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At least 487 records · Page 27

The MESSy aerosol submodel MADE3 (v2.0b): description and a box model test

We introduce MADE3 (Modal Aerosol Dynamics model for Europe, adapted for global applications, 3rd generation; version: MADE3v2.0b), an aerosol dynamics submodel for application within the MESSy framework (Modular Earth Submodel System). MADE3 builds on the predecessor aerosol submodels MADE and MADE-in. Its main new features are the explicit representation of coarse mode particle interactions both with other particles and with condensable gases, and the inclusion of hydrochloric acid (HCl) / chloride (Cl) partitioning between the gas and condensed phases. The aerosol size distribution is represented in the new submodel as a superposition of nine lognormal modes: one for fully soluble particles, one for insoluble particles, and one for mixed particles in each of three size ranges (Aitken, accumulation, and coarse mode size ranges). In order to assess the performance of MADE3 we compare it to its predecessor MADE and to the much more detailed particle-resolved aerosol model PartMC-MOSAIC in a box model simulation of an idealised marine boundary layer test case. MADE3 and MADE results are very similar, except in the coarse mode, where the aerosol is dominated by sea spray particles. Cl is reduced in MADE3 with respect to MADE due to the HCl / Cl partitioning that leads to Cl removal from the sea spray aerosol in our test case. Additionally, the aerosol nitrate concentration is higher in MADE3 due to the condensation of nitric acid on coarse mode particles. MADE3 and PartMC-MOSAIC show substantial differences in the fine particle size distributions (sizes ≲ 2 μm) that could be relevant when simulating climate effects on a global scale. Nevertheless, the agreement between MADE3 and PartMC-MOSAIC is very good when it comes to coarse particle size distributions (sizes ≳ 2 μm), and also in terms of aerosol composition. Finally, considering these results and the well-established ability of MADE in reproducing observed aerosol loadings and composition, MADE3 seems suitable for application within a global model.

Kaiser, J. C.↗

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

Continuing studies associated with the development of the quasi-analytical (QA) sensitivity method for three dimensional transonic flow about wings are presented. Furthermore, initial results using the quasi-analytical approach were obtained and compared to those computed using the finite difference (FD) approach. The basic goals achieved were: (1) carrying out various debugging operations pertaining to the quasi-analytical method; (2) addition of section design variables to the sensitivity equation in the form of multiple right hand sides; (3) reconfiguring the analysis/sensitivity package in order to facilitate the execution of analysis/FD/QA test cases; and (4) enhancing the display of output data to allow careful examination of the results and to permit various comparisons of sensitivity derivatives obtained using the FC/QA methods to be conducted easily and quickly. In addition to discussing the above goals, the results of executing subcritical and supercritical test cases are presented.

Carlson, Leland A.↗

On the possible gain of the application of the SP{sub 3} solution in nodal codes

The simplified P{sub N} method has attracted much attention in reactor physics. The implementation of an increased order expansion has the potential to improve the results. It is investigated if this potential can be released under the specific features of nodal codes with fuel assembly sized calculation cells. One dimensional analytical solutions for the one and two energy-group diffusion, SP{sub 3} and P{sub 3} equations are derived. The results are compared to reference solutions calculated with ONEDANT and HELIOS. Tests are performed on the Brantley/Larsen one-group test case and on a pin cell with real reactor materials. For the evaluation of the differences between the diffusion and the SP{sub 3} solutions in the nodal code configuration, benchmark configurations are investigated. A comparison of the diffusion and the SP{sub 3} results show improvements for the test case using fuel element size nodes, where the reference solution uses the identical cross section basis. Comparing with a multi-group reference solution shows that the diffusion solution sometimes behaves better due to error cancellation. To achieve the full gain of the SP{sub 3} method in nodal calculations, a new standard for light water reactor calculations has to be defined with a refined energy-group structure. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Dynamic simulation of powder packing structure for powder bed additive manufacturing

Here, powder packing structure is a critical parameter of powder bed-based additive manufacturing (AM). Experimental characterization of powder is typically limited to measuring bulk properties, whereas many numerical models of AM powder packing are based on geometrical consideration without accounting for particle-to-particle interactions. In the present paper, the powder packing dynamics is simulated using a discrete element method (DEM)-based model that solves the mechanical contact forces and moments between individual particles. As DEM uses explicit time integration, a main challenge in modeling dynamics of metallic powder packing is the need for extremely fine time increment size (e.g., in the order of 1 ns for a 10-μm-diameter particle). The effect of mass scaling, employed for speeding up the calculation, on the simulation results is examined in a test case of powder particles packed inside a box container. The calculated packing density for two different particle size distributions is validated against independent literature data for laser powder bed AM with AISI 316L stainless steel powder. The sensitivity of key input parameters (e.g., friction coefficient) is further evaluated in this test case. The powder packing model is then applied to a practical situation of binder jet AM involving rolling of multiple layers of IN718 powder particles onto a powder bed, for which the calculated packing density is also validated with independent literature data.

42 ENGINEERING↗

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This study aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interaction of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Finally and furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.

54 ENVIRONMENTAL SCIENCES↗

Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility.

Elmiligui, Alaa↗

BESTEST-GSR (Building Energy Simulation Test - Generation Simulation and Reporting) [SWR 18-23]

Building Energy Simulation Test (BESTEST) is an NREL-developed method to validate the qualitative performance of different whole building simulations engines relative to each other. https://www.nrel.gov/docs/legosti/old/6231.pdf For EnergyPlus® and OpenStudio®, generation of test cases, simulation, and reporting has been a manual or partially automated process that typically took a number of months after a new version of EnergyPlus came out. Building Energy Simulation Test - Generation Simulation and Reporting (BESTEST-GSR) was developed to fully automate this process so it is less error-prone, less time-consuming, and can be quickly run on request for any development branch of EnergyPlus and OpenStudio. The initial use case is to directly support OpenStudio and EnergyPlus development, but the software is configured to support use by external software developers that build tools on top of EnergyPlus and/or OpenStudio. Tools built on top of OpenStudio can leverage the test generation, simulation, and reporting, while tools built on EnergyPlus can leverage the test simulation and reporting. The model generation is accomplished by running OpenStudio measures for envelope, heating, or cooling test cases. At this stage the specified weather file required for a specific test case is assigned to the model. Simulation is enabled using the OpenStudio Command Line Interface (CLI) to run a series of OpenStudio and Reporting measures to a specified seed model. The specified workflow is defined with an OpenStudio OSW file. The first measure generates the test case model, while the second measure is a reporting measure that runs after the simulation to collect necessary simulation results from the EnergyPlus SQL file. The Reporting stage gathers data from individual OpenStudio OSW files and populates a series of BESTEST Microsoft Excel spreadsheets. BESTEST-GSR also gathers zip files from individual simulations for diagnostic purposes.

Goldwasser, David↗

Development and Validation of SAM Multi-dimensional Flow Model for Thermal Mixing and Stratification Modeling

Thermal mixing and stratification in large pools or enclosures are very important phenomena that are critical to nuclear reactor safety. Because of the wide ranges of time and length scales associated with such phenomena, accurate modeling and simulation of thermal mixing and stratification remain as the key unresolved, challenging problems for reactor transient analyses. In traditional system analysis codes, simplified zero-dimensional (0-D) models are widely used for their high numerical efficiency, but they generally suffer from very limited prediction accuracies or range of applicability. Like traditional system analysis codes, the current version of the SAM code has implemented such simplified 0-D and one-dimensional mixing models. On the other hand, high-resolution Computational Fluid Dynamics (CFD) tools are often used to model complex thermal mixing and stratification phenomena. They are, however, generally numerically expensive, and they require large amounts of computational resources. It is therefore desirable to implement advanced and efficient thermal mixing and stratification modeling capabilities embedded in a system analysis code. This approach will improve the accuracy of reactor safety analyses when thermal mixing and stratification are involved, and also avoid using the large computational resources needed for high-resolution CFD analysis. Currently, with the support of the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation program, an effort has been launched to develop and implement a multi-dimensional flow model in the system analysis code SAM, and demonstrate its applications to model thermal mixing and stratification phenomena in large enclosures. The main outcomes of this research and development activity are summarized in this report, which presents an attempt to include a built-in advanced multi-dimensional flow model in a system analysis code with the focus on overcoming the simulation challenges of thermal mixing and stratification phenomena. In this report, we start with the introduction of existing SAM code capabilities to simulate thermal mixing and stratification phenomena, which is followed by a short summary of the multi-dimensional model implemented in the SAM code, including both the physical model and the Finite Element Method code implementation. In this study, two options were implemented in the SAM code to model turbulent flows: a relatively simple built-in turbulence model and an interface to accept externally computed turbulent viscosities (e.g., from a high- resolution CFD simulation). Code validation studies on this newly added capability were then carried out to compare SAM simulation results with experimental data from the SUPERCAVNA facility, which was designed to study the complex flow recirculation and thermal stratification phenomena relevant to sodium fast reactor designs. In this study, one transient and two steady-state test cases were used for code validation. Different approaches have been used to model the complex turbulence flow fields in the SUPERCAVNA facility. A highly simplified zero-equation turbulence model was first used, but it was determined that it is too simple to capture the complex turbulence flow fields in these test cases. Subsequently, the code validation continued with the use of turbulent viscosity data from high-resolution STAR-CCM+ CFD simulations to improve the accuracy of the results. Using this approach, the SAM simulation results showed very good agreement with both the SUPERCAVNA experimental data and STAR-CCM+ simulation results. In this report, we demonstrate the development, implementation, and successful validation of a multi-dimensional flow model in the SAM code, which aims to improve the simulation accuracy for complex thermal mixing and stratification phenomena. Lessons have also been learned, including that in cases where the flow fields are not well predicted by the zero-equation model, the iinput of turbulent viscosities from an external source can enhance the overall predictive capabilities needed to accurately capture complex thermal-hydraulic phenomena. Therefore, future research will be needed to further improve the code’s capabilities, such as by developing a more efficient and robust approach to capture the turbulence effects in the SAM code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Study of mean- and turbulent-velocity fields in a large-scale turbine-vane passage

Laser-Doppler velocimetry, and to a lesser extent hot-wire anemometry, were employed to measure three components of the mean velocity and the six turbulent stresses at four planes within the turbine inlet-guide-vane passage. One variation in the turbulent inlet boundary layer thickness and one variation in the blade aspect ratio (span/axial chord) were studied. A longitudinal vortex (passage vortex) was clearly identified in the exit plane of the passage for the three test cases. The maximum turbulence intensities within the longitudinal vortex were found to be on the order of 2 to 4 percent, with large regions appearing nonturbulent. Because a turbulent wall boundary layer was the source of vorticity that produced the passage vortex, these low turbulence levels were not anticipated. For the three test cases studied, the lateral velocity field extended significantly beyond the region of the longitudinal velocity defect. Changing the inlet boundary layer thickness produced a difference in the location, the strength, and the extent of the passage vortex. Changing the aspect ratio of the blade passage had a measurable but less significant effect. The experiment was performed in a 210 mm pitch, 272 mm axial chord model in low speed wind tunnel at an inlet Mach number of 0.07.

Bailey, D. A.↗

Helicopter flight investigation to determine the effects of a closed-circuit TV on performance of a precision sling-load handling task

Helicopter sling-load operations have been limited during hover and low-speed flight by the degree of precision achieved by the pilot/helicopter/sling-load combination. Previous attempts to improve precision have included stabilization of the load and helicopter and the addition of a pilot station directly facing the load. In these tests, use of a closed-circuit TV as a display that would permit sling-load delivery and placement by the forward-facing pilot was evaluated using a CH-54B helicopter. In all, three test cases were documented, which included the following: (1) forward-facing pilot using the TV display, (2) forward-facing pilot using verbal commands from a load-facing observer, and (3) aft-facing pilot using direct visual cues. The results indicate that a comparable level of performance was achieved for each test case; however, an increase in pilot workload was noted when the TV system was used.

Dicarlo, D. J.↗

A Solution Adaptive Technique Using Tetrahedral Unstructured Grids

An adaptive unstructured grid refinement technique has been developed and successfully applied to several three dimensional inviscid flow test cases. The method is based on a combination of surface mesh subdivision and local remeshing of the volume grid Simple functions of flow quantities are employed to detect dominant features of the flowfield The method is designed for modular coupling with various error/feature analyzers and flow solvers. Several steady-state, inviscid flow test cases are presented to demonstrate the applicability of the method for solving practical three-dimensional problems. In all cases, accurate solutions featuring complex, nonlinear flow phenomena such as shock waves and vortices have been generated automatically and efficiently.

Pirzadeh, Shahyar Z.↗

Fuzzy control of small servo motors

To explore the benefits of fuzzy logic and understand the differences between the classical control methods and fuzzy control methods, the Togai InfraLogic applications engineering staff developed and implemented a motor control system for small servo motors. The motor assembly for testing the fuzzy and conventional controllers consist of servo motor RA13M and an encoder with a range of 4096 counts. An interface card was designed and fabricated to interface the motor assembly and encoder to an IBM PC. The fuzzy logic based motor controller was developed using the TILShell and Fuzzy C Development System on an IBM PC. A Proportional-Derivative (PD) type conventional controller was also developed and implemented in the IBM PC to compare the performance with the fuzzy controller. Test cases were defined to include step inputs of 90 and 180 degrees rotation, sine and square wave profiles in 5 to 20 hertz frequency range, as well as ramp inputs. In this paper we describe our approach to develop a fuzzy as well as PH controller, provide details of hardware set-up and test cases, and discuss the performance results. In comparison, the fuzzy logic based controller handles the non-linearities of the motor assembly very well and provides excellent control over a broad range of parameters. Fuzzy technology, as indicated by our results, possesses inherent adaptive features.

Maor, Ron↗

Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

The numerical simulation of many aerodynamic non-periodic flows of practical interest involves discretized computational domains that often must be artificially truncated. Appropriate boundary conditions are required at these truncated domain boundaries, and ideally, these boundary conditions should be perfectly "absorbing" or "nonreflecting" so that they do not contaminate the flow field in the interior of the domain. The proper specification of these boundaries is critical to the stability, accuracy, convergence, and quality of the numerical solution, and has been the topic of considerable research. The need for accurate boundary specification has been underscored in recent years with efforts to apply higher-fidelity methods (DNS, LES) in conjunction with high-order low-dissipation numerical schemes to realistic flow configurations. One of the most popular choices for specifying these boundaries is the characteristics-based boundary condition where the linearized flow field at the boundaries are decomposed into characteristic waves using either one-dimensional Riemann or other multi-dimensional Riemann approximations. The values of incoming characteristics are then suitably modified. The incoming characteristics are specified at the in flow boundaries, and at the out flow boundaries the variation of the incoming characteristic is zeroed out to ensure no reflection. This, however, makes the problem ill-posed requiring the use of an ad-hoc parameter to allow small reflections that make the solution stable. Generally speaking, such boundary conditions work reasonably well when the characteristic flow direction is normal to the boundary, but reflects spurious energy otherwise. An alternative to the characteristic-based boundary condition is to add additional "buffer" regions to the main computational domain near the artificial boundaries, and solve a different set of equations in the buffer region in order to minimize acoustic reflections. One approach that has been used involves modeling the pressure fluctuations as acoustic waves propagating in the far-field relative to a single noise-source inside the buffer region. This approach treats vorticity-induced pressure fluctuations the same as acoustic waves. Another popular approach, often referred to as the "sponge layer," attempts to dampen the flow perturbations by introducing artificial dissipation in the buffer region. Although the artificial dissipation removes all perturbations inside the sponge layer, incoming waves are still reflected from the interface boundary between the computational domain and the sponge layer. The effect of these refkections can be somewhat mitigated by appropriately selecting the artificial dissipation strength and the extent of the sponge layer. One of the most promising variants on the buffer region approach is the Perfectly Matched Layer (PML) technique. The PML technique mitigates spurious reflections from boundaries and interfaces by dampening the perturbation modes inside the buffer region such that their eigenfunctions remain unchanged. The technique was first developed by Berenger for application to problems involving electromagnetic wave propagation. It was later extended to the linearized Euler, Euler and Navier-Stokes equations by Hu and his coauthors. The PML technique ensures the no-reflection property for all waves, irrespective of incidence angle, wavelength, and propagation direction. Although the technique requires the solution of a set of auxiliary equations, the computational overhead is easily justified since it allows smaller domain sizes and can provide better accuracy, stability, and convergence of the numerical solution. In this paper, the PML technique is developed in the context of a high-order spectral-element Discontinuous Galerkin (DG) method. The technique is compared to other approaches to treating the in flow and out flow boundary, such as those based on using characteristic boundary conditions and sponge layers. The superiority of the current PML technique over other approaches is demonstrated for a range of test cases, viz., acoustic pulse propagation, convective vortex, shear layer flow, and low-pressure turbine cascade flow. The paper is structured as follows. We first derive the PML equations from the non{linear Euler equations. A short description of the higher-order DG method used is then described. Preliminary results for the four test cases considered are then presented and discussed. Details regarding current work that will be included in the final paper are also provided.

Spectral↗

Site-Specific Evaluation of Microgrid Controller Using Controller and Power-Hardware-in-the-Loop: Preprint

Microgrids are built by utilities to improve the resilience and reliability of segments of the distribution system. Controllers with advanced capabilities will operate and control these microgrids with diverse energy technologies, which vary from inverter-based photovoltaics, energy storage systems, and ultra-capacitors to conventional diesel generators. There are multiple challenges to building a microgrid controller for a site because of the unique requirements presented by the controllable and uncontrollable elements in the system. There are also challenges to testing the performance of the microgrid controller for such unique microgrids. The research presented here discusses the challenges to evaluating a microgrid controller for a specific site and provides solutions to those challenges. The paper also presents the controller/power-hardware-in-the-loop evaluation platform built to suit the needs of the microgrid as well as the IEEE 2030.8 consistent test cases used to evaluate the proper operation of the microgrid controller. Finally, the paper presents the results from a subset of the experiments performed to evaluate the microgrid controller. a microgrid controller for a site because of the unique requirements presented by the controllable and uncontrollable elements in the system. There are also challenges to testing the performance of the microgrid controller for such unique microgrids. The research presented here discusses the challenges to evaluating a microgrid controller for a specific site and provides solutions to those challenges. The paper also presents the controller/power-hardware-in-the-loop evaluation platform built to suit the needs of the microgrid as well as the IEEE 2030.8 consistent test cases used to evaluate the proper operation of the microgrid controller. Finally, the paper presents the results from a subset of the experiments performed to evaluate the microgrid controller.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Flexible Service Contracting for Risk Management within Integrated Transmission and Distribution Systems

The general objective of our project has been to investigate the ability of Independent Distribution System Operators (IDSOs), functioning as linkage agents for Integrated Transmission and Distribution (ITD) systems, to facilitate the flexible availability and usage of reserve in support of ITD system operations. This general objective is in accordance with Order 2222 of the U.S. Federal Energy Regulatory Commission (FERC), titled “Participation of Distributed Energy Resource Aggregations in Markets Operated by Regional Transmission Organizations and Independent System Operators”. The Final Rule for FERC Order 2222 was issued on September 17, 2020. The primary contribution of our project is that we have formulated an innovative energy management Transactive Energy Design (TES) approach for ITD systems that provides promising support for our project objective. Specifically, we have developed a new type of IDSO-managed TES design for distribution system operations, as well as new types of swing contracts permitting IDSOs to participate in transmission system operations as providers of reserve harnessed from distribution system resources in return for appropriate compensation. Together, these design elements constitute a scalable market-based approach facilitating efficient reserve procurement for ITD system operations from a fuller range of power resources. The efficacy of our approach has been demonstrated by means of detailed conceptual analyses as well as test case simulations. To implement the latter, we have developed the ITD TES Platform V2.0, a computational platform that permits the modeling and software implementation of ITD system operations over time. The Electric Reliability Council of Texas (ERCOT) energy region has been used as the empirical anchor for the development of this platform. Our conceptual and test-case work has been reported in a Wiley/IEEE Press book, two refereed book chapters, and seven refereed journal articles. The key components comprising the ITD TES Platform V2.0 have been released as documented open-source software at online GitHub repositories.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Fluid and hybrid simulations of the ionization instabilities in Hall thruster

Low-frequency axial oscillations in the range of 5–50 kHz stand out as a pervasive feature observed in many types of Hall thrusters. While it is widely recognized that the ionization effects play the central role in this mode, as manifested via the large-scale oscillations of neutral and plasma density, the exact mechanism(s) of the instabilities remain unclear. To gain further insight into the physics of the breathing mode and evaluate the role of kinetic effects, a one-dimensional time-dependent full nonlinear low-frequency model describing neutral atoms, ions, and electrons is developed in full fluid formulation and compared to the hybrid model in which the ions and neutrals are kinetic. Both models are quasi-neutral and share the same electron fluid equations that include the electron diffusion, mobility across the magnetic field, and the electron energy evolution. The ionization models are also similar in both approaches. Further, the predictions of fluid and hybrid simulations are compared for different test cases. Two main regimes are identified in both models: one with pure low-frequency behavior and the other one, where the low-frequency oscillations coexist with high-frequency oscillations in the range of 100–200 kHz, with the characteristic time scale of the ion channel fly-by time, 100–200 kHz. The other test case demonstrates the effect of a finite temperature of injected neutral atoms, which has a substantial suppression effect on the oscillation amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems

The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Mapping unstructured grid computations to massively parallel computers

Investigated here is this mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time two fold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases.

Hammond, Steven Warren↗