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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Should We Conserve Entropy or Energy when Computing CAPE with Mixed-Phase Precipitation Physics?

Abstract The rapidly increasing resolution of global atmospheric reanalysis and climate model datasets necessitates finding methods for computing convective available potential energy (CAPE) both efficiently and accurately. To this end, this article compares two common methods for computing CAPE which conserve either energy or entropy. Inaccuracies in these computations arise from both physical and numerical errors. For instance, computing CAPE with entropy conserved results in physical errors from nonequilibrium phase transitions but minimizes numerical errors because solutions are analytic at each height. In contrast, computing CAPE with energy conserved avoids these physical errors, but accumulates numerical errors that are grid-resolution-dependent because the numerical integration of a differential equation is required. Analysis of CAPE computed with large databases of soundings from the tropical Amazon and midlatitude storm environments shows that physical errors from the entropy method are typically 1%–3% as large as CAPE, which is comparable to the numerical errors from conserving energy with grid spacing of 25 and 250 m using explicit first-order and second-order integration schemes, respectively. Errors in entropy-based CAPE calculations are also insensitive to vertical grid spacing, in contrast to energy-based calculations whose error strongly scales with the grid spacing. It is shown that entropy-based methods are advantageous when intercomparing datasets with differing vertical resolution because they produce accurate and reasonably fast results that are insensitive to grid resolution, whereas a second-order energy-based method is advantageous when analyzing data with a consistent vertical resolution because of its superior computational efficiency. Significance Statement Convective available potential energy (CAPE) is a measure of instability in the atmosphere that helps forecasters and researchers understand when and where thunderstorms will form. The purpose of this article is to identify the most efficient and accurate methods for computing CAPE. Two methods are considered here, one that relates to the entropy (a measure of thermodynamic disorder) of an air parcel and one that relates to the energy of an air parcel. Results indicate that the entropy method is most accurate and insensitive to the resolution of the data used for the calculation (which can vary considerably), whereas the energy method uses the least computation time.

Peters, John M.↗
DOE OSTI2019

Does Breast Density Increase the Risk of Re-excision for Women with Breast Cancer Having Breast-Conservation Therapy?

Background: Women with dense breasts may have less-accurate preoperative evaluation of extent of disease, potentially affecting the achievement of negative margins. The goal of this study is to examine the association between breast density and re-excision rates in women having breast-conserving surgery for invasive breast cancer. Patients and Methods: Women with stage I/II invasive breast cancer treated with breast-conserving surgery between 1/1/2014 and 10/31/2014 were included. Breast density was assessed by two radiologists. The association between breast density and re-excision was examined using logistic regression. Results: Seven hundred and one women were included. Overall, 106 (15.1%) women had at least one re-excision. Younger age at diagnosis was associated with increased breast density (p < 0.001). On univariable analysis, increased breast density was associated with significantly increased odds of re-excision (odds ratio [OR] 1.38, 95% confidence interval [CI] 1.04–1.83), as was multifocal disease, human epidermal growth factor receptor 2 (HER2) positive status, and extensive intraductal component (EIC) (all p < 0.05). On multivariable analysis, breast density remained significantly associated with increased odds of re-excision (OR 1.37, 95% CI 1.00–1.86), as did multifocality and EIC. HER2 positive status was not significantly associated with re-excision on multivariable analysis. Conclusions: Women with dense breasts are more likely to need additional surgery (re-excision after breast-conserving surgery), but increased breast density did not adversely affect disease-free survival in our study. Our findings support the need for further study in developing techniques that can help decrease re-excisions for women with dense breasts who undergo breast-conserving surgery.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

Structural basis for recognition of the central conserved region of RSV G by neutralizing human antibodies

Respiratory syncytial virus (RSV) is a major cause of severe lower respiratory tract infections in infants and the elderly, and yet there remains no effective treatment or vaccine. The surface of the virion is decorated with the fusion glycoprotein (RSV F) and the attachment glycoprotein (RSV G), which binds to CX3CR1 on human airway epithelial cells to mediate viral attachment and subsequent infection. RSV G is a major target of the humoral immune response, and antibodies that target the central conserved region of G have been shown to neutralize both subtypes of RSV and to protect against severe RSV disease in animal models. However, the molecular underpinnings for antibody recognition of this region have remained unknown. Therefore, we isolated two human antibodies directed against the central conserved region of RSV G and demonstrated that they neutralize RSV infection of human bronchial epithelial cell cultures in the absence of complement. Moreover, the antibodies protected cotton rats from severe RSV disease. Both antibodies bound with high affinity to a secreted form of RSV G as well as to a peptide corresponding to the unglycosylated central conserved region. High-resolution crystal structures of each antibody in complex with the G peptide revealed two distinct conformational epitopes that require proper folding of the cystine noose located in the C-terminal part of the central conserved region. Comparison of these structures with the structure of fractalkine (CX3CL1) alone or in complex with a viral homolog of CX3CR1 (US28) suggests that RSV G would bind to CX3CR1 in a mode that is distinct from that of fractalkine. Collectively, these results build on recent studies demonstrating the importance of RSV G in antibody-mediated protection from severe RSV disease, and the structural information presented here should guide the development of new vaccines and antibody-based therapies for RSV.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Conservation and conviviality in the American West

The emerging field of convivial conservation (CC) draws on the tradition of political ecology (PE) to present a “radical” alternative to contemporary environmentalisms, speaking to the challenges of conservation in the Anthropocene as well as the global ascent of reactionary populism. Building on previous work arguing for the ongoing value of dialogue between PE and the American West, I here develop a conversation between CC and another radical intervention, the collaborative conservation of the West’s so-called “radical center” (RC). Using the nexus of wolf–livestock conflict and public lands grazing, I first trace a genealogical history of western environmental politics before turning to CC as critical corrective to the shortcomings of the RC. Scholarship on the commons and commoning provides an analytical bridge and political toolkit for linking the empirics of place with the aspirational aims of conviviality, and naming and navigating on-the-ground obstacles to collaborative conservation efforts in the region. This dialogue in turn highlights deeply rooted tensions of capitalist political economy and questions of non/belonging rooted in settler colonialism—necessary regional engagements for building from polarized antagonism toward an alternative environmental politics of coexistence and conviviality.

Environmental Sciences & Ecology↗
DOE OSTI2019

High-Order, Stable, and Conservative Boundary Schemes for Central and Compact Finite Differences

Stable and conservative numerical boundary schemes are constructed such that they do not diminish the overall accuracy of the method for interior schemes of orders 4, 6, and 8 using both explicit (central) and compact finite differences. Previous attempts to develop stable numerical boundary schemes for non-linear problems have resulted in schemes which significantly reduced the global accuracy and/or required some form of artificial dissipation. Thus, the schemes developed are the first to not require this tradeoff, while also ensuring discrete conservation and allowing for direct boundary condition enforcement. After outlining a general procedure for the construction of conservative boundary schemes of any order, a simple, yet novel, optimization strategy which focuses directly on the compressible Euler equations is applied. The result of this non-linear optimization process is a set of high-order, stable, and conservative numerical boundary schemes which demonstrate excellent stability and convergence properties on an array of linear and non-linear hyperbolic problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Surrogate Modeling For Efficiently Accurately and Conservatively Estimating Measures of Risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. We adopt a probabilistic description of risk that assigns probabilities to consequences associated with an event and use risk measures, which combine objective evidence with the subjective values of decision makers, to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical estimates obtained from the training data. These surrogate models not only limit over-confidence in reliability and safety assessments, but produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to the specific risk preferences of the stakeholder and then present an approach, based upon stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. The surrogate models introduce a bias that allows them to conservatively estimate the target risk measures. We provide theoretical results that show that this bias decays at the same rate as the L 2 error in the surrogate model. Our numerical examples confirm that risk-aware surrogate models do indeed over-estimate the target risk measures while converging at the expected rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essential because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.

Ghosh, Debojyoti↗
DOE OSTI2017

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods – Part 1: Derivation and properties

Abstract. The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

58 GEOSCIENCES↗
NASA NTRS1971

Application of conservative finite-difference methods to advection problems

The possibility of applying the most recent conservative and widely applied numerical techniques in gas dynamics to problems encountered in meteorological computations is investigated. Solutions of the advection equation are obtained using conservative differencing methods. These results are compared to those obtained by differencing the advection equation directly. The comparison shows that better results are obtained when the conservative form of governing equation is used. In addition, better results are obtained with lower order conservative methods as compared with higher order differencing applied to the advection equation.

Fattahi, B.↗
NASA NTRS1975

ECASTAR: Energy conservation. An assessment of systems, technologies and requirements

A methodology was presented for a systems approach to energy conservation actions and their potentials and impacts in the United States. Constraints affecting the approach were ranked, and the most important ones are the present economic and technical conditions. The following unresolved issues were identified: consumptive lifestyles vs. conservation ethic, environmental standards vs. energy conservation, capital availability, decentralization and vertical integration vs. centralization, fuel rich regions vs. fuel poor regions, supply vs. end use conservation, life cycle costing vs. initial cost, mandatory savings vs. voluntary savings, labor intensive vs. capital intensive, price control vs. free market. The following recommendations were made: provide action/impact assessment, establish regional energy centers, improve technology articulation with government, design total energy systems, utilize existing systems approach expertise.

Source record↗
NASA NTRS1975

Energy conservation and the residential and commercial sector

A detailed analysis of energy conservation actions relevant to the residential and commercial sector has led to the conclusion that the potential for savings is great. The task will not be easy, however, since many of the actions require significant life style changes that are difficult to accomplish. Furthermore, many of the conservation actions cited as instant solutions to the energy crisis are those with only mid to long term potential, such as solar energy or heat pumps. Three significant conservation approaches are viable: adjusting price structure, mandating actions, and educating consumers. The first two appear to be the most feasible. But they are not without a price. Higher utility bills adversely affect the poor and the elderly on fixed incomes. Likewise, strict mandatory measures can be quite distasteful. But the effect of alternatives, such as voluntary savings accomplished through education processes, is minimal in a nation without a true conservation ethic.

Source record↗
NASA NTRS1976

Frequency modulation at a moving material interface and a conservation law for wave number

An integral conservation law for wave numbers is considered. In order to test the validity of the proposed conservation law, a complete solution for the reflection and transmission of an acoustic wave impinging normally on a material interface moving at a constant speed is derived. The agreement between the frequency condition thus deduced from the dynamic equations of motion and the frequency condition derived from the jump condition associated with the integral equation supports the proposed law as a true conservation law. Additional comparisons such as amplitude discontinuities and Snells' law in a moving media further confirm the stated proposition. Results are stated concerning frequency and wave number relations across a shock front as predicted by the proposed conservation law.

Kleinstein, G. G.↗
NASA NTRS1977

The NASA Energy Conservation Program

Large energy-intensive research and test equipment at NASA installations is identified, and methods for reducing energy consumption outlined. However, some of the research facilities are involved in developing more efficient, fuel-conserving aircraft, and tradeoffs between immediate and long-term conservation may be necessary. Major programs for conservation include: computer-based systems to automatically monitor and control utility consumption; a steam-producing solid waste incinerator; and a computer-based cost analysis technique to engineer more efficient heating and cooling of buildings. Alternate energy sources in operation or under evaluation include: solar collectors; electric vehicles; and ultrasonically emulsified fuel to attain higher combustion efficiency. Management support, cooperative participation by employees, and effective reporting systems for conservation programs, are also discussed.

Gaffney, G. P.↗
NASA NTRS1981

On the conservation of the first adiabatic invariant in perpendicular shocks

The conservation of the first adiabatic invariant of particle motion, the particle magnetic moment, at the front of perpendicular magnetosonic fast-mode shock waves is considered. Results of numerical simulations are presented which show that preshock and postshock values of the magnetic moment are on the average equal for particles transmitted by infinitesimally thin perpendicular magnetosonic fast-mode shocks, in contrast to extrapolations from adiabatic theory, which suggest that the first invariant is least likely to be conserved in this situation. The observed conservation is thus attributed to the continuity of the flux of total particle and field angular momentum across the shock front as a result of angular momentum conservation.

Pesses, M. E.↗
NASA NTRS1982

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

Lombard, C. K.↗
NASA NTRS1983

On the symmetric form of systems of conservation laws with entropy

The present investigation has the objective to review the general structure of system of conservation laws with entropy, giving particular attention to a presentation of symmetric formulations of the equations of gas dynamics. Systems of hyperbolic conservation laws are considered, taking into account the case in which a system of equations is symmetric hyperbolic, questions of symmetrization, and entropy functions. The Euler equations for a polytropic gas in conservation form are considered. The symmetric form retains the conservation properties of the equations. Weak solutions remain, therefore, unchanged. Of particular computational interest is the possibility of using the symmetric form.

Harten, A.↗
NASA NTRS1986

Entropy conservative finite element schemes

The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.

Tadmor, E.↗