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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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DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2024

FORCE Update 2024

The Framework for Optimization of Resources and Economics (FORCE) tool suite is the U.S. Department of Energy’s Nuclear Integrated Energy Systems (IES) Program flagship tool suite for technoeconomic IES analysis of IES. This tool suite is useful for analysis designed to evaluate and improve the technoeconomics of energy production systems, particularly for systems including nuclear technology. In this report, we document the development activity for the FORCE tool suite to extend its capabilities as performed during fiscal year 2024. In addition to reliability and accessibility, capability is one of the three standards guiding the development of the FORCE tool suite and the software codes that are its constituent parts. Extending the capabilities of the FORCE tool suite allows analysis both within the IES program as well as industry, university, and laboratory partners to perform analysis with more accuracy, insight, and impactful narrative. Four areas of capability development were the focus of activity this year: economic parameter uncertainty quantification, multiresolution analysis, components-to-optimization workflow automation, and statespace construction workflows for real-time optimal control. In economic parameter uncertainty quantification, the ability of HERON to capture risk due to scenarios (weather and energy demand uncertainty) was expanded to also include uncertainties in financial parameters such as capital cost or operation and maintenance costs. By including these sources of uncertainty, which are sometimes very large compared with scenario uncertainty, HERON is better able to capture the risk posed by investment in various IES technology. Because of this, analysts can also consider the reduction in risks that can be realized by choice of some technologies. In multiresolution analysis, development activity extended on work completed previously. In fiscal year 2023, methods for decomposing time series signals, such as demand, solar and wind availability, and price profiles, were analyzed and down-selected to those most effective at splitting signals into different resolutions. These resolutions allow considering the influence of different energy demand and supply behaviors across different time scales. For example, energy demand might be divided into seasonal, weekly, and hourly profiles. In fiscal year 2024, this preliminary work was extended and implemented within the Risk Analysis Virtual Environment (RAVEN) risk and uncertainty analysis platform, which is used throughout the FORCE framework. This development of the “multi-resolution time series analysis” (MR-TSA) module in RAVEN allows training synthetic history generators on complex time series. These synthetic history generators can then be used in HERON for generating scenarios that represent possible market and weather scenarios that can be analyzed on different time scales. We envision completing this work in the future, implementing multiresolution dispatch optimization strategies that can make the most beneficial use of these stratified time histories. In components-to-optimization workflow development, workflows for translating user inputs of components into algorithms for algebraic optimization were selected and implemented. Similar algorithms within the Holistic Energy Resource Optimization Network (HERON) were separated from the main code base of HERON and gathered with the components-to-optimization workflows in the new Dispatch Optimization Variable Engine (DOVE) software library. This modularization allows FORCE users to analyze dispatch optimization and energy system duty cycles independently of HERON, which previously was a burdensome task. Additionally, these dispatch optimization algorithms, set up in an independent library, can now be used across all software applications within FORCE, especially including the real-time optimal control software Optimization of Real-time Capacity Allocation (ORCA). Allowing FORCE software to share dispatch optimization algorithms within a single library allows for improved software maintenance and reliability. In statespace characterization workflow development, alternative workflows for optimizing dispatch with additional technical accuracy was the focus, particularly to improve the real-time optimization decision making in ORCA. Using algorithms and workflows initially developed for the Feasible Actuator Range Modifier (FARM), workflows for determining the statespace representation of IES were identified and demonstrated. The resulting dispatch optimization required a more robust optimization algorithm than that originally used in HERON (and moved to DOVE), which required adding an alternate workflow to DOVE that can more accurately match the behavior of physical systems using a partial differential equation representation. In conclusion, capability developments in the FORCE tool suite in fiscal year 2024 have improved the ability of the FORCE tool suite to perform

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization↗
DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗