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Results for “Conservative variables”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation

In this work, a high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor basis defined on the time-dependent moving mesh, provide the piece-wise polynomial expansion in the updated Lagrangian formulation. A multi-directional nodal Riemann solver is implemented for computing the grid velocity at the vertices and the numerical flux at the cell boundaries. A characteristic limiting procedure is extended from the primitive variable version to the conservative variable version, and its performance is compared with the limiter on physical variables. A number of benchmark test cases are conducted to assess the accuracy, robustness, and non-oscillatory property of the DG(P0), DG(P1) and rDG(P1P2) methods. The numerical experiments demonstrate that the developed rDG method is able to attain the designed order of accuracy and the characteristic limiting procedure outperforms the limiter on physical variables in terms of the monotonicity and symmetry preservation for shock problems.

42 ENGINEERING↗
DOE OSTI2026

A sweeping positivity-preserving high-order finite difference WENO scheme for Euler equations

We develop a simple, high-order, conservative and robust positivity-preserving sweeping procedure for the density and the nonlinear pressure function in the compressible Euler equations. Using the scaling limiter in Zhang and Shu (J Comput Phys 229:3091–3120, 2010), we obtain a non-trivial extension of the scalar sweeping technique in Liu et al. (J Sci Comput 73:1028–1071, 2017) for the positivity of pressure. The sweeping procedure developed in this paper is a post-processing technique, which can be applied to any concave functions of the conserved variables in hyperbolic conservation law systems. Thus, it has applications beyond the Euler equations. This procedure preserves positivity and conservation of physical quantities without destroying the accuracy of the underlying scheme. The algorithm works for general schemes including finite difference, finite volume and discontinuous Galerkin methods; however, in this paper we focus on finite difference weighted essentially non-oscillatory (WENO) methods. As a result, we provide numerical tests of the fifth-order finite difference WENO scheme to demonstrate the accuracy and robustness of the technique.

Compressible Euler equations↗
DOE OSTI2023

A comparative study of two numerical approaches for solving Kim–Kim–Suzuki phase-field models

Among the standard multi-phase multi-component phase-field (PF) methods, the Kim–Kim–Suzuki (KKS) method has the advantage of decoupling interfacial energy from bulk energy and solving concentration as the conserved variable. There are two approaches to numerically solving a KKS method: the global solution approach (GSA) solves all variables in a global system simultaneously, and the local solution approach (LSA) solves phase concentrations locally using a Newton solver. This work compares the performance of LSA and GSA for solving four KKS models of increasing complexity with the finite element method using the MOOSE framework. The solution accuracy, degrees of freedom (DOFs), memory usage, and computational efficiency are compared. We find that GSA and LSA generate similar solutions, with a maximum difference of only 0.34%. For each model, LSA has a lower number of DOFs, utilizes less memory, and less wall time. Additionally, the savings of memory and wall time in LSA increase with increasing mesh density of the same model and are more pronounced in models with higher dimensionality and more nodes. However, GSA is easier to implement in existing codes and can better solve highly nonlinear systems by utilizing sophisticated solvers.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accurate models of the added mass force of a uniform random distribution of spherical particles or bubbles

The added mass force resulting from the acceleration of a body in a fluid is of fundamental and practical interest in dispersed multiphase flows. Euler–Lagrange (EL) and Euler–Euler (EE) simulations require closure terms for the added mass force in order to accurately couple the conserved variables between phases. Presently, a more thorough understanding of the added mass force in a multi-particle system is developed based on potential flow resulting in a resistance matrix formulation analogous to Stokesian dynamics. This formulation is then used to generate a dataset of added mass resistance matrices for large systems of randomly generated particles. This methodology is used to create a volume fraction corrected binary model for predicting the added mass force in large systems as well as generate statistics of the added mass force in such systems. This work provides clarification to the theory of the added mass force for particle clouds, and modelling options that may be implemented in existing EL and EE codes.

42 ENGINEERING↗
DOE OSTI2022

Convective and Turbulent Motions in Nonprecipitating Cu. Part II: LES Simulated Cloud Represented by a Starting Plume

The dynamic structure of a small trade wind cumulus (Cu) is analyzed using a novel approach. Cu developing in a shear-free environment is simulated by 10-m-resolution LES model with spectral bin microphysics. The aim is to clarify the dynamical nature of cloud updraft zone (CUZ) including entrainment and mixing in growing Cu. The validity of concept stating that a cloud at developing state can be represented by a parcel or a jet is tested. To investigate dynamical entrainment in CUZ performed by motions with scales larger than the turbulence scales, the modeled fields of air velocity were filtered by wavelet filter that separated convective motions from turbulent ones. Two types of objects in developing cloud were investigated: small volume ascending at maximal velocity (point parcel) and CUZ. It was found that the point parcel representing the upper part of cloud core is adiabatic. The motion of the air in this parcel ascending from cloud base determines cloud-top height. The top-hat (i.e., averaged) values of updraft velocity and adiabatic fraction in CUZ are substantially lower than those in the point parcel. Evaluation of the terms in the dynamical equation typically used in 1D cloud parcel models show that this equation can be applied for calculation of vertical velocities at the developing stage of small Cu, at least up to the heights of the inversion layer. Dynamically, the CUZ of developing cloud resembles the starting plume with the tail of nonstationary jet. Both the top-hat vertical velocity and buoyancy acceleration linearly increase with the height, at least up to the inversion layer. An important finding is that lateral entrainment of convective (nonturbulent) nature has a little effect on the top-hat CUZ velocity and cannot explain the vertical changes of conservative variables qt and θl. In contrast, entrained air lifting inside CUZ substantially decreases top-hat liquid water content and its adiabatic fraction. Possible reasons of these effects are discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evaluating the Conservation of Energy Variables in Simulations of Deep Moist Convection

Abstract It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE − IB and MSE + KE, wherein IB is the path integral of buoyancy ( B ) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large-eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE − IB and MSE + KE better predict quantities along trajectories than MSE alone. MSE − IB is better conserved in isolated deep convection, whereas MSE − IB and MSE + KE perform comparably in squall-line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE − IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE − IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE − IB or MSE + KE instead of MSE with properly formulated heat capacities and latent heats.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

The MOOSE fluid properties module

The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. Here, this paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities

Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on $\sim 10^2$ ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.

axisymmetry↗
DOE OSTI2021

The minor pilin PilV provides a conserved adhesion site throughout the antigenically variable meningococcal type IV pilus

Type IV pili (T4P) are among the most widespread adhesive factors in prokaryotes. In pathogenic Neisseria, the major pilin, which provides the structural framework for the filamentous T4P, undergoes antigenic variation allowing the bacteria to evade the humoral immune response without impacting host-cell adhesion. Here, we show that a minor pilin, PilV, is distributed throughout the pilus and contributes to Neisseria meningitidis adhesion and that antibodies to PilV block meningococcal adhesion in vivo. Our results provide a mechanism whereby N. meningitidis varies its immunodominant major pilin to escape antibody recognition while maintaining conserved sites throughout the pilus for host receptor binding. They further suggest a strategy to prevent or block deadly N. meningitidis infections by targeting this minor pilin.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Predicting variable gene content in Escherichia coli using conserved genes

Having the ability to predict the protein-encoding gene content of an incomplete genome or metagenome-assembled genome is important for a variety of bioinformatic tasks. In this study, as a proof of concept, we built machine learning classifiers for predicting variable gene content in Escherichia coli genomes using only the nucleotide k-mers from a set of 100 conserved genes as features. Protein families were used to define orthologs, and a single classifier was built for predicting the presence or absence of each protein family occurring in 10%–90% of all E. coli genomes. The resulting set of 3,259 extreme gradient boosting classifiers had a per-genome average macro F1 score of 0.944 [0.943–0.945, 95% CI]. We show that the F1 scores are stable across multi-locus sequence types and that the trend can be recapitulated by sampling a smaller number of core genes or diverse input genomes. Surprisingly, the presence or absence of poorly annotated proteins, including “hypothetical proteins” was accurately predicted (F1 = 0.902 [0.898–0.906, 95% CI]). Models for proteins with horizontal gene transfer-related functions had slightly lower F1 scores but were still accurate (F1s = 0.895, 0.872, 0.824, and 0.841 for transposon, phage, plasmid, and antimicrobial resistance-related functions, respectively). Finally, using a holdout set of 419 diverse E. coli genomes that were isolated from freshwater environmental sources, we observed an average per-genome F1 score of 0.880 [0.876–0.883, 95% CI], demonstrating the extensibility of the models. Overall, this study provides a framework for predicting variable gene content using a limited amount of input sequence data.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Geometric adiabatic angle in anisotropic oscillators

We discuss a classical anisotropic oscillator and the Foucault pendulum as examples illustrating non-conservation of action variables in integrable classical mechanical systems with adiabatically slow evolution. We also emphasize the importance of the mass parameter of a harmonic oscillator, alongside its frequency, in explicitly time-dependent situations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows

A variation of moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is developed for solving the compressible Euler equations. The MDG-ICE method, originating from the work of Corrigan et al. [1], [2], [3], [4], is based on the space-time DG formulation, where both flow field and grid geometry are considered as independent variables and the conservation laws are enforced both on discrete elements and element interfaces. The element conservation laws are solved in the standard discontinuous solution space to determine conservative quantities, while the interface conservation is enforced using a variational formulation in a continuous space to determine discrete grid geometry. The resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation can then be solved in a least-squares sense, leading to an unconstrained nonlinear least-squares problem that is regularized and solved by Levenberg-Marquardt method. A number of numerical experiments for both 1D unsteady and 2D steady state compressible flow problems are conducted to assess the accuracy and robustness of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to implicitly detect and track all types of discontinuities via interface conservation enforcement and satisfy the conservation law on both elements and interfaces via grid movement and grid management, demonstrating that an exponential rate of convergence for Sod and Lax-Harden shock tube problems can be achieved and highly accurate solutions without overheating to both double-rarefaction wave and Noh problems can be obtained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the ion poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Disentangling Alzheimer’s disease neurodegeneration from typical brain ageing using machine learning

Abstract Neuroimaging biomarkers that distinguish between changes due to typical brain ageing and Alzheimer’s disease are valuable for determining how much each contributes to cognitive decline. Supervised machine learning models can derive multivariate patterns of brain change related to the two processes, including the Spatial Patterns of Atrophy for Recognition of Alzheimer’s Disease (SPARE-AD) and of Brain Aging (SPARE-BA) scores investigated herein. However, the substantial overlap between brain regions affected in the two processes confounds measuring them independently. We present a methodology, and associated results, towards disentangling the two. T1-weighted MRI scans of 4054 participants (48–95 years) with Alzheimer’s disease, mild cognitive impairment (MCI), or cognitively normal (CN) diagnoses from the Imaging-based coordinate SysTem for AGIng and NeurodeGenerative diseases (iSTAGING) consortium were analysed. Multiple sets of SPARE scores were investigated, in order to probe imaging signatures of certain clinically or molecularly defined sub-cohorts. First, a subset of clinical Alzheimer’s disease patients (n = 718) and age- and sex-matched CN adults (n = 718) were selected based purely on clinical diagnoses to train SPARE-BA1 (regression of age using CN individuals) and SPARE-AD1 (classification of CN versus Alzheimer’s disease) models. Second, analogous groups were selected based on clinical and molecular markers to train SPARE-BA2 and SPARE-AD2 models: amyloid-positive Alzheimer’s disease continuum group (n = 718; consisting of amyloid-positive Alzheimer’s disease, amyloid-positive MCI, amyloid- and tau-positive CN individuals) and amyloid-negative CN group (n = 718). Finally, the combined group of the Alzheimer’s disease continuum and amyloid-negative CN individuals was used to train SPARE-BA3 model, with the intention to estimate brain age regardless of Alzheimer’s disease-related brain changes. The disentangled SPARE models, SPARE-AD2 and SPARE-BA3, derived brain patterns that were more specific to the two types of brain changes. The correlation between the SPARE-BA Gap (SPARE-BA minus chronological age) and SPARE-AD was significantly reduced after the decoupling (r = 0.56–0.06). The correlation of disentangled SPARE-AD was non-inferior to amyloid- and tau-related measurements and to the number of APOE ε4 alleles but was lower to Alzheimer’s disease-related psychometric test scores, suggesting the contribution of advanced brain ageing to the latter. The disentangled SPARE-BA was consistently less correlated with Alzheimer’s disease-related clinical, molecular and genetic variables. By employing conservative molecular diagnoses and introducing Alzheimer’s disease continuum cases to the SPARE-BA model training, we achieved more dissociable neuroanatomical biomarkers of typical brain ageing and Alzheimer’s disease.

Hwang, Gyujoon↗
DOE OSTI2022

Demand Driven Energy Management for PIPO Auxiliary Power Supply Architecture

In this paper, a demand driven energy management (DDEM) technique is implemented on modular parallel input parallel output DC/DC auxiliary power supply (APS) structure. In this method, modules are brought in/out of the operation making them operate under high loading conditions, avoiding low efficiency under light load. Such a method finds its application in power conservative systems with variable load. Implementation of DDEM and the energy saved is shown using APS comprised of two 15W commercially off-the-shelf DC-DC modules, with 100–1000 VDC input and 24 V output voltage. Along with the DDEM, the lifetime of the power stage devices is controlled minimizing their junction temperature swing through control of cooling system. This control method uses digital twin as interface to virtualize the power devices loading operation/ health condition. Accordingly, no extra sensor or closed loop control required to measure the junction temperature of the devices or feedback the losses to the cooling flow.

Azadeh, Yalda↗
DOE OSTI2021

Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis

An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived by approximating the Hamiltonian formulation of the inviscid shallow water flows based on the vorticity-divergence variables. These schemes also conserve the first-order moments such as mass and vorticity, as usual. The conservative properties of the schemes stem from the skew-symmetry and singularities of the Poisson brackets, which are carefully retained in the discrete approximations. Here, the schemes operate on unstructured orthogonal dual meshes, over bounded or unbounded domains, and they are also shown to possess the same optimal dispersive wave relations as those of the Z-grid scheme, which is a consequence of the use of the vorticity and divergence variables.

54 ENVIRONMENTAL SCIENCES↗