows the capability to accurately and adaptively co-simulate fluid transport and deformation as well as the propagation of multiple fractures.

42 ENGINEERING↗

DOE OSTI2022

Experimentally validated high-fidelity simulations of a liquid jet in supersonic crossflow

Here, utilizing recent advancements in computational schemes for compressible, multiphase flows, this work features a parametric study of a pure liquid jet in supersonic crossflow that involves simulating the atomization process for four values of momentum-flux ratio. These simulations are validated against experimental results measured with high-speed X-ray imaging, which confirm the accuracy of the numerical approach. Also, the effect of numerical resolution on some flow behavior is investigated, revealing convergence of the jet shape and surface instability wavelength. Analysis of the resulting sprays includes statistical descriptions of the liquid distribution, liquid structures created through breakup, interfacial instabilities, and dominant flow features. As the flowrate increases, the spray penetrates further, it becomes more disperse, and less liquid impacts the wall, but the droplet size distribution changes little. The wavelength of instabilities on the windward side of the jet diverges from measured trends in subsonic crossflows. In a visualization of the time-averaged flow, counter-rotating vortices are observed along the jet core and in the wake, affecting the process of primary atomization and early droplet trajectories.

42 ENGINEERING↗

DOE OSTI2021

Colloidal CdSe nanocrystals are inherently defective

Abstract Colloidal CdSe nanocrystals (NCs) have shown promise in applications ranging from LED displays to medical imaging. Their unique photophysics depend sensitively on the presence or absence of surface defects. Using simulations, we show that CdSe NCs are inherently defective; even for stoichiometric NCs with perfect ligand passivation and no vacancies or defects, we still observe that the low energy spectrum is dominated by dark, surface-associated excitations, which are more numerous in larger NCs. Surface structure analysis shows that the majority of these states involve holes that are localized on two-coordinate Se atoms. As chalcogenide atoms are not passivated by any Lewis base ligand, varying the ligand should not dramatically change the number of dark states, which we confirm by simulating three passivation schemes. Our results have significant implications for understanding CdSe NC photophysics, and suggest that photochemistry and short-range photoinduced charge transfer should be much more facile than previously anticipated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

An accurate, non-empirical method for incorporating decoherence into Ehrenfest dynamics

In mixed quantum-classical nonadiabatic molecular dynamics methods, the anchoring of the electronic wave function to a single nuclear geometry results in both quantitative and qualitative errors in the dynamics. In the context of both Ehrenfest and trajectory surface hopping methods, methods for incorporating decoherence are widely used to eliminate these errors. However, the accuracy of these methods often depends strongly on the parameterization of the decoherence time and/or other related quantities. Here, we present a refinement of the recently introduced collapse to a block (TAB) scheme for incorporating decoherence into Ehrenfest dynamics. The proposed approach incorporates an approximation to the history of the population dynamics and treats the coherence decay as Gaussian, rather than exponential. This method uses parameters that can be obtained from first principles, rather than empirical fitting. Application to one-dimensional models indicates excellent agreement with numerically exact simulations. We also introduce a second refinement to the TAB method: a robust linear least-squares algorithm for determining collapse probabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

NUMERICAL MODELING OF A SOLID OXIDE FUEL CELL FOR USE IN REAL-TIME SIMULATION AND CYBER-PHYSICAL SYSTEMS

Cyber-physical systems provide a mechanism with which to investigate the physical phenomena and behavior of traditionally cost-prohibitive or otherwise fragile equipment. For the National Energy Technology Laboratory (NETL), this approach resulted in the Hybrid Performance (Hyper) facility which features a gas turbine-SOFC hybrid cycle utilizing real turbomachinery and a simulated SOFC stack. This allows for the investigation of combined cycle performance and control strategies, in an exhaustive manner, both without fear of destroying delicate state-of-the-art fuel cells, and with the full accuracy of real-world turbomachinery. Issues arose between the transient response of the SOFC model being limited to a sample time of 80 milliseconds, due to the calculation time of the SOFC model taking on average 40 milliseconds to calculate for a given timestep with spikes in calculation time reaching the 80 millisecond threshold. In order to be able to match the speed of transients from the turbomachinery and likewise better discern transient behavior, it was determined that the SOFC model must be optimized to operate at a sample time of 5 milliseconds. Therefore, it is necessary to optimize the SOFC model in order to decrease the calculation time from around 40 milliseconds, down to at the most 5 milliseconds. To do this, both the electrochemical algorithm and the thermal algorithm used to simulate the physical behavior of the SOFC are investigated to determine where improvements can be made. To this end the rootfinding numerical recipes of the electrochemical algorithm are investigated as the complex electrochemistry requires a highly iterative nested dual convergence loop to resolve the voltage-current relationship, and likewise the temporal discretization of the thermal algorithm is modified for the sake of higher accuracy and stability. Ultimately the new electrochemical algorithm featuring higher order rootfinding schemes proves to be efficient enough to reach the sub 5 millisecond target, signifying an order of magnitude reduction in calculation time, and when coupled with the new temporal discretization similar calculation time characteristics show that a fully implicit, higher order temporal discretization can also successfully be used if desired. Ultimately this result means that the cyber-physical simulation system can operate at higher sample rates, and resolve transient events at significantly higher resolution and fidelity.

Arias, Jesus↗

DOE OSTI2024

Enhancing Lattice Kinetic Schemes for Fluid Dynamics with Lattice-Equivariant Neural Networks

A new class of equivariant neural networks is presented, hereby dubbed lattice-equivariant neural networks (LENNs), designed to satisfy local symmetries of a lattice structure. The approach develops within a recently introduced framework aimed at learning neural network-based surrogate models’ lattice Boltzmann collision operators. Whenever neural networks are employed to model physical systems, respecting symmetries and equivariance properties has been shown to be key for accuracy, numerical stability, and performance. Here, hinging on ideas from group representation theory, trainable layers are defined whose algebraic structure is equivariant with respect to the symmetries of the lattice cell. In this work, the presented method naturally allows for efficient implementations, in terms of both memory usage and computational costs, supporting scalable training/testing for lattices in two spatial dimensions and higher (in which the size of symmetry group grows). The approach is validated and tested considering 2D and 3D flowing dynamics, both in laminar and turbulent regimes. It is compared with group-averaged-based symmetric networks and with plain, nonsymmetric, networks, showing how the presented approach unlocks the (a posteriori) accuracy and training stability of the former models and the train/inference speed of the latter networks. (LENNs are about one order of magnitude faster than group-averaged networks in 3D.) The work in this paper opens toward practical use of machine learning-augmented lattice Boltzmann CFD in real-world simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

High-order partitioned spectral deferred correction solvers for multiphysics problems

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1], [2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Improving the Physical Basis for Updraft Dynamics in Deep Convection Parameterizations

This article presents a new deep convective parameterization that determines cloud characteristics based on a specified cloud size distribution. The vertical profiles of cloud properties are determined by analytic equations, which formulate entrainment with an inverse relationship to cloud width. In line with recent studies of large eddy simulations (LES), cloud widths are assumed to be constant with height and vertical mass flux (M) characteristics of the clouds are therefore regulated by the vertical velocity profile. The parameterization is configured to work with existing cloud base M closure formulations, with the closure predicting the total cloud area rather than the cloud base M directly. Analytic formula are also used to connect the vertical wind shear magnitude to the cloud size distribution, wherein larger shear magnitudes result in more numerous large updrafts than weaker shear magnitudes, which is in line with recent research results. The parameterization is compared against 10 deep convective LES with varying thermodynamic and vertical wind shear profiles. Results show dramatic improvements in the prediction of normalized M, detrainment, and the properties of detrained air over the existing Zhang and McFarlane (1995) scheme. In particular, the new model is able to correctly portray the transition from a bottom-heavy M profile in weakly sheared environments, to a top-heavy M profile in strongly sheared environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Matter power spectra in modified gravity: a comparative study of approximations and N -body simulations

ABSTRACT Testing gravity and the concordance model of cosmology, $\Lambda$CDM, at large scales is a key goal of this decade’s largest galaxy surveys. Here we present a comparative study of dark matter power spectrum predictions from different numerical codes in the context of three popular theories of gravity that induce scale-independent modifications to the linear growth of structure: nDGP, Cubic Galileon, and K-mouflage. In particular, we compare the predictions from N-body simulations solving the full scalar field equation, two N-body codes with approximate time integration schemes, a parametrized modified N-body implementation, and the analytic halo model reaction approach. We find the modification to the $\Lambda$CDM spectrum is in 2 per cent agreement at $z\le 1$ and $k\le 1~h\,{\rm Mpc}^{-1}$ over all gravitational models and codes, in accordance with many previous studies, indicating these modelling approaches are robust enough to be used in forthcoming survey analyses under appropriate scale cuts. We further make public the new code implementations presented, specifically the halo model reaction K-mouflage implementation and the relativistic Cubic Galileon implementation.

Bose, B. (ORCID:0000000319658614)↗

DOE OSTI2024

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed here. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.

58 GEOSCIENCES↗

DOE OSTI2023

A numerical simulation of CCN impacts on weather modification efficiency

Aerosols affect development of clouds and precipitation by serving as cloud condensation nuclei (CCN) and ice nuclei (IN). Considering the dramatically changing ambient aerosol concentration, it is important to examine the potential “side effect” of aerosol pollution on precipitation enhancement by weather modification. In this study, the cloud seeding was performed on a precipitation event in Beijing in the summer of 2008, which is simulated by the NSSL two-moment cloud scheme of the Weather Research and Forecasting (WRF) model. Sensitivity tests were conducted by modifying the ambient aerosol concentration and the ice crystal seeding amount to investigate the cloud seeding efficacy in different CCN concentration scenarios. There was a slight difference in the precipitation distribution between the simulations with two ambient CCN concentrations: the northern precipitation center in polluted scenario was weaker and the southern center was stronger. Compared with normal CCN scenario, the cloud liquid water mass and ice crystal mass in the severe pollution scenario is larger, and the total contents of snow and graupel were not sensitive to the CCN concentration. With the same amount of man-made ice crystals seeding, the precipitation enhancement was quite different under different CCN conditions. The higher the CCN concentration usually leads to stronger precipitation suppression. As CCN concentration increase, the deposition growth of snow, auto-conversion and accretion of ice crystals to snow were weakened, as well as the conversion of melting snow and graupel into rainwater.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Weighted relaxation for multigrid reduction in time

Current trends in computer architectures now mean that faster computation speed must come primarily from increased concurrency, not faster clock speeds, which are stagnating. Thus, this situation creates bottlenecks for serial algorithms, including the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. Here, in this work, we consider multigrid-reduction-in-time (MGRIT), a multilevel method applied to the time dimension that computes multiple time-steps in parallel. Like all multigrid methods, MGRIT relies on the complementary relationship between relaxation on a fine-grid and a correction from the coarse grid to solve the problem. All current MGRIT implementations are based on unweighted-Jacobi relaxation; here we introduce the concept of weighted relaxation to MGRIT. We derive new convergence bounds for weighted relaxation, and use this analysis to guide the selection of relaxation weights. Numerical results then demonstrate that by choosing appropriate non-unitary relaxation weights, one can achieve faster convergence rates and lower iteration counts for MGRIT when compared with unweighted relaxation. In most cases, weighted relaxation yields a 10%–20% saving in iterations, which is significant when using large high-performance computers. For A-stable integration schemes, results also illustrate that under-relaxation can restore convergence in some cases where unweighted relaxation is not convergent.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A fragmentation approach to jet flavor

An intuitive definition of the partonic flavor of a jet in quantum chromodynamics is often only well-defined in the deep ultraviolet, where the strong force becomes a free theory and a jet consists of a single parton. However, measurements are performed in the infrared, where a jet consists of numerous particles and requires an algorithmic procedure to define their phase space boundaries. To connect these two regimes, we introduce a novel and simple partonic jet flavor definition in the infrared. We define the jet flavor to be the net flavor of the partons that lie exactly along the direction of the Winner-Take-All recombination scheme axis of the jet, which is safe to all orders under emissions of soft particles, but is not collinear safe. Collinear divergences can be absorbed into a perturbative fragmentation function that describes the evolution of the jet flavor from the ultraviolet to the infrared. The evolution equations are linear and a small modification to traditional DGLAP and we solve them to leading-logarithmic accuracy. The evolution equations exhibit fixed points in the deep infrared, we demonstrate quantitative agreement with parton shower simulations, and we present various infrared and collinear safe observables that are sensitive to this flavor definition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Comparing numerical accuracy and stability for different horizontal discretizations in MPAS-Ocean

This manuscript investigates the effectiveness of two possible horizontal discretizations for the global ocean model MPAS-Ocean, both applied to Spherical Centroidal Voronoi Tessellations (SCVTs). The first discretization is TRiSK, a C-grid, finite-volume method, that possesses many desirable mimetic properties, but has a low order accuracy. The second discretization was introduced for the first time by Peixoto (2016), and consists of modifications to the TRiSK scheme designed to achieve at least first-order accuracy in the L ∞ norm, with the loss of some of the mimetic properties. Tests on shallow-water and primitive-equation models show that the scheme due to Peixoto is indeed more accurate, but presents stability issues with respect to TRiSK. Here, TRiSK is indeed found to be often more stable in time and more robust with respect to errors in the geometric properties of the grid.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Interface flux recovery framework for constructing partitioned heterogeneous time-integration methods

A common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. Here, in this article, we present a novel framework for partitioned heterogeneous time-integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial-in-time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time-integrators for the individual subproblems without compromising the time-accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time-integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air-sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time-integrators from the explicit Runge-Kutta and Adams-Moulton families.

97 MATHEMATICS AND COMPUTING↗