Improvements in Iterative Convergence of FUN3D Solutions
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In situ multi-tier auto-ignition detection applied to dual-fuel combustion simulations
Here we use an anomaly detection methodology that is centered on analyzing fourth-order joint moments (co-kurtosis), particularly focusing on its application in auto-ignition of combustion problems with large numbers of species. Unsupervised anomaly detection is challenging to generalize across problem types and domains. A recent technique, centered on analyzing information in the fourth-order joint moment co-kurtosis, has shown promise, especially for high-dimensional scientific data. In this work we present developments to the co-kurtosis based anomaly detection method needed to make it effective and scalable for large-scale distributed scientific data, such as those generated by massively parallel simulations. An in situ co-kurtosis algorithm is employed as the anomaly detection method for identifying ignition kernels in simulations of turbulent combustion. Here, we extend an existing methodology which identifies regions of the domain where anomalies are present, and add another tier of anomaly detection where the individual samples contributing to the anomaly are identified. We apply this algorithm on-the-fly to a variety of turbulent reacting flow problems and compare it to the widely used (but significantly more expensive) chemical explosive mode analysis (CEMA). We demonstrate the ability of the method to detect and identify the onset of low and high temperature ignition which can be used for computational steering, as chemical and combustion anomalies occur intermittently at spatio-temporal locations unknown a priori. Finally, we apply our lightweight in situ algorithm to an exascale high-fidelity simulation with a total of 2.4 Trillion degrees of freedom, performed using an adaptive mesh refinement solver. Furthermore, through a scalability analysis, we show that the relative computational cost of this in-situ anomaly detection algorithm compared to an iteration of the reacting flow solver is negligible.
97 MATHEMATICS AND COMPUTING↗
A semi-direct procedure using a local relaxation factor and its application to an internal flow problem
Generally, fast direct solvers are not directly applicable to a nonseparable elliptic partial differential equation. This limitation, however, is circumvented by a semi-direct procedure, i.e., an iterative procedure using fast direct solvers. An efficient semi-direct procedure which is easy to implement and applicable to a variety of boundary conditions is presented. The current procedure also possesses other highly desirable properties, i.e.: (1) the convergence rate does not decrease with an increase of grid cell aspect ratio, and (2) the convergence rate is estimated using the coefficients of the partial differential equation being solved.
Chang, S. C.↗
TLNS3D/CDISC Multipoint Design of the TCA Concept
This paper presents the work done to date by the authors on developing an efficient approach to multipoint design and applying it to the design of the HSR TCA (High Speed Research Technology Concept Aircraft) configuration. While the title indicates that this exploratory study has been performed using the TLNS3DMB flow solver and the CDISC (Constrained Direct Iterative Surface Curvature) design method, the CDISC method could have been used with any flow solver, and the multipoint design approach does not require the use of CDISC. The goal of the study was to develop a multipoint design method that could achieve a design in about the same time as 10 analysis runs.
Campbell, Richard L.↗
Numerical Behaviour of a Smooth Local Correlation-based Transition Model in a Newton-Krylov Flow Solver
The numerical behaviour of transport-equation-based transition models, including both iterative and grid convergence, is influenced by the source terms. Transition models contain source terms that are large and highly nonlinear, and can be destabilizing in a strong implicit solver. Linearization strategies with varying levels of coupling are evaluated in conjunction with a source-term time step restriction to determine best-practices for solving the SA-sLM2015smooth local correlation-based transition model in an implicit Newton-Krylov flow solver. Achieving deep iterative convergence facilitates a detailed investigation of the grid convergence of these free-transition simulations, which are evaluated relative to fully-turbulent simulations performed using the Spalart-Allmaras turbulence model. Simulations of the NLF0416 general aviation airfoil, VA-2 supercritical airfoil, and NASA CRM-NLF wing-body geometry are performed over a range of grid levels. The results demonstrate that both a fully-coupled linearization strategy and a source-term time step restriction improve nonlinear convergence as the complexity of the free-transition simulations increases. In general, additional grid resolution is required for free-transition simulations relative to fully-turbulent simulations in order to achieve a similar level of accuracy, with the grid convergence of free-transition simulations sensitive to the streamwise grid spacings in the transition regions.
AATT↗
Simulating energetic ions and enhanced fusion rates from ion-cyclotron resonance heating with a full-wave/Fokker–Planck model
Reproducing fast-ion enhanced fusion rates from ion-cyclotron resonance heating (ICRH) in tokamaks requires the self-consistent coupling of a full-wave solver and a Fokker–Planck solver, which evolves multiple simultaneously resonant ion species. We introduce a new self-consistent model that iterates the TORIC full-wave solver with the CQL3D Fokker–Planck solver using the integrated plasma simulator (IPS). This model evolves the bounce-averaged ion distribution functions in both parallel and perpendicular velocity-space with a quasilinear radio frequency (RF) diffusion operator valid in the ion finite Larmor radius (FLR) limit and the RF electric fields with the resultant non-Maxwellian FLR dielectric tensor. This produces non-Maxwellian ICRH simulations that are fully self-consistent, fast, and interoperable with integrated modeling frameworks, such as TRANSP/GACODE/IPS-FASTRAN. We demonstrate our model's capabilities by validating it against experimental data in Alcator C-Mod. We then perform the first RF heating simulations of SPARC using self-consistent non-Maxwellian ion distributions to investigate the potential to enhance fusion rates using ion cyclotron resonance heating generated fast ions.
Physics↗
Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics
Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.
Martin, E. D.↗
A semi-direct solver for compressible 3-dimensional rotational flow
An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.
Chang, S. C.↗
Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods
The Lagrangian finite volume (FV) cell-centered hydrodynamic (CCH) method and the Lagrangian discontinuous Galerkin (DG) CCH method have been demonstrated to be quite stable and capable of producing very accurate solutions on many mesh topologies. However, some challenges can arise with higher-order elements and polygonal elements that have many deformational degrees of freedom. With these types of meshes, elements can deform in unphysical ways and the mesh can tangle. In this study, we present methods for obtaining more robust Lagrangian solutions on polygonal and higher-order elements. The robustness is achieved by (1) incorporating a new iterative method that modifies the velocity reconstructions in the corners of the elements, and (2) a new multidirectional approximate Riemann solver that, when coupled with the iterative method, reduces spurious mesh motion. Lastly, the details of the numerical methods are discussed and their utility is demonstrated on a diverse suite of test problems using higher-order and polygonal elements.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Accelerated coupled Monte Carlo-Thermal hydraulic calculations using a hybrid GTF-diffusion-based prediction block: first results
Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections' variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint Eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Accelerated Coupled Monte Carlo-Thermal Hydraulic Calculations using a Hybrid GTF-Diffusion-based Prediction Block: First Results
Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work [1, 2] investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections’ variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC
The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2D method of characteristics (MOC) solver, which is the focus of this work. Here in this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop$-$as is the case with the Gauss-Seidel sweeper$-$to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8$-$10% increase in the overall memory requirement.
97 MATHEMATICS AND COMPUTING↗
Plutonium Critical Mass Curve Comparison to Mass at Upper Subcritical Limit (USL) Using Whisper
Whisper is computational software designed to assist the nuclear criticality safety analyst with validation studies with the MCNP ® Monte Carlo radiation transport package. Standard approaches to validation rely on the selection of benchmarks based upon expert judgment. Whisper uses sensitivity/uncertainty (S/U) methods to select relevant benchmarks to a particular application or set of applications being analyzed. Using these benchmarks, Whisper computes a calculational margin. Whisper attempts to quantify the margin of subcriticality (MOS) from errors in software and uncertainties in nuclear data. The combination of the Whisper-derived calculational margin and MOS comprise the baseline upper subcritical limit (USL), to which an additional margin may be applied by the nuclear criticality safety analyst as appropriate to ensure subcriticality. A series of critical mass curves for plutonium, similar to those found in Figure 31 of LA-10860-MS, have been generated using MCNP6.1.1 and the iterative parameter study software, WORM_Solver. The baseline USL for each of the data points of the curves was then computed using Whisper 1.1. The USL was then used to determine the equivalent mass for plutonium metal-water system. ANSI/ANS-8.1 states that it is acceptable to use handbook data, such as the data directly from the LA-10860-MS, as it is already considered validated (Section 4.3 4) “Use of subcritical limit data provided in ANSI/ANS standards or accepted reference publications does not require further validation.”). This paper attempts to take a novel approach to visualize traditional critical mass curves and allows comparison with the amount of mass for which the k eff is equal to the USL (calculational margin + margin of subcriticality). However, the intent is to plot the critical mass data along with USL, not to suggest that already accepted handbook data should have new and more rigorous requirements for validation.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem
Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applications. We first train a deep neural operator (DeepONet) to solve wave propagation problems described by the Helmholtz equation in a domain without scatterers but at different wavenumbers and with a complex absorbing boundary condition. We then design two classes of fast meta-solvers by combining DeepONet with either relaxation methods, such as Jacobi and Gauss-Seidel, or with Krylov methods, such as GMRES and BiCGStab, using the trunk basis of DeepONet as a coarse-scale preconditioner. We leverage the spectral bias of neural networks to account for the lower part of the spectrum in the error distribution while the upper part is handled inexpensively using relaxation methods or fine-scale preconditioners. The meta-solvers are then applied to solve scattering problems with different shape of scatterers, at no extra training cost. We first demonstrate that the resulting meta-solvers are shape-agnostic, fast, and robust, whereas the standard standalone solvers may even fail to converge without the DeepONet. We then apply both classes of meta-solvers to scattering from a submarine, a complex three-dimensional problem. We achieve very fast solutions, especially with the DeepONet-Krylov methods, which require orders of magnitude fewer iterations than any of the standalone solvers.
97 MATHEMATICS AND COMPUTING↗
Data transfers for full core heterogeneous reactor high- fidelity multiphysics studies
Multiphysics simulations for nuclear reactor analysis are usually performed by resorting to operator splitting and fixed point iterations between single-physics solvers. This enables the separate solution of each physics, such as neutronics, fuel performance, and thermal hydraulics, on meshes tailored to the requirements of the respective numerical discretizations of the equations. As the equations are coupled, several fields must be transferred between single-physics solves. Projecting fields between meshes while preserving order of accuracy, conservation properties, and mapping non-overlapping geometries is a complex endeavor. This conference paper will present the transfers as implemented in MOOSE, which can handle arbitrary meshes, arbitrary mappings, conservation of integral quantities, and are made to scale with distributed simulations on both ends of the transfers. Their adequacy for advanced nuclear reactor multiphysics coupling is shown through examples and numerical studies.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Optimal Load Ensemble Control in Chance-Constrained Optimal Power Flow
Distribution system operators (DSOs) world-wide foresee a rapid roll-out of distributed energy resources. From the system perspective, their reliable and cost effective integration requires accounting for their physical properties in operating tools used by the DSO. This work describes an decomposable approach to leverage the dispatch flexibility of thermostatically controlled loads (TCLs) for operating distribution systems with a high penetration level of photovoltaic resources. Each TCL ensemble is modeled using the Markov Decision Process (MDP). The MDP model is then integrated with a chance constrained optimal power flow that accounts for the uncertainty of PV resources. Since the integrated optimization model cannot be solved efficiently by existing dynamic programming methods or off-the-shelf solvers, this paper proposes an iterative Spatio-Temporal Dual Decomposition algorithm (ST-D2). Finally, we demonstrate the merits of the proposed integrated optimization and ST-D2 algorithm on the IEEE 33-bus test system.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. Herein, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the ptychographical iterative engine, a workhorse in the optics community.
97 MATHEMATICS AND COMPUTING↗
Detailed modeling analysis for soot formation and radiation in microgravity gas jet diffusion flames
Radiation heat transfer in combustion systems has been receiving increasing interest. In the case of hydrocarbon fuels, a significant portion of the radiation comes from soot particles, justifying the need for detailed soot formation model and radiation transfer calculations. For laminar gas jet diffusion flames, results from this project (4/1/91 8/22/95) and another NASA study show that flame shape, soot concentration, and radiation heat fluxes are substantially different under microgravity conditions. Our emphasis is on including detailed soot transport models and a detailed solution for radiation heat transfer, and on coupling them with the flame structure calculations. In this paper, we will discuss the following three specific areas: (1) Comparing two existing soot formation models, and identifying possible improvements; (2) A simple yet reasonably accurate approach to calculating total radiative properties and/or fluxes over the spectral range; and (3) Investigating the convergence of iterations between the flame structure solver and the radiation heat transfer solver.
Ku, Jerry C.↗