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DOE OSTI2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with 𝒪⁡(100) simulations rather than 𝒪⁡(1000) simulations. In conclusion, we then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

general physics↗

DOE OSTI2023

Observations of Boundary Layer Convergence Lines and Associated Updrafts in the U.S. Southern Great Plains

Abstract Boundary layer convergence lines (CLs) are highly effective at deep-convection initiation (DCI), suggesting that their associated updraft properties differ from those of more widespread turbulent updrafts in the planetary boundary layer (PBL). This study exploits observations at the Atmospheric Radiation Measurement Southern Great Plains (ARM SGP) observatory in Oklahoma from 2011 to 2016 to quantify CL properties and their relation to turbulent PBL eddies preceding CL arrival. Two independent methods for estimating CL properties are developed at two locations in the SGP region, both relying on the assumption of a 2D circulation in the CL-normal plane but using different combinations of instruments. The first (the radar method) relies mainly on scanning radar data and is applied to 61 CLs passing near a high-resolution scanning radar based in Nardin, Oklahoma, while the second (the surface method) relies mainly on surface wind data and is applied to 68 CLs crossing the SGP facility in nearby Lamont, Oklahoma. Mean daytime (1000–1900 LST) CL width (∼2 km) and convergence magnitude (∼0.003 s −1 ) are similar for both methods, and mean daytime CL depth is ∼0.75 km. The two methods disagree at night (0000–1000 and 1900–2400 LST), where the surface method estimates wider and weaker CLs than the radar method. This difference may stem from the radar beam overshooting the shallow, highly stable nocturnal PBL. The largest CL updrafts are slightly wider (∼20%) and stronger (∼40%) than the largest PBL updrafts in the pre-CL period, generating 50%–100% larger updraft mass fluxes over most of the PBL depth. Significance Statement Deep convection is commonly initiated by boundary layer convergence lines (CLs), which are associated with intense surface-based wind convergence and strong updrafts that may lift air to saturation. Although CLs form regularly, they are far less common than ordinary, short-lived turbulent thermals in the daytime boundary layer. To better understand why CLs are so effective at deep-convection initiation, we observationally quantify their morphologies and strengths and compare these properties to those of surrounding turbulent updrafts. Perhaps surprisingly, the CLs are found to exhibit only slightly larger scales and strengths as the turbulent updrafts. Although these marginal increases help to explain the preference for storms to initiate along CLs, they likely are not the whole story.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Diverse signatures of convergent evolution in cactus-associated yeasts

Many distantly related organisms have convergently evolved traits and lifestyles that enable them to live in similar ecological environments. However, the extent of phenotypic convergence evolving through the same or distinct genetic trajectories remains an open question. Here, we leverage a comprehensive dataset of genomic and phenotypic data from 1,049 yeast species in the subphylum Saccharomycotina (Kingdom Fungi, Phylum Ascomycota) to explore signatures of convergent evolution in cactophilic yeasts, ecological specialists associated with cacti. We inferred that the ecological association of yeasts with cacti arose independently approximately 17 times. Using a machine learning–based approach, we further found that cactophily can be predicted with 76% accuracy from both functional genomic and phenotypic data. The most informative feature for predicting cactophily was thermotolerance, which we found to be likely associated with altered evolutionary rates of genes impacting the cell envelope in several cactophilic lineages. We also identified horizontal gene transfer and duplication events of plant cell wall–degrading enzymes in distantly related cactophilic clades, suggesting that putatively adaptive traits evolved independently through disparate molecular mechanisms. Notably, we found that multiple cactophilic species and their close relatives have been reported as emerging human opportunistic pathogens, suggesting that the cactophilic lifestyle—and perhaps more generally lifestyles favoring thermotolerance—might preadapt yeasts to cause human disease. This work underscores the potential of a multifaceted approach involving high-throughput genomic and phenotypic data to shed light onto ecological adaptation and highlights how convergent evolution to wild environments could facilitate the transition to human pathogenicity.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Convergence of oscillator spectral estimators for counted-frequency measurements.

A common intermediary connecting frequency-noise calibration or testing of an oscillator to useful applications is the spectral density of the frequency-deviating process. In attempting to turn test data into predicts of performance characteristics, one is naturally led to estimation of statistical values by sample-mean and sample-variance techniques. However, sample means and sample variances themselves are statistical quantities that do not necessarily converge (in the mean-square sense) to actual ensemble-average means and variances, except perhaps for excessively large sample sizes. This is especially true for the flicker noise component of oscillators. This article shows, for the various types of noises found in oscillators, how sample averages converge (or do not converge) to their statistical counterparts. The convergence rate is shown to be the same for all oscillators of a given spectral type.

Tausworthe, R. C.↗

NASA NTRS1973

Rate of convergence of a class of methods of feasible directions.

This paper deals with the rate of convergence of four methods of feasible directions: the Zoutendijk procedures 1 and 2 and two modifications of these procedures due to the authors. It is shown that of these methods, the two due to the authors converge linearly under convexity assumptions, that the Zoutendijk procedure 2 converges sublinearly under these assumptions, and that the Zoutendijk procedure 1 converges linearly provided the solution of the problem is a vertex of the constraint set.

Pironneau, O.↗

NASA NTRS1975

On a numerical sufficiency test for monotonic convergence of finite element models

Finite element analyses characterized by monotonic convergence include the discipline for meaningful measurements of convergence rate and consequently economical extrapolation. Few proposers of element models guarantee monotonic convergence for their elements. Thus, a need exists for an automatic test to classify available element models. This paper describes such a test - a test can be performed using a digital computer to guarantee that a particular element model imbues monotonicity. It describes the test and its basis. It examines seven element models for a rectangular membrane to illustrate the value of the tests. Besides confirming results already known, the application yields new data. It 'proves' monotonicity for two improved models, defines the range of element proportions for which another element can be guaranteed to exhibit monotonicity, and suggests that another element is deficient. In the special case of absolutely convergent membrane displacement models, proof of monotonicity is a necessary and sufficient condition to insure that upper bound estimates of strain energy are developed. Accordingly, the test furnishes a proof of bound solutions independently of requirements on displacement continuity the element basis may or may not satisfy.

Melosh, R. J.↗

NASA NTRS1979

An observational test of the quasi-geostrophic relation between eddy momentum flux convergence and eddy fluxes of potential vorticity and potential temperature

The quasi-geostrophic relation between the fluxes of momentum, potential vorticity and potential temperature is tested with atmospheric data by computing the convergence of momentum flux as a residual of the potential temperature and potential vorticity flux and comparing it to the momentum flux convergence computed directly. It is shown that in the troposphere between 18 and 74 deg N the observed momentum flux convergence differs from the quasi-geostrophic convergence by 25-60% depending on tropospheric level and season.

Heck, W. J.↗

NASA NTRS1980

Moisture convergence using satellite-derived wind fields - A severe local storm case study

Five-minute interval 1-km resolution SMS visible channel data were used to derive low-level wind fields by tracking small cumulus clouds on NASA's Atmospheric and Oceanographic Information Processing System. The satellite-derived wind fields were combined with surface mixing ratios to derive horizontal moisture convergence in the prestorm environment of April 24, 1975. Storms began developing in an area extending from southwest Oklahoma to eastern Tennessee 2 h subsequent to the time of the derived fields. The maximum moisture convergence was computed to be 0.0022 g/kg per sec and areas of low-level convergence of moisture were in general indicative of regions of severe storm genesis. The resultant moisture convergence fields derived from two wind sets 20 min apart were spatially consistent and reflected the mesoscale forcing of ensuing storm development. Results are discussed with regard to possible limitations in quantifying the relationship between low-level flow and between low-level flow and satellite-derived cumulus motion in an antecedent storm environment.

Negri, A. J.↗

NASA NTRS1982

Topics in global convergence of density estimates

The problem of estimating a density f on R sup d from a sample Xz(1),...,X(n) of independent identically distributed random vectors is critically examined, and some recent results in the field are reviewed. The following statements are qualified: (1) For any sequence of density estimates f(n), any arbitrary slow rate of convergence to 0 is possible for E(integral/f(n)-fl); (2) In theoretical comparisons of density estimates, integral/f(n)-f/ should be used and not integral/f(n)-f/sup p, p 1; and (3) For most reasonable nonparametric density estimates, either there is convergence of integral/f(n)-f/ (and then the convergence is in the strongest possible sense for all f), or there is no convergence (even in the weakest possible sense for a single f). There is no intermediate situation.

Devroye, L.↗

NASA NTRS1982

Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms

Various aspects of the convergence, uniqueness, and existence properties associated with solutions generated via the elliptically constrained incremental Newton-Raphson (ECINR) algorithm are analyzed. Several theorems are developed, and the formal behavior of the elliptically constrained scheme developed by Padovan (1981) is discussed in detail. Consideration is given to global and local rates of convergence, to the determination of the occurrence of safety zones wherein the algorithm yields inherently convergent results, to formal limitations on the class of functions which the scheme can be applied to solve, and to single and multidimensional formalisms on existence uniqueness and convergence. Special attention is given to functions whose Jacobian matrix exhibit positive, negative, semi and indefinite properties. Several significant advantages of ECINR over the classical INR are mentioned.

Padovan, J.↗

NASA NTRS1983

Acceleration of convergence of vector sequences

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Sidi, A.↗

NASA NTRS1985

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Brand, J. C.↗

NASA NTRS1986

Acceleration of convergence of vector sequences

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iterative. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Sidi, A.↗

NASA NTRS1987

On the relationship between scatterometer-derived convergences and atmospheric moisture

Fields of divergence calculated from the Seasat-A Satellite Scatterometer winds and fields of integrated water vapor and rainrate from the Scanning Multichannel Microwave Radiometer on Seasat are constructed for three different midlatitude cyclones. These storms include an explosively deepening cyclone that occurred in the North Atlantic (also known as the Queen Elizabeth II cyclone), a storm that occurred in the North Pacific, and a Southern Ocean storm. In all three cases, the regions of convergence and atmospheric water (vapor and rain) are consistent with each other and help to define features of each storm. The vertical distribution of moisture is inferred for one case using both the convergence pattern and the integrated water vapor field. In another, interpretation of the convergence field in a data gap region is aided by the water vapor field. In all three cases, surface low pressure centers, fronts, and even frontal waves are clearly evident as areas of convergence, and increased water vapor and rainrate.

Mcmurdie, Lynn A.↗

NASA NTRS1988

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).

Tadmor, Eitan↗

NASA NTRS1988

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗

NASA NTRS1990

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Sidi, Avram↗