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NASA NTRS2018

Demonstration of Probabilistic Sensitivity Analyses Tools on the Structural Response of a Representative Inflatable Space Structure

This work provides an initial step toward demonstrating a probabilistic numerical simulation capability to support trade studies and the development of a certification plan for inflatable space habitats. This study concentrates on interpreting the results from probabilistic analysis and numerical simulation tools to identify parameter sensitivities for a novel inflatable airlock concept, specifically the Non‐Axisymmetric Inflatable Pressure Structure (NAIPS) that was designed and tested under NASA's Minimalistic Advanced Softgoods Hatch (MASH) Program. A brief overview of the finite element model is provided along with the probabilistic sensitivity analysis approach. The sensitivity studies required a model that was numerically stable and efficient enough that hundreds of simulations could be completed in the allotted time. Therefore, the existing full model was simplified by: extracting a quarter symmetry section of the dome; focusing on a single inflation pressure; and replacing the non‐linear material stress‐strain curves with linear, isotropic materials defined by elastic moduli. Responses of interest include the sensitivity of various structural component loads to material properties, cord lengths, inflation pressure and friction. Multiple sensitivity studies were completed and three are reported here. The first study focused on utilizing wide input parameter ranges to provide an opportunity to assess numerical robustness. The next two studies narrowed the parameter ranges to enable focus on understanding uncertainty at a fixed operating condition. The completion of the sensitivity studies improved understanding of the interdependence of multiple inputs on the responses. In addition, numerical stability of the simulations over wide parameter ranges, shows the feasibility of incorporating uncertainty‐based methods in the design and certification of inflatable space habitats. With the experience and trust gained, it is anticipated that these same methods will be applied to nonlinear, orthotropic models in the future.

Lyle, Karen H.↗

NASA NTRS1986

Efficient solutions of two-dimensional incompressible steady viscous flows

A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.

Morrison, J. H.↗

NASA NTRS1988

Efficient solutions of two-dimensional incompressible steady viscous flows

Morrison, J. H.↗

DOE OSTI2018

Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction–diffusion systems

The generalized fractional reaction–diffusion equations which exist in the form of noninteger order partial differential equations have now found wide application for illustrating important and useful physical phenomena, such as subdiffusive and superdiffusive scenarios. The space fractional derivatives are defined in the Riesz sense on the intervals 0 < α < 1 and 1 < α ≤ 2. We propose robust numerical techniques, such as a spectral representation of the fractional Laplacian operator in conjunction with the exponential time differencing method, and present the equivalent relationship between the Riesz fractional derivative and fractional Laplacian operator. We apply these techniques to numerically solve a range of chaotic processes, such as the Chua’s equations, Rössler system, Lorenz and Lorenz-type systems. Simulation results revealed various complex and spatiotemporal chaos, spiral chaos, intermittent chaos and spots patterns in two-dimensional space fractional reaction–diffusion problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2026

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

DOE OSTI2024

DECOVALEX-2023: Task G, SAFENET Final Report

DECOVALEX Task G deals with fracture mechanics at several scales using a combined approach of experimental work, related model development, benchmarking and experimental analysis. Fig. 0.1 provides a graphical abstract for Task G. The experimental basis for the related mechanical (M), hydro-mechanical (HM), and thermo-mechanical (TM) processes comes from the rock mechanics laboratories of Universities of Freiberg (TUBAF) and Edinburgh, as well as the Korea Institute of Civil Engineering and Building Technology (KICT). The experimental work in the rock laboratories is closely linked to the underground research laboratories (URLs) Reiche Zeche (Germany), KURT (Korea), and Mont Terri (Switzerland). The scientific key questions are related to fracture permeability evolution under THM conditions, anisotropy effects on fracturing processes, and thermal fracture slip, which are being addressed in specific steps of the task. A large variety of numerical methods have been developed and applied for experimental analysis, ranging from continuum to discontinuum approaches. A detailed comparison of mechanical and hydro-mechanical processes is given in the section 3 via the benchmarking exercises. As a result of DECOVALEX-2023 Task G we further improved our understanding and predictability of fracturing processes under THM conditions. This was based on robust numerical simulation methods and in-depth experimental analysis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS2024

Development and Implementation of Large-Scale Numerical Models for Shape Memory Mars Spring Tires

The current work focuses on implementation of the user-defined shape memory alloy (SMA) model in the finite element analysis program ABAQUS for large-scale simulations of the Spring Tires made of SMA developed at the NASA Glenn Research Center. The main objective of this study was to improve and optimize the structural design of the SMA tires through in-depth numerical analysis and sensitivity studies. Various design variables (wire diam., coil diam., pitch, spring length, and bead angle) were varied to study their influence on the global load-displacement response of the tire construct. A detailed investigation of the three-dimensional stress states was also carried out to enhance understanding of the local changes as the tire goes through global deformation. It was concluded that a robust numerical model with a good predictive capability, together with a thoughtfully crafted sensitivity study, can result in reduced design iterations required to reach a desired tire performance. This will, in turn, lead to significantly reduced manufacturing time, required labor, and testing expense.

shape memory alloys↗

DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids. LDRD Final Report

This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. In this project, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality. At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5x improvement in accuracy and allows for taking an 8x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method. The report concludes with a brief summary of ongoing projects and collaborations that utilize or extend the products of this work.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Numerical and Experimental Study of a Novel Additively Manufactured Metal-Polymer Composite Heat-Exchanger for Liquid Cooling Electronics

In order to meet increasing power-dissipation requirements of the electronics industry, compact, low-cost, and lightweight heat exchangers (HXs) are desired. With proper design, materials, and manufacture, polymer composite heat exchangers could meet these requirements. This paper presents a novel crossflow air-to-water, low-cost, and lightweight metal-polymer composite HX. This HX, which is entirely additively manufactured, utilizes a novel cross-media approach that provides direct heat exchange between air and liquid sides by using connecting fins. A robust numerical model was developed, which includes the dimensional effects of additive manufacturing. The study consists of a simplified 3D CFD model based on ellipsoidal-shaped staggered tube banks for the laminar range. It then uses an analytical approach to compute entire HX performance. The model is validated experimentally within 8% for thermal performance, 12% for air-side impedance, and 18% for water-side impedance. Finally, HX is compared with a conventional CPU radiator and performs within 10% of the conventional unit for reasonable flow rates and pressure-drop ranges. Moreover, HX also provides added design and cost advantages over the conventional unit, which makes the HX a potential candidate for electronic cooling applications.

30 DIRECT ENERGY CONVERSION↗

NASA NTRS2003

Finite Volume Methods: Foundation and Analysis

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Barth, Timothy↗

DOE OSTI2019

A Classical Field Theory Formulation for the Numerical Solution of Time Harmonic Electromagnetic Fields

Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the “curl-curl” equation for the fields. We present a variational formulation which solves for the four-potential instead, based on classical field theory. Borrowing from quantum electrodynamics, we modify the Lagrangian by adding an implicit gauge-fixing term. This reformulation explicitly accounts for Gauss’ law through the coupling between $\phi$ and $\rho$ , and enables the use of nodal basis functions instead of edge elements for time-harmonic problems. Here, we demonstrate how this formulation, adhering to the deeper underlying symmetries of the four-dimensional covariant field description, provides a highly general, robust numerical framework.

43 PARTICLE ACCELERATORS↗

DOE OSTI2019

Approximate Green’s Function Coupled Cluster A Method Employing Effective Dimension Reduction

The Green’s function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structures of molecular structures and periodic systems, especially when electrons are strongly correlated. However, in order for the GFCC method to become an approach that can be routinely used in the electronic structure calculations, more robust linear algebraic techniques and approximations need to be employed to reduce its extremely high computational overhead. In our recent studies, we showed that the GFCC equation can be numerically solved by seeking solutions of multiple linear systems in the frequency regime of interest, which can be easily distributed in a massively parallel environment, and broaden the avenue for more state-of-the-art numerical linear algebraic tools associated with multiple linear systems to be kicked in to this field. In the present pursuit of this practice, we show a successful application of model order reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires a high resolution of spectral function, instead of solving GFCC linear equation in the original dimension for every single frequency point, an easily-solvable linear system model with reduced dimension can be built upon projecting the original GFCC linear system into a subspace, from which the interpolation and extrapolation can give a reasonable approximation to the results of the original GFCC linear equations. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some select frequencies inside the frequency regime. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The approach is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems including carbon monoxide, 1,3-butadiene, benzene, and adenine molecules. As a byproduct, the high quality linear system model is also found to be able to provide high quality initial guess for the existing linear solver to improve the convergence performance.

Peng, Bo↗

DOE OSTI2021

Towards Resolving the Risk of Turbine Collision on Fish: FY21-22 Seedling Report Phase I

The most important concern for permitting tidal and river turbines is the collision risk of marine animals with the turbine blades. Our understanding of the risk to individual fish from colliding with turbine blades is poor; if these collisions were to occur, it is unknown whether fish will sustain recoverable injuries or be killed. Equally unknown is the impact these collisions might have on populations, particularly for threatened, endangered, or commercially managed fish species. In addition to observations of interactions of fish with turbines, numerical models need to be developed or expanded to predict impacts on fish populations. These models could replace expensive and technically challenging monitoring programs in high energy, often murky, tidal or river waters. In this project, a multi-pronged approach was taken to understand the state of knowledge for collision risk of fish with turbines and build a pathway forward. This approach included a workshop with experts, a literature review of modeling and empirical studies, the development of a research framework, and the identification of case studies to address through future work. This project is a first step towards the future development of effective and robust numerical models for assessing the collision risk of fish around turbines. This will achieve a balanced and improved estimate of the severity of collision risk to fish at the population scale.

Garavelli, Lysel↗

DOE OSTI2018

Development of Stable A- $\Phi$ Time-Domain Integral Equations for Multiscale Electromagnetics

Applications involving quantum physics are becoming an increasingly important area for electromagnetic engineering. To address practical problems in these emerging areas, appropriate numerical techniques must be utilized. However, the unique needs of many of these applications require new computational electromagnetic solvers to be developed. The A-4:1. formulation is a novel approach that can address many of these needs. This formulation utilizes equations developed in terms of the magnetic vector potential (A) and electric scalar potential (t.). The resulting equations overcome many of the limitations of traditional solvers and are ideal for coupling to quantum mechanical calculations. In this work, the A-4. formulation is extended by developing time domain integral equations suitable for multiscale perfect electric conducting objects. These integral equations can be stably discretized and constitute a robust numerical technique that is a vital step in addressing the needs of many emerging applications. To validate the proposed formulation, numerical results are presented which demonstrate the stability and accuracy of the method.

42 ENGINEERING↗

NASA NTRS1989

Robust eigenstructure assignment by a projection method - Applications using multiple optimization criteria

A methodology for robust eigenstructure assignment for multivariable feedback systems is presented. The algorithm is based upon a pole placement technique using projections onto subspaces of admissible eigenvectors. New ideas are introduced to generate target (desired) sets of unitary eigenvectors and determine optimal feasible eigenvectors in a least-square sense. Useful connections are established between the pole-placement by independent modal space control and the method introduced in this paper. A multicriterion optimization algorithm is also presented, which takes efficient advantage of the present eigenstructure assignment method. These developments show significant improvement over an earlier version of this algorithm in both computational cost and accuracy. This optimization process appears to be numerically robust and suitable for high-dimensional multicriterion optimizations; it is especially attractive for computer-aided design of control systems.

Rew, D. W.↗

NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.

Accelerance decoupling↗

NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

Accelerance decoupling↗