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All sources NASA NTRS DOE OSTI

DOE OSTI2023

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗

NASA NTRS1980

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Stephens, W. B.↗

DOE OSTI2017

Drekar v.2.0

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools. The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.

Seefeldt, Ben↗

DOE OSTI2020

Efficient solvers for hybridized three-field mixed finite element coupled poromechanics

We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible conditions. The efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a Schur-complement approximation strategy. Robustness, computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures.

42 ENGINEERING↗

DOE OSTI2026

Adsorption of Mixed Micelles of Polysorbate 80 and Oleic Acid to the Air–Water Interface

The solubilization of long chain amphiphiles with limited solubility into mixed micelles composed of highly soluble surfactants plays a crucial role in modulating the stability and functionality of formulations in pharmaceutical and food systems. Subsequently, the mixed micelles adsorb from solution to the air−water surface, defining the transport mechanism of the insoluble amphiphiles to the interface. We use X-ray reflectivity to measure the composition and provide insight into the structure of these mixed monolayers, and, alongside interfacial tension measurements, we provide an understanding of how the bulk composition determines the surface composition and the dynamics of tension reduction. We use a model system consisting of an insoluble fatty acid, oleic acid (OA), and a soluble micelle-forming surfactant, polysorbate 80 (PS80). PS80 forms spherical micelles, and, above the critical micelle concentration (cmc), OA is readily solubilized inside the micelles. We show that the adsorption of PS80/OA mixed micelles to the air−water interface rapidly reduces the tension and lowers the equilibrium tension in proportion to the OA concentration. X-ray reflectivity data, fit using Parratt-slab models, quantitively demonstrates that the monolayers become enriched with OA, and we show how the OA intercalates into the PS80 monolayers.

36 MATERIALS SCIENCE↗

NASA NTRS2005

Effect of Stability on Mixing in Open Canopies

In open canopies, the within-canopy flux from the ground surface and understory can account for a significant fraction of the total flux above the canopy. This study incorporates the important influence of within-canopy stability on turbulent mixing and subcanopy fluxes into a first-order closure scheme. Toward this goal, we analyze within-canopy eddy-correlation data from the old aspen site in the Boreal Ecosystem - Atmosphere Study (BOREAS) and a mature ponderosa pine site in Central Oregon, USA. A formulation of within-canopy transport is framed in terms of a stability- dependent mixing length, which approaches Monin-Obukhov similarity theory above the canopy roughness sublayer. The new simple formulation is an improvement upon the usual neglect of the influence of within-canopy stability in simple models. However, frequent well-defined cold air drainage within the pine subcanopy inversion reduces the utility of simple models for nocturnal transport. Other shortcomings of the formulation are discussed.

Lee, Young-Hee↗

DOE OSTI2024

Influence of Carboxymethyl Cellulose as a Thickening Agent for Glauber’s Salt-Based Low Temperature PCM

This work is focused on a novel, promising low temperature phase change material (PCM), based on the eutectic Glauber’s salt composition. To allow phase transition within the refrigeration range of temperatures of +5 °C to +12 °C, combined with a high repeatability of melting–freezing processes, and minimized subcooling, the application of three variants of sodium carboxymethyl cellulose (Na-CMC) with distinct molecular weights (700,000, 250,000, and 90,000) is considered. The primary objective is to optimize the stabilization of this eutectic PCM formulation, while maintaining the desired enthalpy level. Preparation methods are refined to ensure repeatability in mixing components, thereby optimizing performance and stability. Additionally, the influence of Na-CMC molecular weight on stabilization is examined through differential scanning calorimetry (DSC), T-history, and rheology tests. The PCM formulation of interest builds upon prior research in which borax, ammonium chloride, and potassium chloride were used as additives to sodium sulfate decahydrate (Glauber’s salt), prioritizing environmentally responsible materials. The results reveal that CMC with molecular weights of 250 kg/mol and 90 kg/mol effectively stabilize the PCM without phase separation issues, slowing crystallization kinetics. Conversely, CMC of 700 kg/mol proved ineffective due to the disruption of gel formation at its low gel point, hindering higher concentrations. Calculations of ionic concentration indicate higher Na ion content in PCM stabilized with 90 kg/mol CMC, suggesting increased ionic interactions and gel strength. A tradeoff is discovered between the faster crystallization in lower molecular weight CMC and the higher concentration required, which increases the amount of inert material that does not participate in the phase transition. After thermal cycling, the best formulation had a latent heat of 130 J/g with no supercooling, demonstrating excellent performance. This work advances PCM’s reliability as a thermal energy storage solution for diverse applications and highlights the complex relationship between Na-CMC molecular weight and PCM stabilization.

25 ENERGY STORAGE↗

NASA NTRS1996

Homotopy Algorithm for Fixed Order Mixed H2/H(infinity) Design

Recent developments in the field of robust multivariable control have merged the theories of H-infinity and H-2 control. This mixed H-2/H-infinity compensator formulation allows design for nominal performance by H-2 norm minimization while guaranteeing robust stability to unstructured uncertainties by constraining the H-infinity norm. A key difficulty associated with mixed H-2/H-infinity compensation is compensator synthesis. A homotopy algorithm is presented for synthesis of fixed order mixed H-2/H-infinity compensators. Numerical results are presented for a four disk flexible structure to evaluate the efficiency of the algorithm.

Whorton, Mark↗

DOE OSTI2025

An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Preparation of resveratrol-loaded nanoporous silica materials with different structures

Solid, nanoporous silica-based spherical mesoporous MCM-41 and KIL-2 with interparticle mesoporosity as well as nanosized zeolite BEA materials differing in morphology and pore size distribution, were used as carriers for the preparation of resveratrol-loaded delivery systems. Two preparation methods have been applied: (i) loading by mixing of resveratrol and mesoporous carrier in solid state and (ii) deposition in ethanol solution. The parent and the resveratrol loaded carriers were characterized by XRD, TEM, N2 physisorption, thermal analysis, and FT-IR spectroscopy. The influence of the support structure on the adsorption capacity and the release kinetics of this poorly soluble compound were investigated. Our results indicated that the chosen nanoporous silica supports are suitable for stabilization of trans-resveratrol and reveal controlled release and ability to protect the supported compound against degradation regardless of loading method. The solid-state dry mixing appears very effective for preparation of drug formulations composed of poorly soluble compound. - Graphical abstract: trans-Resveratrol was stabilized in the pores of BEA zeolite, MCM-41and KIL2 mesoporous silicas. - Highlights: • BEA, KIL-2 and MCM-41 materials were used as carriers for resveratrol loading. • Resveratrol encapsulation in ethanol solution and solid state procedure were applied. • The solid-state preparation appears very effective for stabilization of trans-resveratrol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

An energy-stable time-integrator for phase-field models

Here, we introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Development of an Environmentally Acceptable Hydraulic Fluid

Hydroelectric plants operators like the United States Army Corps of Engineers seek their traditional petroleum-based fluids with environmentally acceptable hydraulic fluids (EAHF) to reduce their impact and liability related to spills and leakages to the water and environment. Artesion, Inc. and its sub-contractor Washington State University (WSU) sought to optimize WSU’s existing EAHF blend into an improved product that would demonstrate long-term stability while meeting the EAHF requirements of the EPA’s Vessel General Permit (VGP). Multiple rounds of Design of Experiments testing were performed from WSU’s base formulation, modifying mixing ratios to generate multiple test fluids. These fluids were then tested for hydraulic fluid properties. It was found that there was a significant tradeoff between oxidative stability and biodegradability; highly stable materials were not sufficiently biodegradable, while the highly biodegradable materials quickly failed in stability tests. After four rounds of Design of Experiments, AI and WSU had found a base fluid which met the VGP, but only had a Rotating Pressure Vessel Oxidative Test (RPVOT) of 284-minute RPVOT stability, far short of the 500-minute target that would be needed for hydroelectric plants. It was determined that WSU’s route had shown initial promise but needed more refinement to be able to produce an acceptable EAHF.

36 MATERIALS SCIENCE↗

DOE OSTI2013

The mixed Wentzel-Kramers-Brillouin-full-wave approach and its application to lower hybrid wave propagation and absorption

The mixed Wentzel-Kramers-Brillouin (WKB)-full-wave approach for the calculation of the 2D mode structure in tokamak plasmas is further developed based on our previous work [A. Cardinali and F. Zonca, Phys. Plasmas 10, 4199 (2003) and Z. X. Lu et al., Phys. Plasmas 19, 042104 (2012)]. A new scheme for theoretical analysis and numerical implementation of the mixed WKB-full-wave approach is formulated, based on scale separation and asymptotic analysis. Besides its capability to efficiently investigate the initial value problem for 2D mode structures and linear stability, in this work, the mixed WKB-full-wave approach is extended to the investigation of radio frequency wave propagation and absorption, e.g., lower hybrid waves. As a novel method, its comparison with other approaches, e.g., WKB and beam tracing methods, is discussed. Its application to lower hybrid wave propagation in concentric circular tokamak plasmas using typical FTU discharge parameters is also demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Disturbance Regimes Predictably Alter Diversity in an Ecologically Complex Bacterial System

Diversity is often associated with the functional stability of ecological communities from microbes to macroorganisms. Understanding how diversity responds to environmental perturbations and the consequences of this relationship for ecosystem function are thus central challenges in microbial ecology. Unimodal diversity-disturbance relationships, in which maximum diversity occurs at intermediate levels of disturbance, have been predicted for ecosystems where life history tradeoffs separate organisms along a disturbance gradient. However, empirical support for such peaked relationships in macrosystems is mixed, and few studies have explored these relationships in microbial systems. Here we use complex microbial microcosm communities to systematically determine diversity-disturbance relationships over a range of disturbance regimes. We observed a reproducible switch between community states, which gave rise to transient diversity maxima when community states were forced to mix. Communities showed reduced compositional stability when diversity was highest. To further explore these dynamics, we formulated a simple model that reveals specific regimes under which diversity maxima are stable. Together, our results show how both unimodal and non-unimodal diversity-disturbance relationships can be observed as a system switches between two distinct microbial community states; this process likely occurs across a wide range of spatially and temporally heterogeneous microbial ecosystems.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2010

On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.

It is well known that the continuous Galerkin method (in its standard form) is not locally conservative, yet many stabilized methods are constructed by augmenting the standard Galerkin weak form. In particular, the Variational Multiscale (VMS) method has achieved popularity for combating numerical instabilities that arise for mixed formulations that do not otherwise satisfy the LBB condition. Among alternative methods that satisfy local and global conservation, many employ Raviart-Thomas function spaces. The lowest order Raviart-Thomas finite element formulation (RT0) consists of evaluating fluxes over the midpoint of element edges and constant pressures within the element. Although the RT0 element poses many advantages, it has only been shown viable for triangular or tetrahedral elements (quadrilateral variants of this method do not pass the patch test). In the context of heterogenous materials, both of these methods have been used to model the mixed form of the Darcy equation. This work aims, in a comparative fashion, to evaluate the strengths and weaknesses of either approach for modeling Darcy flow for problems with highly varying material permeabilities and predominantly open flow boundary conditions. Such problems include carbon sequestration and enhanced oil recovery simulations for which the far-field boundary is typically described with some type of pressure boundary condition. We intend to show the degree to which the VMS formulation violates local mass conservation for these types of problems and compare the performance of the VMS and RT0 methods at boundaries between disparate permeabilities.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Anisotropic elastoplastic response of double-porosity media

Here we present a continuum framework to simulate fluid flow through anisotropic elastoplastic media with double porosity. Two effective stress measures σ' and δ" emerge from the thermodynamic formulation, which are energy-conjugate to the elastic and plastic components of strain, respectively. Both effective stress measures can be expressed as a combination of the total Cauchy stress σ and the average pore pressure $\bar{p}$ in the two pore scales. In the effective stress for elasticity, $\bar{p}$ is scaled with a rank-2 Biot tensor, whereas the effective stress for plasticity follows the Terzaghi form in which $\bar{p}$ is scaled by the Kronecker delta. The Biot tensor and storage coefficients are derived as functions of elasticity parameters and porosities. A mixed finite element formulation is introduced to discretize the domain and solve initial boundary-value problems. A stabilization scheme is employed on equal-order interpolation for both displacement and pressure fields throughout the entire range of drainage responses. Numerical simulations reproduce the hydromechanical response of Opalinus shale in one-dimensional consolidation tests throughout the range of primary and secondary consolidation under different external loads. Numerical simulations of the consolidation of a rectangular domain subjected to a strip load demonstrate the efficacy of the proposed stabilization scheme, as well as illustrate the impacts of stress history, mass transfer, and different pore systems on the hydromechanical response.

42 ENGINEERING↗

DOE OSTI2022

Nanoscale Photoexcited Carrier Dynamics in Perovskites

The optoelectronic properties of lead halide perovskite thin films can be tuned through compositional variations and strain, but the associated nanocrystalline structure makes it difficult to untangle the link between composition, processing conditions, and ultimately material properties and degradation. Here, we study the effect of processing conditions and degradation on the local photoconductivity dynamics in [(CsPbI 3 ) 0.05 (FAPbI 3 ) 0.85 (MAPbBr 3 ) 0.15 ] and (FA 0.7 Cs 0.3 PbI 3 ) perovskite thin films using temporally and spectrally resolved microwave near-field microscopy with a temporal resolution as high as 5 ns and a spatial resolution better than 50 nm. For the latter FACs formulation, we find a clear effect of the process annealing temperature on film morphology, stability, and spatial photoconductivity distribution. After exposure of samples to ambient conditions and illumination, we find spectral evidence of halide segregation-induced degradation below the instrument resolution limit for the mixed halide formulation, while we find a clear spatially inhomogeneous increase in the carrier lifetime for the FACs formulation annealed at 180 degrees C.

14 SOLAR ENERGY↗