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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Yan, Jue↗
NASA NTRS2003

Robust Control for Microgravity Vibration Isolation using Fixed Order, Mixed H2/Mu Design

Many space-science experiments need an active isolation system to provide a sufficiently quiescent microgravity environment. Modern control methods provide the potential for both high-performance and robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H(infinity) methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/H(infinity), controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure, for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark↗
NASA NTRS2004

Robust Control for The G-Limit Microgravity Vibration Isolation System

Many microgravity science experiments need an active isolation system to provide a sufficiently quiescent acceleration environment. The g-LIMIT vibration isolation system will provide isolation for Microgravity Science Glovebox experiments in the International Space Station. While standard control system technologies have been demonstrated for these applications, modern control methods have the potential for meeting performance requirements while providing robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H infinity methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/mu controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark S.↗
DOE OSTI2021

A variational multiscale immersed meshfree method for heterogeneous materials

Abstract We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.

36 MATERIALS SCIENCE↗
NASA NTRS1962

Comparison of the Effectiveness of Flares With That of Fins for Stabilizing Low Fineness Ratio Bodies at Mach Numbers From 0.6 to 5.8

An experimental and analytical investigation has been made of the effectiveness of flares and of fins for providing aerodynamic stability of low-fineness-ratio bodies near zero angle of attack. Wind-tunnel tests were performed at Mach numbers from 0.6 to 3.8 to measure the normal force, center of pressure, and drag of bodies consisting of conical noses in combination with cylindrical midsections and finned or flared aftersections. This study included an investigation of the effects of nose bluntness, midbody length, flare angle (from 0° to 20°), and fin leading-edge bluntness. The results showed that for the same plan-form area, flares were more effective than fins, but for the same drag, fins were more effective than flares. Flow separation, which occurred ahead of a flare at certain Mach numbers, resulted in an increase in the stabilizing effectiveness of the flare and a decrease in the drag. However, flow separation led to large undesirable shifts in the center of pressure. Blunt fins were found to be more effective than sharp fins, with the vertical as well as the horizontal fins contributing to the effectiveness. Comparisons of the analytical with the experimental results indicated that the analytical method employed gave good estimates of the stabilizing effectiveness of both fins and flares throughout the supersonic Mach number range.

Leland H Jorgensen↗
NASA NTRS1973

An experimental investigation of vortex stability, tip shapes, compressibility, and noise for hovering model rotors

Schlieren methods of flow visualization and hot-wire anemometry for velocity measurements were used to investigate the wakes generated by hovering model propellers and rotors. The research program was directed toward investigating (1) the stability of the tip vortex, (2) the effects produced by various tip shapes on performance and tip vortex characteristics, and (3) the shock formation and noise characteristics associated with various tip shapes. A free-wake analysis was also conducted for comparison with the vortex stability experimental results. Schlieren photographs showing wake asymmetry, interaction, and instability are presented along with a discussion of the effects produced by the number of blades, collective pitch, and tip speed. Two hot-wire anemometer techniques, used to measure the maximum circumferential velocity in the tip vortex, are discussed.

Tangler, J. L.↗
DOE OSTI2020

An epoxy-reinforced ceramic sheet as a durable solid electrolyte for solid state Na-ion batteries

In a conventional Na-ion battery system using liquid electrolyte, there are critical safety issues due to the instability of the liquid electrolyte. Na 3 Zr 2 Si 2 PO 12 (NASICON) solid electrolyte is a material that is sufficient to replace a liquid electrolyte as it has high ionic conductivity and thermal and electrochemical stability. However, as there is a large interfacial resistance in the NASICON solid electrolyte powder, even when used in combination with a polymer electrolyte, the advantageous effects of ceramics are not easily exhibited. In this study, we propose a top-down method of combining a polymer with a ceramic in which an ion transport channel is previously formed. In this method, a NASICON solid electrolyte is partially sintered to form ion transport channels. Then the NASICON solid electrolyte pores are filled with an epoxy polymer to increase the strength of the epoxy-NASICON composite electrolyte. This method demonstrates the possibility of our composite electrolyte being used as a thin and strong film. As a result of our methods, the ionic conductivity and thermal and electrochemical stability of NASICON were maintained, while the physical strength was enhanced by approximately 2 times. In addition, a capacity of 120 mA h g -1 and stability of 20 cycles were confirmed in a half cell with a Na 3 V 2 (PO 4 ) 3 cathode and Na metal. This method proposes a new direction for research regarding composite electrolytes created using an oxide-based solid electrolyte.

25 ENERGY STORAGE↗
NASA NTRS1985

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Majda, G.↗
DOE OSTI2025

Stability-preserving Lossy Compression for Large-scale Partial Differential Equations

Checkpoint/Restart (C/R) strategies are vital for fault tolerance in PDE-based scientific simulations, yet traditional checkpointing incurs significant I/O overhead. Lossy compression offers a scalable solution by reducing checkpoint data size, but conventional methods often lack control over physical invariants (e.g., energy), leading to instability such as oscillations or divergence in Partial Differential Equations (PDE) systems. This paper introduces a stability-preserving compression approach tailored for PDE simulations by explicitly controlling kinetic and potential energy perturbations to ensure stable restarts. Extensive experiments conducted across diverse PDE configurations demonstrate that our method maintains numerical stability with minimal error magnification—even across multiple checkpoint-restart cycles—outperforming state-of-the-art lossy compressors. Parallel evaluations on the Frontier supercomputer show up to 8.4× improvement in checkpoint write performance and 6.3× in read performance, while maintaining relative L2 errors ∼ 2e-6 throughout continued simulation. These results provide practical guidance for balancing compression accuracy, stability, and computational efficiency in large-scale PDE applications.

Gong, Qian [ORNL] (ORCID:0000000235704142)↗
NASA NTRS1998

Blended-Wing-Body Structural Technology Study

In most studies of stability of plates, the axial stress has been taken as uniform compression throughout flat rectangular plates. Buckling of isotropic plates under a compressive stress that varies linearly from one loaded edge to the other has been studied by Libove et al. Cases of practical interest exist, however, in which the axial stress is not uniform but varies from tension at both loaded edges to compression in the middle. An example is the stability of the crown of the hat stiffened panel, a candidate configuration of the upper and lower skin of the Blended Wing Body (BWB) Aircraft. The BWB Aircraft is an advanced long-range ultra-high-capacity airliner with the principal feature being the pressurized wide double-deck body which is blended into the wing. In the present research, analytical methods are used to investigate the local stability of the crown in order to minimize its weight while optimizing its buckling strength. The crown is modeled as a rectangular laminated composite plate subjected to a second degree parabolic variation of axial stresses in the longitudinal direction. A varying tension-compression- tension axial stresses are induced in the crown of the stiffeners due to bending. The change in axial stresses is equilibrated by nonuniform shear stresses along the plate edges and transverse normal stresses.

Ashraf Badir↗
DOE OSTI2025

Hybrid data-driven cement-stabilized soil design: An integration of machine learning, multi-objective optimization, and life cycle assessment

Soil stabilization is crucial in geotechnical engineering, yet conventional methods are often time-consuming, resource-intensive, and environmentally unsustainable. Despite growing interest in Machine Learning (ML) and optimization tools for mix design, few studies integrate these methods with decision-making techniques and environmental assessment to support practical implementation. This study proposes a hybrid data-driven framework for predicting strength, optimizing mix compositions, and evaluating environmental impacts via life cycle assessment of cement-stabilized soft soils. Six ML models were evaluated, and the top-performing eXtreme Gradient Boosting (XGB) model was further improved using the Grey Wolf Optimizer (GWO). The optimized XGB-GWO model, integrated with a polynomial cost function, served as the objective function in a multi-objective optimization problem solved via the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), with final mix selection guided by the entropy-weighted TOPSIS method. Validation through a case study produced mix designs offering superior strength-cost trade-offs, with the optimal mix achieving 2243.2 kPa unconfined compressive strength and a 16.07 % reduction in carbon emissions compared to the highest-cost design. In conclusion, this study offers a sustainable, scalable approach to soil stabilization and supports informed decision-making in construction.

Life cycle assessment↗
NASA NTRS1973

The Lyapunov stabilization of satellite equations of motion using integrals

A method is introduced that weakens the Lyapunov or in track instability of satellite equations of motion. The method utilizes a linearized energy integral of satellite motion as a constraint on solutions obtained by numerical integration. The procedure prevents local numerical error from altering the frequency associated with the fast angular variable and thereby reduces the Lyapunov instability and the global numerical error. Applications of the method to satellite motion show accuracy improvements of two to three orders of magnitude in position and velocity after 50 revolutions. A modification of the method is presented that allows the use of slowly varying integrals of motion.

Nacozy, P. E.↗
NASA NTRS1987

Reynolds stress closure in jet flows using wave models

Numerical methods were developed that will form the computational part of the turbulence closure scheme. A wave model was developed for the two-dimensional shear layer. This configuration is being used as a test case for the closure schemes. Various numerical schemes were examined to give efficient solutions of the Rayleigh equation for this geometry. These include both spectral and finite difference methods. Secondly, numerical methods are under development to solve the non-separable Rayleigh equation. This solution is required for the closure scheme in more complex geometries. A model problem was used to assist in the algorithm development. Two-dimensional spectral methods and a hybrid spectral/finite difference technique were developed. An analytic solution of the Rayleigh equation for a basic elliptic flow was obtained. This will be used to verify the stability codes developed for arbitrary geometries. Other numerical methods for solving the Rayleigh equation based on the boundary element technique were also examined. These solutions are forming the basis of a model for the shock structure in jets of arbitrary geometry.

Morris, P. J.↗
NASA NTRS1985

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Noor, A. K.↗
DOE OSTI2024

Reliability, stability during long-term storage, and intra-individual variation of circulating levels of osteopontin, osteoprotegerin, vascular endothelial growth factor-A, and interleukin-17A

Background: Studies in many populations have reported associations between circulating cytokine levels and various physiological or pathological conditions. However, the reliability of cytokine measurements in population studies, which measure cytokines in multiple assays over a prolonged period, has not been adequately examined; nor has stability during sample storage or intra-individual variation been assessed. Methods: We assessed (1) analytical reliability in short- and long-term repeated measurements; (2) stability and analytical reliability during long-term sample storage, and (3) variability within individuals over seasons, of four cytokines—osteopontin (OPN), osteoprotegerin (OPG), vascular endothelial growth factor-A (VEGF-A), and interleukin-17A (IL-17A). Measurements in plasma or serum samples were made with commercial kits according to standard procedures. Estimation was performed by fitting a random or mixed effects linear model on the log scale. Results: In repeated assays over a short period, OPN, OPG, and VEGF-A had acceptable reliability, with intra- and inter-assay coefficients of variation (CV) less than 0.11. Reliability of IL-17A was poor, with inter- and intra-assay CV 0.85 and 0.43, respectively. During long-term storage, OPG significantly decayed (-33% per year; 95% confidence interval [-54, -3.7]), but not OPN or VEGF-A (-0.3% or -6.3% per year, respectively). Intra- and inter-assay CV over a long period were comparable to that in a short period except for a slight increase in inter-assay CV of VEGF-A. Within-individual variation was small for OPN and VEGF-A, with intra-class correlations (ICC) 0.68 and 0.83, respectively, but large for OPG (ICC 0.11). Conclusions: We conclude that OPN and VEGF-A can be reliably measured in a large population, that IL-17A is suitable only for small experiments, and that OPG should be assessed with caution due to degradation during storage and intra-individual variation. The overall results of our study illustrate the need for validation under relevant conditions when measuring circulating cytokines in population studies.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Analytically differentiable metrics for phase stability

Here, in this work, a long-established but sparsely documented method of obtaining semi-analytic derivatives of thermodynamic properties with respect to equilibrium conditions is briefly reviewed and rigorously derived. This procedure is then leveraged to construct general forms of derivatives of the residual driving force, a metric for measuring phase stability used in CALPHAD model optimization, with respect to overall system and individual phase compositions. Applied examples – calculating heat capacity in the Al-Fe system, thermodynamic factors in the Nb-V-W system, and residual driving force derivatives in the Ni-Ti system – demonstrate the versatility, accuracy, and extensibility of this method. Using the developed method, residual driving force gradients can be applied directly in CALPHAD model optimizers, as well as in materials design frameworks, to identify regions of phase stability with an efficient, gradient-based approach.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Realizability-preserving discontinuous Galerkin method for spectral two-moment radiation transport in special relativity

Here we present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this discontinuous-Galerkin-implicit-explicit method.

79 ASTRONOMY AND ASTROPHYSICS↗