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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Performance Evaluation of a Two-Dimensional Flood Model on Heterogeneous High-Performance Computing Architectures

This paper describes the implementation of a two-dimensional hydrodynamic flood model with two different numerical schemes on heterogeneous high-performance computing architectures. Both schemes were able to solve the nonlinear hyperbolic shallow water equations using an explicit upwind first-order approach on finite differences and finite volumes, respectively, and were conducted using MPI and CUDA. Four different test cases were simulated on the Summit supercomputer at Oak Ridge National Laboratory. Both numerical schemes scaled up to 128 nodes (768 GPUs) with a maximum 98.2x speedup of over 1 GPU. The lowest run time for the 10 day Hurricane Harvey event simulation at 5 meter resolution (272 million grid cells) was 50 minutes. GPUDirect communication proved to be more convenient than the standard communication strategy. Both strong and weak scaling are shown.

Sharif, Md Bulbul↗
DOE OSTI2022

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

A pseudospectral implicit particle-in-cell method with exact energy and charge conservation

The standard particle-in-cell (PIC) method employs explicit finite-difference (FD) methods (e.g. the leap-frog scheme) for both spatial and temporal integrations. Here, we employ a pseudospectral method for solving the Poisson equation and a fully implicit time integration to achieve exact energy conservation. The advantage of a pseudospectral field solver is its spectral accuracy in solving field solutions. Earlier studies of implicit time integration of PIC FD equations can enforce exact energy exchange between field and particles, resulting in exact energy-conserving schemes. Here, we prove that the exact energy conservation property can be carried over to the pseudospectral scheme. Simultaneously, we provide a solution to ensure a pseudospectral charge continuity equation. We demonstrate the new scheme in a 2D electrostatic PIC code. In conclusion, theoretical results are confirmed via numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗
DOE OSTI2024

Divertor heat load estimates on NSTX and DIII-D using new and open-source 2D inversion analysis code

A thermography inversion algorithm has been developed in the open-source Python-based computer code, HYPERION, to calculate the heat flux incident on plasma-facing components (PFCs) in axisymmetric tokamaks. The chosen mesh size at the surface significantly affects the calculated transient heat flux results. The calculated transient heat flux will exceed the real value when the mesh size tends to zero but will underestimate the real value when the mesh size is large. A criterion for determining the appropriate mesh size for the transient heat flux calculation will be discussed. The numerical scheme for HYPERION uses a 2D fully implicit finite-difference approach, allowing temperature-dependent thermal properties of PFC materials. The inversion algorithm is benchmarked against established heat flux calculation codes, TACO and THEODOR, based on thermography data from NSTX and DIII-D respectively. The primary benefits of HYPERION compared to TACO and THEODOR are that it is open-source and it allows for the optimization of mesh thickness along the substrate. The algorithm also accounts for the thermal properties of thin surface layers that characteristically form on PFCs due to plasma-material interactions. The agreement between HYPERION and THEODOR is excellent, as the percent difference between the codes is ~5% on average in the case of the DIII-D data for moderate to high heat flux. Verification tests with TACO show slightly higher average percent differences of 8% and 12%. In using HYPERION to study filaments in heat flux, the initial results indicate that small ELMs filaments significantly broaden the divertor heat flux, and decrease divertor peak flux. Compared to the inter-ELM, the small ELM filaments decrease the divertor peak surface temperature. With intermittent divertor filaments, the divertor heat flux width is comparable with that found in L-mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Neutron transport methods for multiphysics heterogeneous reactor core simulation in Griffin

Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-S ) to discretize the field variable of the multigroup neutron transport equation. Multiphysics feedback is handled using two-step tabulated cross-section methodology. Feedback quantities are evaluated using the MOOSE-MultiApp system to couple various engineering phenomena, such as heat conduction and thermal fluids. The multiphysics DFEM-S system is solved using fixed-point iteration with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference acceleration, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with two transients: one initiated by a single heat-pipe failure and another by control drum rotation. Importantly, these examples demonstrate the ability of Griffin to tractably solve the neutron transport equation considering seven independent variables and feedback.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

MPACT Theory Manual (V.4.3)

This manual presents the theory underlying the three-dimensional (3D) whole-core, pin-resolved neutron transport calculation methodologies employed in the MPACT code. MPACT’s primary goal is to provide accurate sub-pin power distributions in a computationally efficient manner. To accomplish this, MPACT offers several different transport method options. The 2D/1D method, in which 3D problems are decomposed into an axial stack of radial “slices,” is currently the most commonly used. In this option, two-dimensional (2D) planar solutions are provided by the method of characteristics (MOC), and axial solutions are provided via one-dimensional (1D) approximate diffusion, or P3 solutions. The radial and axial solutions are coupled by (i) axial and radial transverse leakages, and (ii) a global 3D coarse mesh finite difference (CMFD) solve, which provides both acceleration and stability to the solution iteration scheme. The subsequent chapters of this manual present a range of topics, including MOC, CMFD, axial nodal transport solvers, 2D/1D, self-shielding, depletion, thermal-hydraulics, and transient methods. Development of the underlying theory of the 2D/1D method is presented, diagrams are included to highlight important algorithmic flow, and important concepts are discussed as appropriate. This manual is intended to be self-sufficient, but references to published articles and other materials are included for further reading. MPACT is a relatively new code, with new capabilities and many computational methods that did not exist until recently. This manual is an even newer document, with chapters written by several different code contributors working under time constraints. For these reasons, the manual is not yet complete and finalized. Future versions of this manual will address current deficiencies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improvements to the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A finite element method for angular discretization of the radiation transport equation on spherical geodesic grids

Discrete ordinate (S N ) and filtered spherical harmonics (FP N ) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical scenarios. We present a new method based on a finite element approach in angle that combines the strengths of both methods and mitigates their disadvantages. The angular variables are specified on a spherical geodesic grid with functions on the sphere being represented using a finite element basis. A positivity-preserving limiting strategy is employed to prevent non-physical values from appearing in the solutions. Here, the resulting method is then compared with both S N and FP N schemes using four test problems and is found to perform well when one of the other methods fail.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

Here we present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with Nv discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all Nv cell centers to each other. The overall CPU time and memory requirement scale as O(Nv log2 Nv) for any bounded two-dimensional (2D) domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an O(Nv4/3) CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency domain methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-of-the-art supercomputer at Lawrence Berkeley National Laboratory.

Hadamard--Babich ansatz↗
DOE OSTI2022

High-order accurate finite difference discretisations on fully unstructured dual quadrilateral meshes

Here, we present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which when differentiated provides the derivatives of the original function. The method generalises traditional finite difference methods to meshes of arbitrary topology in any number of dimensions for any order of derivative and accuracy. We demonstrate the accuracy of the numerical scheme using dual quadrilateral meshes and a refinement method based on subdivision surfaces. The scheme is applied to the solution of a range of partial differential equations, including both linear and nonlinear, second and fourth order equations, and a time-dependent first order equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum dynamics simulation of the advection-diffusion equation

The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.

Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗
DOE OSTI2022

A User Guide to PARET/ANL

PARET was originally created in 1969 at what is now Idaho National Laboratory (INL), to analyze reactivity insertion events in research and test reactor cores cooled by light or heavy water, with fuel composed of either plates or pins. The use of PARET is also appropriate for fuel assemblies with curved fuel plates when their radii of curvatures are large with respect to the fuel plate thickness. The PARET/ANL version of the code has been developed at Argonne National Laboratory (ANL) under the sponsorship of the U.S. Department of Energy/NNSA since the inception of the Reactor Conversion Program. Since Reduced Enrichment for Research and Test Reactors (RERTR) began in 1978, PARET/ANL has been benchmarked to experimental data including SPERT testing, and used to determine the expected transient behavior of a large number of reactors regardless of enrichment both inside and outside the Reactor Conversion Program. This document provides the pertinent information for the use of PARET/ANL Version 7.6. PARET/ANL models the various fueled regions of a reactor core as channels. Each of these channels consists of a single flat fuel plate/pin (including cladding and, optionally, a gap) with water coolant on each side. In slab geometry the coolant channels for a given fuel plate are of identical dimensions (mirror symmetry), but they can be of different thickness in each channel. There can be many channels, but each channel is independent and coupled only through reactivity feedback effects to the whole core. The time-dependent differential equations that represent the system are replaced by an equivalent set of finite-difference equations in space and time, which are integrated numerically. PARET/ANL uses fundamentally the same numerical scheme as RELAP5 for the time-integration of the point-kinetics equations. The one-dimensional thermal-hydraulic model includes temperature-dependent thermal properties of the solid materials, such as heat capacity and thermal conductivity, as well as the transient heat production and heat transfer from the fuel meat to the coolant. Temperature- and pressure-dependent thermal properties of the coolant such as enthalpy, density, thermal conductivity, and viscosity are also used in determining parameters such as friction factors and heat transfer coefficients. The code first determines the steady-state solution for the initial state. Then the solution of the transient is obtained by integration in time and space. Multiple heat transfer, DNB and flow instability correlations are available. The code was originally developed to model reactors cooled by an open loop, which was adequate for rapid transients in pool-type cores. An external loop model appropriate for Miniature Neutron Source Reactors (MNSR’s) was also added to PARET/ANL to model natural circulation within the vessel, heat transfer from the vessel to pool and heat loss by evaporation from the pool. PARET/ANL also contains models for decay heat after shutdown, control rod reactivity versus time or position, time-dependent pump flow, and loss-of-flow event with flow reversal as well as logic for trips on period, power, and flow. Feedback reactivity effects from coolant density changes and temperature changes are represented by tables. Feedback reactivity from fuel heat-up (Doppler Effect) is represented by a four-term polynomial in powers of fuel temperature. Photo-neutrons produced in beryllium or in heavy water may be included in the point-kinetics equations by using additional delayed neutron groups.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Ultrafast Laser Material Damage Simulation—A New Look at an Old Problem

The chirped pulse amplification technique has enabled the generation of pulses of a few femtosecond duration with peak powers multi-Tera and Peta–Watt in the near infrared. Its implementation to realize even shorter pulse duration, higher energy, and higher repetition rate laser systems relies on overcoming the limitations imposed by laser damage of critical components. In particular, the laser damage of coatings in the amplifiers and in post-compression optics have become a bottleneck. The robustness of optical coatings is typically evaluated numerically through steady-state simulations of electric field enhancement in multilayer stacks. However, this approach cannot capture crucial characteristics of femtosecond laser induced damage (LID), as it only considers the geometry of the multilayer stack and the optical properties of the materials composing the stack. This approach neglects that in the interaction of an ultrashort pulse and the materials there is plasma generation and associated material modifications. Here, we present a numerical approach to estimate the LID threshold of dielectric multilayer coatings based on strong field electronic dynamics. In this dynamic scheme, the electric field propagation, photoionization, impact ionization, and electron heating are incorporated through a finite-difference time-domain algorithm. We applied our method to simulate the LID threshold of bulk fused silica, and of multilayer dielectric mirrors and gratings. The results are then compared with experimental measurements. The salient aspects of our model, such as the implementation of the Keldysh photoionization model, the impact ionization model, the electron collision model for ‘low’-temperature, dense plasma, and the LID threshold criterion for few-cycle pulses are discussed.

36 MATERIALS SCIENCE↗