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NASA NTRS2016

An Inviscid Decoupled Method for the Roe FDS Scheme in the Reacting Gas Path of FUN3D

An approach is described to decouple the species continuity equations from the mixture continuity, momentum, and total energy equations for the Roe flux difference splitting scheme. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This work lays the foundation for development of an efficient adjoint solution procedure for high speed reacting flow.

Thompson, Kyle B.↗

NASA NTRS2016

Coordination Logic for Repulsive Resolution Maneuvers

This paper presents an algorithm for determining the direction an aircraft should maneuver in the event of a potential conflict with another aircraft. The algorithm is implicitly coordinated, meaning that with perfectly reliable computations and information, it will in- dependently provide directional information that is guaranteed to be coordinated without any additional information exchange or direct communication. The logic is inspired by the logic of TCAS II, the airborne system designed to reduce the risk of mid-air collisions between aircraft. TCAS II provides pilots with only vertical resolution advice, while the proposed algorithm, using a similar logic, provides implicitly coordinated vertical and horizontal directional advice.

Narkawicz, Anthony J.↗

NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗

NASA NTRSDate not supplied

Recent Progress in OVERFLOW Convergence Improvements

Improvements have been made to the implicit symmetric successive overrelaxation algorithm in the OVERFLOW 2.3 structured, overset grid, computational fluid dynamics flow solver. These improvements, consisting of implicit boundary conditions, improved flux Jacobian linearizations, and CFL number ramping, are a series of evolutionary changes to the linear solver that have resulted in increased nonlinear convergence rates and faster time to solution. A series of test cases are presented that demonstrate the effect of the changes through comparison with the original SSOR path and other linear solver implementations within OVERFLOW.

Joseph M Derlaga↗

NASA NTRSDate not supplied

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↗

NASA NTRSDate not supplied

Wall-Modeled Large Eddy Simulation Method for Unstructured-Grid Navier-Stokes Solvers

This paper reports on the implementation and assessment of a Wall-Modeled Large-Eddy Simulation (WMLES) methodology in an unstructured-grid, node-centered flow solver, FUN3D that is developed and supported at the NASA Langley Research Center. Finite-volume (FV) and finite-element (FE) discretization schemes considered in the study provide formal second-order spatial accuracy. Large-Eddy Simulations (LES) resolve large-scale turbulent-flow features and filter out small-scale effects using the Vreman subgrid-scale model. At solid-wall boundaries, a shear-stress model is employed to provide a proper boundary-flux closure. The nonlinear equations are integrated in time using either an optimized backward difference formula or an implicit multistage Runge-Kutta temporal scheme. The implicit equations at each time step are solved by strong nonlinear iteration schemes. WMLES demonstrations are shown for two high-lift configurations, namely, the McDonnell Douglas 30P30N multielement airfoil and a NASA High-Lift Common Research Model. Results show that the WMLES approaches implemented in the FV and FE discretization methods produce consistent solutions and are capable of capturing key aerodynamic characteristics and flow structures for high-lift configurations at a wide range of angles of attack including maximum-lift conditions. In the 30P30N example, correct trends in the variations of integrated aerodynamic forces and moments, surface pressure distributions, and boundary-layer profiles are captured as the Reynolds number is increased.

CFD; turbulence modeling; High-Lift flow simulatio↗

NASA NTRS2024

3D Cloud Masking Across A Broad Swath Using Multi-Angle Polarimetry and Deep Learning

Understanding the 3-dimensional structure of clouds is of crucial importance to modeling our changing climate. Active sensors, such as radar and lidar, provide accurate vertical cloud profiles, but are mostly restricted to along-track sampling. Passive sensors can capture a wide swath, but struggle to see beneath cloud tops. In essence, both types of products are restricted to two dimensions: as a cross-section in the active case, and an image in the passive case. However, multi-angle sensor configurations contain implicit information about 3D structure, due to parallax and atmospheric path differences. Extracting that implicit information can be challenging, requiring computationally expensive radiative transfer techniques. Machine learning, as an alternative, may be able to capture some of the complexity of a full 3D radiative transfer solution with significantly less computational expense. In this work, we make three contributions towards understanding 3D cloud structure from multi-angle polarimetry. First, we introduce a large-scale, publicly available dataset that fuses existing cloud products into a format more amenable to machine learning. This dataset treats multi-angle polarimetry as an input, and radar-based vertical cloud profiles as an output. Second, we describe and evaluate strong baseline machine learning models based that predict these profiles from the passive imagery. Notably, these models are trained only on center-swath labels, but can predict cloud profiles over the entire passive imagery swath. Third, we leverage the information-theoretic nature of machine learning to draw conclusions about the relative utility of various sensor configurations, including spectral channels, viewing angles, and polarimetry. These findings have implications for Earth-observing missions such as NASA’s Plankton, Aerosol, Cloud-ocean Ecosystem (PACE) and Atmosphere Observing System (AOS) missions, as well as in informing future applications of computer vision to atmospheric remote sensing.

clouds↗

DOE OSTI2015

Conformation of Single Pentablock Ionomer Chains in Dilute Solutions

The conformation of single chain pentablock ionomers (A-B-C-B-A) containing randomly sulfonated polystyrene in the center block, tethered to poly-ethylene-r-propylene end-capped by poly-t-butyl styrene is studied in dilute solutions by molecular dynamics simulations. Multi-block copolymers offer a means to tailor several properties into one molecule, taking advantage of their rich phase diagram together with unique properties of specific blocks. For this pentablock the ionic block facilitates transport while the A and B components are incorporated for mechanical stability. The present study investigates the confirmation of a single chain of pentablock ionomer of molecular weight M w ~ 50,000 g/mol and sulfonated polystyrene of the same molecular weight as that of the center block for six sulfonation fractions f from f=0.0-0.55. For the sulfonated systems Na + counterions are included. Results for the equilibrium conformation of the chains and the three blocks in water and 1:1 mixture of cyclohexane and n-heptane are compared to simulations in implicit poor solvents with dielectric constants ε =1.0 and 77.73. In water, the pentablock is collapsed with sulfonated groups on the outer surface. As the sulfonation fraction f increases, the ionic, center block is increasingly segregated from the hydrophobic regions. In the 1:1 mixture of cyclohexane and heptane both the flexible and end blocks are swollen while the center ionic block is collasped for f>0, while for f=0 all blocks are swollen. In both implicit poor solvents the pentablock is collapsed into a nearly spherical shape for all f. The sodium counterions are dispersed widely throughout the simulation cell for both water and ε =77.73 whereas for ε =1.0 the counterions are largely condensed on the collapsed pentablock.

Aryal, Dipak↗

DOE OSTI2019

Numerical Simulation of Critical Factors Controlling Heat Extraction from Geothermal Systems Using a Closed-Loop Heat Exchange Method

Closed-loop heat exchange for geothermal energy production involves injecting working fluid down a well that extends through the geothermal resource over a significant length to absorb heat by conduction through the well pipe. The well then needs to return to the surface for energy recovery and fluid re-injection to complete the cycle. We have carried out mixed convective-conductive fluid-flow modeling using a wellbore flow model for TOUGH2 called T2Well to investigate the critical factors that control closed-loop geothermal energy recovery. T2Well solves a mixed explicit-implicit set of momentum equations for flow in the pipe with full coupling to the implicit three-dimensional integral finite difference equations for Darcy flow in the porous medium. T2Well has the option of modeling conductive heat flow from the porous medium to the pipe by means of a semi-analytical solution which makes the computation very efficient because the porous medium does not have to be discretized. When the fully three-dimensional option is chosen, the porous medium is discretized and heat flow to the pipe is by conduction and convection, depending on reservoir permeability and other factors. Simulations of the closed-loop system for a variety of parameter values have been carried out to elucidate the heat recovery process. To the extent that convection may occur to aid in heat delivery to the pipe, the permeability of the geothermal reservoir, whether natural or stimulated, is an important property in heat extraction. The injection temperature and flow rate of the working fluid strongly control the ultimate energy recovery. Pipe diameter also plays a strong role in heat extraction, but is correlated with flow rate. Similarly, the choice of working fluid plays an important role, with water showing better heat extraction than CO2 for certain flow rates, while the CO2 has higher pressure at the production wellhead which can aid in surface energy recovery. In general, we find complex interactions between the critical factors that will require advanced computational approaches to fully optimize.

Oldenburg, Curtis↗

DOE OSTI2020

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗

DOE OSTI2023

A Conservative Finite-Volume Based Interface-Tracking Algorithm Using the Signed Distance Function

Methods for tracking an interface between two fluid phases are developed to ensure desired fluid properties, conservation, and stability are preserved in a finitevolume (FV) discretization. Here, the interface is tracked using a level set method where the signed distance function implicitly defines the interface. Marching methods are used to evaluate the value of the signed distance function, including a novel initialization method to initialize any implicit function to the signed distance function around sharp corners in the level set. Global conservation and consistency with a set of governing equations is enforced by a compression coefficient that measures the volumetric compression or expansion due to inaccuracies in the level set evaluation. A redistribution method is integrated into the volume correction to eliminate the small-cell instability while maintaining global conservation. This suite of methods is implemented and tested using static uniform velocity, and potential flow cases with multiple interface geometries. Results show these methods achieve up to second order accuracy, and are conservative. The application for these methods is intended to track the interface of a 3D printing filament in a finite-volume discretization of the all-speed Navier-Stokes equations.

42 ENGINEERING↗

DOE OSTI2020

BISON Robustness and Performance Improvements

BISON is a modern finite-element based nuclear fuel performance code that has been under development at the Idaho National Laboratory (USA) since 2009 [1]. The code is applicable to both steady and transient fuel behavior and can be used to analyze 1D (spherically symmetric), 2D (axisymmetric and generalized plane strain) or 3D geometries. BISON is the fuel performance code used within CASL for LWR fuel under both normal operating and accident conditions. BISON is built using the INL Multiphysics ObjectOriented Simulation Environment, or MOOSE [2, 3]. MOOSE is a massively parallel, finite element-based framework to solve systems of coupled non-linear partial differential equations using the Jacobian-Free Newton Krylov (JFNK) method [4]. This enables investigation of computationally large problems, for example a full stack of discrete pellets in a LWR fuel rod, or every rod in a full reactor core. MOOSE supports the use of complex two and three-dimensional meshes and uses implicit time integration, important for the widely varied time scale in nuclear fuel simulation. An object-oriented architecture is employed which greatly minimizes the programming effort required to add new material and behavioral models. The flexibility of the implicit and fully coupled multiphysics approach comes with a need for constructing suitable approximations for the Jacobian matrix of the coupled system used for either preconditioning a Krylov solve or in a direct Newton solve. Preconditioning options for Bison problems need to be revisited with new preconditioning methods becoming available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2013

Resonance self-shielding effects on Eigenvalue sensitivity

We present a quick and accurate way to compute the eigenvalue sensitivity coefficients in multigroup lattice cell calculations. We look at both the explicit and implicit sensitivities, the latter resulting from the resonance self-shielding process. A self-shielding model is presented, and we show how to obtain cross section sensitivities to a variation on a light isotope density. As an example, we look at how a perturbation on the hydrogen density affects the multigroup cross sections for resonant reactions such as U'capture and U'fission, in two uranium spheres with different enrichments. Explicit sensitivities are also computed, and we discuss the relative importance of the implicit sensitivities. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Entropy viscosity method applied to Euler equations

The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Coupling CTF to MPACT for Improved Thermal-Hydraulic Feedback for Transients

As computational power and techniques continue to advance, reactor analysis codes are afforded the opportunity to employ a more detailed physics model. One area where this has manifested is with coupled neutron kinetics and thermal-hydraulics codes for transient analysis, in which the feedback is critical for accurate modeling. The Michigan Parallel Characteristics Transport (MPACT) code is a 3-D method of characteristics neutron transport code capable of generating sub-pin level power distributions being developed by the University of Michigan through the Consortium for Advanced Simulation of LWRs (CASL) program. Currently, MPACT handles thermal-hydraulic feedback with an internal 1-D radial heat transfer model assuming constant moderator temperature. While this relatively simple treatment of thermal-hydraulic feedback has been shown to accurately model transients where Doppler feedback is the dominant feedback mechanism, coupling MPACT to a detailed thermal-hydraulic code will greatly expand the range of transient problems that can be accurately modeled. COBRA-TF (CTF) is a 3-D two-phase flow, subchannel thermal-hydraulics code maintained by Penn State University through CASL. CTF is based upon the Semi-Implicit Method for Pressure-Linked Equations, and it is especially well suited to model heat transfer and fluid flow phenomena associated with a nuclear reactor through a wide range of conditions. We present an initial effort coupling MPACT to CTF for transients, which provides a wider range of transient problems that can be modeled with increased accuracy. We have successfully coupled the thermal-hydraulics code CTF to the neutronics code MPACT for transient calculations by implicit and Crank-Nicolson methods, which have been demonstrated with single pin and 3x3 configurations. This capability extends the ability of MPACT to accurately model transients through a wider range of conditions than the existing thermal-hydraulic feedback, which is severely limited by the assumption of constant moderator temperature and density. By employing CTF for the thermal- hydraulic feedback, the transient physics can be described more completely at minimal computational expense. (authors)

42 ENGINEERING↗

DOE OSTI2017

Implementation of Weighted Delta-Tracking with Scattering in the Serpent 2 Monte Carlo Code

Serpent 2, a continuous-energy Monte Carlo Reactor physics burnup code developed at the VTT Technical Research Centre of Finland, uses a common rejection sampling technique, known as Woodcock delta-tracking. This method improves the efficiency of Monte Carlo in the complicated geometric layout of nuclear reactors and is widely used despite drawbacks that make it inefficient in specific cases, such as in the presence of strong absorbers. At present, Serpent actively uses delta-tracking, falling back to a surface tracking option in situations where delta-tracking is inefficient to partially offset these weaknesses. Morgan and Kotlyar introduced a Weighted Delta Tracking (WDT) routine to address these issues, replacing the rejection sampling of absorption events with an implicit event. In this research, we examine the theoretical basis for rejection sampling and implicit events, and how they relate to WDT. We then discuss implementation of a routine that extends the WDT routine to include scattering events. The routine is implemented and tested within Serpent. We examine various test cases including a Boiling Water Reactor (BWR) pin cell, and homogenous fuel media based on the content of the fuel of the Transient Test Reactor (TREAT) at Idaho National Lab (INL)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2017

The Parareal Method for Solving Space-Dependent Neutron Kinetics Equations in Hexagonal-z Geometry

Neutron kinetics plays an important role in reactor safety and analysis. The backward Euler method is the most widely used time integration method in the calculation of space-dependent nuclear reactor kinetics. Xia (2006) used this method to discretize the derivative of flux, and adopted the analytic integration to discretize the delayed neutron precursor concentrations. Diagonally Implicit Runge-Kutta (DIRK) method owns high accuracy and excellent stability, and it was applied in the rectangle core for calculating core the nuclear reactor kinetics by Wenbo Zhao (2013). Recently, DIRK was applied to the neutron kinetics for hexagonal-z geometry application (CAI, 2016). As solving the neutron kinetics equations is very time-consuming and the number of available cores continues to increase with parallel architectures evolving, parallel algorithms need to be designed in order to effectively utilize the available resources. However, it is difficult to parallel in time axis because the later moment is strongly dependent on the previous moment. Some methods have been proposed to parallel in time algorithm over the last decades. One of the famous methods to realize time parallelism is the Parareal algorithm (Lions, 2001), which offers a promising approach to increase the degree of concurrency. More than one decade from this method first proposed, this method has been studied and applied in the many fields of applied mathematics, physics, chemistry, parallel computing, etc. Fischer (2014 applied the Parareal method in the field of the Navier-Stokes Equations. Baudron (2014) combined the Parareal method with finite element method to solve the neutron kinetics equations, where the Parareal method was implemented based on the implicit Euler method or method. In this paper, the Parareal method is studied in the hexagonal-z geometry with the help of DIRK developed for neutron kinetics equations (CAI, 2016)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2014

Analog neutron transport for nuclear instrumentation applications with the Monte-Carlo code TRIPOLI-4 - Paper 3

Monte-Carlo codes simulating particle transport usually make use of well-known variance reduction techniques, leading to more efficient simulations. Even in configurations which do not deal with deep-penetration, some of these techniques, such as the implicit capture, are actually often used by default. The statistical weight of the simulated particles is then modified in order to take into account the modification of the sampling without introducing any bias in the estimation process. For instance, the implicit capture decreases the statistical weight of the particles at each collision, whereas the sampling of a single outgoing particle increases this statistical weight in case of scattering reactions producing multiple neutrons. In addition, Russian roulette and splitting operations, which are usually also played at each collision, lead to other modifications of the statistical weights. As a result, Monte-Carlo codes provide particle histories that are valid on average, but collect statistical weights which differ from 1, when tallying the estimation of the quantities of interest. Yet, some nuclear instrumentation calculations inherently need to work with statistical weights equal to 1, since either individual events have to be collected (such as the arrival of a particle at a detector, the measurement of a time of flight, etc), or the coincidence of events or also correlations between individual events have to be taken into account. To address these specific applications with Monte-Carlo simulation codes, users need a full analog simulation mode. The continuous-energy Monte-Carlo code TRIPOLI4{sup R} is mainly dedicated to shielding, reactor physics and criticality safety calculations. Its capabilities have recently been extended to widen its use to nuclear instrumentation with the possibility of γ-spectrometry calculations and the simulation of photonuclear reactions for instance. Other features needed by nuclear instrumentation applications have been available in TRIPOLI-4 for a long time, such as the sampling of the time variable and the possibility of tallying in a time grid for most of the available tallies (fluxes, reaction rates, dose equivalent rates, energy depositions, etc). In TRIPOLI-4, the transport between two consecutive collisions is analog if no variance reduction technique is requested by the user to handle deep-penetration configurations. However, up to the version 9 of the code, the collision itself is sampled in a non-analog way. This paper presents a first implementation of a full analog neutron transport mode in TRIPOLI-4, preliminary verification results and an application of this functionality to the simulation of the Nucifer detector located in Saclay, France. It should be noted that only neutron transport is dealt with in this work and that all nuclear data come from JEFF-3.1.1 or ENDF/B-VII.0 evaluations, including fission data when needed. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗