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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

PPINN: Parareal physics-informed neural network for time-dependent PDEs

Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree. While effective for relatively short-term time integration, when long time integration of the time-dependent PDEs is sought, the time–space domain may become arbitrarily large and hence training of the neural network may become prohibitively expensive. To this end, we develop a parareal physics-informed neural network (PPINN), hence decomposing a long-time problem into many independent short-time problems supervised by an inexpensive/fast coarse-grained (CG) solver. In particular, the serial CG solver is designed to provide approximate predictions of the solution at discrete times, while initiate many fine PINNs simultaneously to correct the solution iteratively. There is a two-fold benefit from training PINNs with small-data sets rather than working on a large-data set directly, i.e., training of individual PINNs with small-data is much faster, while training the fine PINNs can be readily parallelized. Consequently, compared to the original PINN approach, the proposed PPINN approach may achieve a significant speed-up for long-time integration of PDEs, assuming that the CG solver is fast and can provide reasonable predictions of the solution, hence aiding the PPINN solution to converge in just a few iterations. To investigate the PPINN performance on solving time-dependent PDEs, we first apply the PPINN to solve the Burgers equation, and subsequently we apply the PPINN to solve a two-dimensional nonlinear diffusion–reaction equation. Furthermore, our results demonstrate that PPINNs converge in a few iterations with significant speed-ups proportional to the number of time-subdomains employed.

42 ENGINEERING↗
DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2023

Hybrid eigensolvers for nuclear configuration interaction calculations

We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based subspace iterations and the residual minimization method accelerated by direct inversion of iterative subspace (RMM-DIIS) and describe how these algorithms compare with the standard Lanczos algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm. Although the RMM-DIIS method does not exhibit rapid convergence when the initial approximations to the desired eigenvectors are not sufficiently accurate, it can be effectively combined with either the block Lanczos or the LOBPCG method to yield a hybrid eigensolver that has several desirable properties. We will describe a few practical issues that need to be addressed to make the hybrid solver efficient and robust.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Carbon nanotubes decorated with Pt as a viable electrocatalyst system using electrochemical atomic layer deposition

Surface limited redox replacement (SLRR) is an electrochemical deposition method designed to deposit metal thin films, typically onto other metals, that are mere monolayers in thickness, where such low dimensions allows catalyst-support interactions to affect catalyst efficiency. Here we explore the growth of Pt, using iterative Cu-mediated SLRR cycles, directly onto carbon nanotubes (CNTs) which are potentially good candidates as electrocatalyst supports due to their electrical conductivity and chemical resistance. Here scanning electron microscope images showed that Pt grew as nanoparticles, and hydrogen underpotential deposition from cyclic voltammetry showed that the active surface area approached an asymptotic value around eight iterations. Catalytic activity, measured using the oxygen reduction reaction, reached a maximum at ten iterations. Both are shown to be influenced by the growth mode, but electrochemical modeling indicates that the trend in activity is also due to a change in activation energy, possibly due to changes in Pt electronic structure due to interactions with the CNTs. Durability cycling showed a greater than 85% retention of surface area for the first 10,000 cycles of accelerated stress testing but decayed steadily to about 50% after 30,000 cycles. This performance may be related to the phenomenon that limits surface area growth.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow

With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and robustness to a single point-of-failure. The Alternating Direction Method of Multipliers (ADMM) is a popular distributed optimization algorithm; however, its convergence performance is highly dependent on the selection of penalty parameters, which are usually chosen heuristically. In this work, we use reinforcement learning (RL) to develop an adaptive penalty parameter selection policy for alternating current optimal power flow (ACOPF) problem solved via ADMM with the goal of minimizing the number of iterations until convergence. We train our RL policy using deep Q-learning and show that this policy can result in significantly accelerated convergence (up to a 59% reduction in the number of iterations compared to existing, curvatureinformed penalty parameter selection methods). Furthermore, we show that our RL policy demonstrates promise for generalizability, performing well under unseen loading schemes as well as under unseen losses of lines and generators (up to a 50% reduction in iterations). This work thus provides a proof-of-concept for using RL for parameter selection in ADMM for power systems applications.

alternating current optimal power flow↗
DOE OSTI2014

A fusion nuclear science facility for a fast-track path to DEMO

An accelerated fusion energy development program, a fast-track approach, requires proceeding with a nuclear and materials testing program in parallel with research on burning plasmas, ITER. A Fusion Nuclear Science Facility (FNSF) would address many of the key issues that need to be addressed prior to DEMO, including breeding tritium and completing the fuel cycle, qualifying nuclear materials for high fluence, developing suitable materials for the plasma-boundary interface, and demonstrating power extraction. The Advanced Tokamak (AT) is a strong candidate for an FNSF as a consequence of its mature physics base, capability to address the key issues, and the direct relevance to an attractive target power plant. The standard aspect ratio provides space for a solenoid, assuring robust plasma current initiation,and for an inboard blanket, assuring robust tritium breeding ratio (TBR) >1 for FNSF tritium self-sufficiency and building of inventory needed to start up DEMO. An example design point gives a moderate sized Cu-coil device with R/a = 2.7 m/0.77 κ = 2.3, B T = 5.4 T, I P = 6.6 MA, β N = 2.75, P fus = 127 MW. The modest bootstrap fraction of f BS = 0.55 provides an opportunity to develop steady state with sufficient current drive for adequate control. Lastly, proceeding with a FNSF in parallel with ITER provides a strong basis to begin construction of DEMO upon the achievement of Q ~ 10 in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Enabling co-simulation of tokamak plant models and plasma control systems

A system for connecting the Plasma Control System and a model of the tokamak Plant in closed loop co-simulation for plasma control development has been in routine use at DIII-D for more than 20 years and at other fusion labs that use variants of the DIII-D PCS for approximately the last decade. Here, co-simulation refers to the simultaneous execution of two independent codes with the exchange of data - Plant actuator commands and tokamak diagnostic data - between them during execution. Interest in this type of PCS-Plant simulation technology has also been growing recently at other fusion facilities. In fact, use of such closed loop control simulations is assumed to play an even larger role in the development of both the ITER Plasma Control System (PCS) and the experimental operation of the ITER device, where they will be used to support verification/validation of the PCS and also for ITER pulse schedule development and validation. We describe the key use cases that motivate the co-simulation capability and the features that must be provided by the Plasma Control System to support it. These features could be provided by the PCS itself or by a model of the PCS. If the PCS itself is chosen to provide them, there are requirements imposed on its architecture. If a PCS model is chosen, there are requirements imposed on the initial implementation of this simulation as well as long-term consequences for its continued development and maintenance. We describe these issues for each use case and discuss the relative merits of the two choices. Several examples are given illustrating uses of the co-simulation method to address problems of plasma control during the operation of DIII-D and of other devices that use the DIII-D PCS.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Deuterium pellet fueling in type-III ELMy H-mode plasmas on EAST superconducting tokamak

Type-III ELMy H-mode plasmas are a valuable operating scenario, as they may simultaneously achieve fusion power gain of Q = 10 and acceptable steady-state and peak power fluxes to the plasma-facing components. It is important to investigate cryogenic deuterium pellet injection fueling in this kind of H-mode plasma since it has been chosen as a main plasma fueling technique for ITER. Recently, pellet fueling experiments have been successfully carried out on EAST, an ITER-like tokamak. A maximum electron density of 0.73 × n GW has been obtained. It is found that ELM behavior was modified immediately and a string of small ELMs were induced when pellets were injected at a low velocity from ¯40 cm above the mid-plane on the low field side, which is different from the fact that pellets trigger signal ELMs in Type-I ELMy H-mode plasmas in other tokamaks. Furthermore, the decreased edge temperature caused by the cryogenic pellet was proposed as the reason for this ELM modification. These results will provide a useful reference for the pellet fueling in a Type-III ELMy H-mode plasma on ITER in the future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Tuning successive linear programming to solve AC optimal power flow problem for large networks

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy’s (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. Here the results show that our proposed algorithm is tractable and can solve more than 80% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Exponential Runge-Kutta Parareal for non-diffusive equations

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimization of the Second Target Station cold source moderators using an automated workflow

The Second Target Station (STS) at the US Department of Energy’s Oak Ridge National Laboratory is designed to become the world’s highest peak-brightness spallation source of cold neutrons. Successful completion of the STS, which is currently in the preliminary design phase, will provide transformative new capabilities to examine novel materials for future technologies. At STS, neutrons will be generated by spallation reactions in a solid tungsten target. They will be moderated and thermalized in two cold (20 K) para-hydrogen moderators. Careful optimization of these moderators is essential to the project’s success. To find optimal moderator designs, an advanced optimization workflow integrates high-fidelity neutronics calculations using the Monte Carlo N-Particle (MCNP) transport code MCNP6.2 with state-of-the-art optimization algorithms in the Dakota optimization toolkit. For each design iteration, a parametrized solid CAD geometry is generated in Creo and automatically converted into an unstructured mesh geometry by Attila 4MC for the neutronics calculation with MCNP. Iterations repeat until optimal designs are found. Herein this paper presents the results of a sensitivity and optimization study for the cylindrical and tube moderators. Both moderators can be optimized for maximum peak brightness, maximum time-integrated brightness, or any combination between these extremes. Maximum peak brightness is achieved by using smaller optimal dimensions of the moderators, whereas maximum time-integrated brightness is achieved by using larger dimensions. A Pareto front details the designs that optimally balance both brightness metrics. The Pareto front can be found in only 40–110 iterations with 4–5 design parameters when using the efficient global and Pareto-set optimization algorithms in Dakota. Additionally, important engineering constraints can be taken into account, such as the coupling between the cylindrical moderator radius and aluminum vessel wall thicknesses required to ensure structural integrity of the vessels. This interaction has a significant impact on the resulting optimal designs. Our new, highly efficient, fully automated optimization workflow will be used to optimize additional STS components in the future and can be adopted for design and optimization studies at other experimental neutron and accelerator facilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Data on erosion and hydrogen fuel retention in Beryllium plasma-facing materials

ITER will use beryllium as a plasma-facing material in the main chamber, covering a total surface area of about 620 m 2 . Given the importance of beryllium erosion and co-deposition for tritium retention in ITER, significant efforts have been made to understand the behaviour of beryllium under fusion-relevant conditions with high particle and heat loads. This paper provides a comprehensive report on the state of knowledge of beryllium behaviour under fusion-relevant conditions: the erosion mechanisms and their consequences, beryllium migration in JET, fuel retention and dust generation. The paper reviews basic laboratory studies, advanced computer simulations and experience from laboratory plasma experiments in linear simulators of plasma–wall interactions and in controlled fusion devices using beryllium plasma-facing components. A critical assessment of analytical methods and simulation codes used in beryllium studies is given. The overall objective is to review the existing set of data with a broad literature survey and to identify gaps and research needs to broaden the database for ITER.

Erosion–deposition↗
DOE OSTI2024

Survey of tungsten gross erosion from main plasma facing components in WEST during a L-mode high fluence campaign

An initial high fluence campaign was performed in WEST, in 2023, on the newly installed actively cooled tungsten divertor composed of ITER-grade monoblocks. The campaign consisted in the repetition of a 60 s long Deuterium L-mode pulse in attached divertor conditions, cumulating over 10000s of plasma exposure. A maximum deuterium fluence of approximately 5⋅1⁢026 m−2 was reached in the outer strike point region, representative of a few high performance ITER pulses. Gross tungsten erosion inferred from visible spectroscopy shows that the most eroded plasma facing component is the inner divertor target with rates ten times larger than on the outer divertor target. The outer midplane tungsten bumpers, located a few centimeters from the plasma, show gross erosion rates two times lower than at the outer divertor. We conclude that the outer midplane bumpers have a negligible contribution to the long range tungsten migration and deposition onto the lower divertor. The cumulated gross erosion rate on the inner divertor translates in an effective gross erosion thickness of about 20μ⁢m, while it is about 2μ⁢m for the outer divertor. Strikingly, these orderings coincide with the thickness of deposits found locally on the divertor: the exposed surfaces of high field side monoblocks are covered with several tens of μ⁢m tungsten deposits, while on the lower field side, few μ⁢m thin tungsten deposits are only found on the magnetically shadowed parts of monoblocks. The strong impact of those deposits on WEST operation, namely perturbation of surface temperature measurement with infra-red thermography, and the emission of flakes causing radiative perturbation of the confined plasma, calls for anticipating similar issues in ITER. In particular, the start of research operation shall consider the definition of a divertor erosion budget in order to anticipate the formation of deleterious deposits.

Fedorczak, N.↗
DOE OSTI2025

Experiment-modeling studies comparing energy dissipation in the DIII-D SAS and SAS-VW divertors

Recent DIII-D experiments on Small Angle Slot (SAS) divertors have confirmed that a combination of divertor closure and target shaping can enhance cooling across the divertor target and increase energy dissipation, but with significant dependence on B T (toroidal magnetic field) direction. In these novel divertors, the roles of closure, target shaping, drifts, and scale lengths are all interconnected in optimizing dissipation, with the separatrix electron density n eSEP being the key parameter associated with the level of dissipation/detachment. After modifying the original flat-targeted graphite SAS to include a V shape with a tungsten coating on the outer side of the divertor (SAS-VW), matched series of discharges were run to compare to detailed SOLPS-ITER modeling. Experimentally, when run as designed with the outer strike point at the slot vertex, SAS-VW requires nearly identical n eSEP for detachment as the original SAS, with little difference in dissipation for the new geometry. This is in contrast to (1) earlier modeling predictions that a small change of the SAS geometry to a V shape should enhance dissipation at the same n eSEP for magnetic configurations having better H-mode access (ion B × ∇B drift directed into the divertor), and (2) despite the achievement of significantly higher (2-7x) neutral pressures and compression in the SAS-VW slot. Comparisons of experimental density scans to the most recent SOLPS-ITER modeling with ExB drifts show reasonable agreement for dissipation/detachment onset when using separatrix density as the independent parameter. In order to help understand the discrepancy in modeled vs actual performance for the new configuration, additional measurements varying gas injection location and impurity injection were undertaken. In-slot D 2 gas fueling is more effective (5–22 %) in promoting detachment, in accord with modeling. In-slot impurity injection (N 2 or Ne) can yield 30 % lower core Z eff and 15 % less confinement degradation after detachment compared to main chamber puffing, as well as relatively lower tungsten leakage from the divertor. Modeling can also reproduce the improved detachment seen as the strike point moves inboard of the slot vertex. While we can explain the effects of the most important parameters causing energy dissipation in these slot divertors, it remains that many aspects of their behavior cannot be accurately modeled using state-of-art codes such as SOLPS-ITER. This is of concern for future model-driven designs utilizing similar V-shaped geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Hierarchical Krylov and nested Krylov methods for extreme-scale computing

The solution of large, sparse linear systems is typically a dominant phase of computation for simulations based on partial differential equations, which are ubiquitous in scientific and engineering applications. While preconditioned Krylov methods are widely used and provide many advantages for solving sparse linear systems that do not have highly convergent, geometric multigrid solvers or specialized fast solvers, Krylov methods encounter well-known scaling difficulties for over 10,000 processor cores because each iteration requires at least one vector inner product, which in turn requires a global synchronization that scales poorly because of internode latency. To aid in overcoming these difficulties, we have developed hierarchical Krylov methods and nested Krylov methods in the PETSc library that reduce the number of global inner products required across the entire system (where they are expensive), though freely allow vector inner products across smaller subsets of the entire system (where they are inexpensive) or use inner iterations that do not invoke vector inner products at all. Nested Krylov methods are a generalization of inner-outer iterative methods with two or more layers. Hierarchical Krylov methods are a generalization of block Jacobi and overlapping additive Schwarz methods, where each block itself is solved by Krylov methods on smaller blocks. Conceptually, the hierarchy can continue recursively to an arbitrary number of levels of smaller and smaller blocks. As a specific case, we introduce the hierarchical FGMRES method, or h-FGMRES, and we demonstrate the impact of two-level h-FGMRES with a variable preconditioner on the PFLOTRAN subsurface flow application. We also demonstrate the impact of nested FGMRES, BiCGStab and Chebyshev methods. These hierarchical Krylov methods and nested Krylov methods significantly reduced overall PFLOTRAN simulation time on the Cray XK6 when using 10,000 through 224,000 cores through the combined effects of reduced global synchronization due to fewer global inner products and stronger inner hierarchical or nested preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Performance of asynchronous optimized Schwarz with one-sided communication

In asynchronous iterative methods on distributed-memory computers, processes update their local solutions using data from other processes without an implicit or explicit global synchronization that corresponds to advancing the global iteration counter. Here in this work, we test the asynchronous optimized Schwarz domain-decomposition iterative method using various one-sided (remote direct memory access) communication schemes with passive target completion. The results show that when one-sided communication is well-supported, the asynchronous version of optimized Schwarz can outperform the synchronous version even for perfectly balanced partitionings of the problem on a supercomputer with uniform nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗