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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Linking Synoptic Patterns to Cloud Properties and Local Circulations Over Southeastern Texas

This report classifies meteorological regimes in the southeastern Texas region to identify environmental conditions that favor sea-breeze induced convection. The classification is accomplished using a Self-Organizing Map (SOM) approach. We applied SOM to 10 years of 700-hPa geopotential height anomalies during the summer months from reanalysis data to distinguish three dominant synoptic regimes, with a continuum of transitional states between those. The primary regimes include: (a) a pre-trough regime associated with a synoptic trough, (b) a post-trough regime with upper-level northerly flow, and (c) an anticyclonic regime within the westward extent of the Bermuda High. We project the data from the Geostationary Operational Environmental Satellite and the Next Generation Weather Radar system onto each SOM node to investigate the characteristics of cloud and precipitation properties in different regimes. When southeastern Texas is positioned to the southwest quadrant of a maritime high pressure system, an increased cloud frequency is observed over the region during the afternoon hours due to significant moisture advection. A confluence of synoptic southerly flow and sea-breeze circulation commonly occurs in this regime. When a high pressure system is over southeastern Texas, the area is dominated by large-scale subsidence with weak pressure gradients and moderate precipitable water vapor. This weak synoptic forcing is favorable for the formation of a sea-breeze circulation. This is confirmed by an enhanced onshore flow and a decreased temperature at the surface in the early afternoon, as well as a sharp increase in radar echo top height.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Observability of dark matter substructure with pulsar timing correlations

Dark matter substructure on small scales is currently weakly constrained, and its study may shed light on the nature of the dark matter. In this work we observe the gravitational effects of dark matter substructure on measured pulsar phases in pulsar timing arrays (PTAs). Due to the stability of pulse phases observed over several years, dark matter substructure around the Earth-pulsar system can imprint discernible signatures in gravitational Doppler and Shapiro delays. We compute pulsar phase correlations induced by general dark matter substructure, and project constraints for a few models such as monochromatic primordial black holes (PBHs), and Cold Dark Matter (CDM)-like NFW subhalos. This work extends our previous analysis, which focused on static or single transiting events, to a stochastic analysis of multiple transiting events. We find that stochastic correlations, in a PTA similar to the Square Kilometer Array (SKA), are uniquely powerful to constrain subhalos as light as ~ 10 -13 M ⊙ , with concentrations as low as that predicted by standard CDM.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A massively parallel and scalable multi-CPU material point method

Harnessing the power of modern multi-GPU architectures, we present a massively parallel simulation system based on the Material Point Method (MPM) for simulating physical behaviors of materials undergoing complex topological changes, self-collision, and large deformations. Our system makes three critical contributions. First, we introduce a new particle data structure that promotes coalesced memory access patterns on the GPU and eliminates the need for complex atomic operations on the memory hierarchy when writing particle data to the grid. Second, we propose a kernel fusion approach using a new Grid-to-Particles-to-Grid (G2P2G) scheme, which efficiently reduces GPU kernel launches, improves latency, and significantly reduces the amount of global memory needed to store particle data. Finally, we introduce optimized algorithmic designs that allow for efficient sparse grids in a shared memory context, enabling us to best utilize modern multi-GPU computational platforms for hybrid Lagrangian-Eulerian computational patterns. We demonstrate the effectiveness of our method with extensive benchmarks, evaluations, and dynamic simulations with elastoplasticity, granular media, and fluid dynamics. In comparisons against an open-source and heavily optimized CPU-based MPM codebase [Fang et al. 2019] on an elastic sphere colliding scene with particle counts ranging from 5 to 40 million, our GPU MPM achieves over 100x per-time-step speedup on a workstation with an Intel 8086K CPU and a single Quadro P6000 GPU, exposing exciting possibilities for future MPM simulations in computer graphics and computational science. Moreover, compared to the state-of-the-art GPU MPM method [Hu et al. 2019a], we not only achieve 2x acceleration on a single GPU but our kernel fusion strategy and Array-of-Structs-of-Array (AoSoA) data structure design also generalizes to multi-GPU systems. Our multi-GPU MPM exhibits near-perfect weak and strong scaling with 4 GPUs, enabling performant and large-scale simulations on a 10243 grid with close to 100 million particles with less than 4 minutes per frame on a single 4-GPU workstation and 134 million particles with less than 1 minute per frame on an 8-GPU workstation.

Wang, Xinlei↗
DOE OSTI2022

Nature and Scalings of Density Fluctuations of Compressible Magnetohydrodynamic Turbulence with Applications to the Solar Wind

Abstract The solar wind is a magnetized and turbulent plasma. Its turbulence is often dominated by Alfvénic fluctuations and often deemed as nearly incompressible far away from the Sun, as shown by in situ measurements near 1 au. However, for solar wind closer to the Sun, the plasma β decreases (often lower than unity) while the turbulent Mach number M t increases (can approach unity, e.g., transonic fluctuations). These conditions could produce significantly more compressible effects, characterized by enhanced density fluctuations, as seen by several space missions. In this paper, a series of 3D MHD simulations of turbulence are carried out to understand the properties of compressible turbulence, particularly the generation of density fluctuations. We find that, over a broad range of parameter space in plasma β , cross helicity, and polytropic index, the turbulent density fluctuations scale linearly as a function of M t , with the scaling coefficients showing weak dependence on parameters. Furthermore, through detailed spatiotemporal analysis, we show that the density fluctuations are dominated by low-frequency nonlinear structures, rather than compressible MHD eigenwaves. These results could be important for understanding how compressible turbulence contributes to solar wind heating near the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Pore-Scale Dynamics of Liquid CO2–Water Displacement in 2D Axisymmetric Porous Micromodels Under Strong Drainage and Weak Imbibition Conditions: High-Speed μPIV Measurements

Resolving pore-scale transient flow dynamics is crucial to understanding the physics underlying multiphase flow in porous media and informing large-scale predictive models. Surface properties of the porous matrix play an important role in controlling such physics, yet interfacial mechanisms remain poorly understood, in part due to a lack of direct observations. This study reports on an experimental investigation of the pore-scale flow dynamics of liquid CO 2 and water in two-dimensional (2D) circular porous micromodels with different surface characteristics employing high-speed microscopic particle image velocimetry (μPIV). The design of the micromodel minimized side boundary effects due to the limited size of the domain. The high-speed μPIV technique resolved the spatial and temporal dynamics of multiphase flow of CO 2 and water under reservoir-relevant conditions, for both drainage and imbibition scenarios. When CO 2 displaced water in a hydrophilic micromodel (i.e., drainage), unstable capillary fingering occurred and the pore flow was dominated by successive pore-scale burst events (i.e., Haines jumps). When the same experiment was repeated in a nearly neutral wetting micromodel (i.e., weak imbibition), flow instability and fluctuations were virtually eliminated, leading to a more compact displacement pattern. Energy balance analysis indicates that the conversion efficiency between surface energy and external work is less than 30%, and that kinetic energy is a disproportionately smaller contributor to the energy budget. This is true even during a Haines jump event, which induces velocities typically two orders of magnitude higher than the bulk velocity. These novel measurements further enabled direct observations of the meniscus displacement, revealing a significant alteration of the pore filling mechanisms during drainage and imbibition. While the former typically featured burst events, which often occur only at one of the several throats connecting a pore, the latter is typically dominated by a cooperative filling mechanism involving simultaneous invasion of a pore from multiple throats. This cooperative filling mechanism leads to merging of two interfaces and releases surface energy, causing instantaneous high-speed events that are similar, yet fundamentally different from, burst events. Finally, pore-scale velocity fields were statistically analyzed to provide a quantitative measure of the role of capillary effects in these pore flows.

Li, Yaofa↗
DOE OSTI2025

Testing gravitational physics by combining DESI DR1 and weak lensing datasets using the E_G estimator

The action of gravitational physics across space-time creates observable signatures in the behaviour of light and matter. We perform combined-probe studies using data from the Baryon Oscillation Spectroscopic Survey (BOSS) and Dark Energy Spectroscopic Instrument survey Data Release 1 (DESI-DR1), in combination with three existing weak lensing surveys, the Kilo-Degree Survey (KiDS), the Dark Energy Survey (DES), and the Hyper Suprime-Cam Survey (HSC), to test and constrain General Relativity (GR) in the context of the standard model of cosmology (LCDM). We focus on measuring the gravitational estimator statistic, E_G, which describes the relative amplitudes of weak gravitational lensing and galaxy velocities induced by a common set of overdensities. By comparing our amplitude measurements with their predicted scale- and redshift-dependence within the GR+LCDM model, we demonstrate that our results are consistent with the predictions of the Planck cosmology. The redshift span of the DESI dataset allows us to perform these E_G measurements at the highest redshifts achieved to date, z ~ 1.

cosmology↗
DOE OSTI2023

Cosmological structure formation and soliton phase transition in fuzzy dark matter with axion self-interactions

Herein we investigate cosmological structure formation in fuzzy dark matter (FDM) with the attractive self-interaction (SI) with numerical simulations. Such a SI would arise if the FDM boson were an ultra-light axion, which has a strong CP symmetry-breaking scale (decay constant). Although weak, the attractive SI may be strong enough to counteract the quantum ‘pressure’ and alter structure formation. We find in our simulations that the SI can enhance small-scale structure formation, and soliton cores above a critical mass undergo a phase transition, transforming from dilute to dense solitons.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Kinetically constrained freezing transition in a dipole-conserving system

Here, we study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fractonlike conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase, where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Developing high performance RF heating scenarios on the WEST tokamak

High power experiments, up to 9.2 MW with LHCD and ICRH, have been carried out in the full tungsten tokamak WEST. Quasi non inductive discharges have been achieved allowing to extend the plasma duration to 53s with stationary conditions in particular with respect to tungsten contamination. Transitions in H mode are obtained lasting up to 4s with weak energy increment at the power crossing the separatrix is close to the threshold. Hot L mode plasmas (Te(0)>3keV) with a confinement time following the ITER L96 scaling are routinely obtained. The weak aspect ratio dependence of this scaling law is confirmed. Tungsten accumulation is generally not an operational issue on WEST. Difficulty of burning through tungsten can prevent from accessing to a hot core plasma in the ramp-up phase or can lead to rapid collapse of the central temperature when radiation is enhanced by a slight decrease of the temperature. Apart few pulses post-boronization, the plasma radiation is rather high (Prad/Ptot~50%) and is dominated by tungsten. This fraction does not vary as the RF power is ramped up and is quite similar in ICRH and/or LHCD heated plasmas. An estimate of the contribution of the RF antennas to the plasma contamination in tungsten is given.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Revealing atomic-scale switching pathways in van der Waals ferroelectrics

Two-dimensional (2D) van der Waals (vdW) materials hold the potential for ultrascaled ferroelectric (FE) devices due to their silicon compatibility and robust polarization down to atomic scale. However, the inherently weak vdW interactions enable facile sliding between layers, introducing complexities beyond those encountered in conventional ferroelectric materials and presenting substantial challenges in uncovering intricate switching pathways. Here, we combine atomic-resolution imaging under in situ electrical biasing conditions with first-principles calculations to unravel the atomic-scale switching mechanisms in SnSe, a vdW group IV monochalcogenide. Our results uncover the coexistence of a consecutive 90° switching pathway and a direct 180° switching pathway from antiferroelectric (AFE) to FE order in this vdW system. Atomic-scale investigations and strain analysis reveal that the switching processes simultaneously induce interlayer sliding and compressive strain, while the lattice remains coherent despite the presence of multidomain structures. These findings elucidate vdW ferroelectric switching dynamics at atomic scale and lay the foundation for the rational design of 2D ferroelectric nanodevices.

Li, Xinyan [Rice University, Houston, TX (United S↗
DOE OSTI2023

Evidence for Suppression of Structure Growth in the Concordance Cosmological Model

We present evidence for a suppressed growth rate of large-scale structure during the dark-energy dominated era. Modeling the growth rate of perturbations with the ``growth index'' γ, we find that current cosmological data strongly prefer a higher growth index than the value γ=0.55 predicted by general relativity in a flat ΛCDM cosmology. Both the cosmic microwave background data from Planck and the large-scale structure data from weak lensing, galaxy clustering, and cosmic velocities separately favor growth suppression. When combined, they yield γ = 0.633$^{+0.025}_{–0.024}$, excluding γ = 0.55 at a statistical significance of 3.7σ. The combination of fσ8 and Planck measurements prefers an even higher growth index of γ = 0.639$^{+0.024}_{–0.025}$, corresponding to a 4.2σ-tension with the concordance model. In Planck data, the suppressed growth rate offsets the preference for nonzero curvature and fits the data equally well as the latter model. Furthermore, a higher γ leads to a higher matter fluctuation amplitude S 8 inferred from galaxy clustering and weak lensing measurements, and a lower S 8 from Planck data, effectively resolving the S 8 tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Theoretical study of various nonlinear phenomena in plasma systems and scaling of magneto-inertial-fusion targets

Plasma physics is an exciting field of study with a wide variety of nonlinear processes that come into play. Examples of such processes include the interaction of small-scale turbulence with large-scale plasma structures and the nonlinear saturation of plasma instabilities, for example those of magneto-hydrodynamical nature. During this Truman LDRD project, I studied a collection of nonlinear problems that are of interest to the field of plasma physics. This LDRD report summarizes four main research accomplishments. First, a new statistical model for describing inhomogeneous drift-wave turbulence inter- acting with zonal flows was developed. This new model includes the effects of nonlinear wave-wave collisions, which are expected to change the spectrum of the underlying DW turbulence and therefore the generation of zonal flows. Second, a new mathematical formalism was proposed to systematically apply the non- linear WKB approximation to general field theories, including those often used in fluid dynamics. This formalism represents an interesting tool for studying physical systems that show an explicit scale separation. Third, a weakly nonlinear model was developed to describe the magneto-Rayleigh-Taylor instability. This instability is of paramount importance to understand as it can reduce the performance of magnetic-inertial-fusion (MIF) platforms. The developed models captures the effects of harmonic generation and saturation of the linear growth of the instability. Finally, a framework was proposed for scaling magneto-inertial fusion (MIF) targets to larger pulsed-power drivers. From this framework, a set of scaling rules were derived that conserve the physical regimes of MIF systems when scaling up in peak current. By doing so, deleterious nonlinear processes that affect MIF performance may be kept at bay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

The gravitational lensing imprints of DES Y3 superstructures on the CMB: a matched filtering approach

Low-density cosmic voids gravitationally lens the cosmic microwave background (CMB), leaving a negative imprint on the CMB convergence |$\kappa$|⁠. This effect provides insight into the distribution of matter within voids, and can also be used to study the growth of structure. We measure this lensing imprint by cross-correlating the Planck CMB lensing convergence map with voids identified in the Dark Energy Survey Year 3 (DES Y3) data set, covering approximately 4200 deg|$^2$| of the sky. We use two distinct void-finding algorithms: a 2D void-finder that operates on the projected galaxy density field in thin redshift shells, and a new code, Voxel, which operates on the full 3D map of galaxy positions. We employ an optimal matched filtering method for cross-correlation, using the Marenostrum Institut de Ciències de l’Espai N-body simulation both to establish the template for the matched filter and to calibrate detection significances. Using the DES Y3 photometric luminous red galaxy sample, we measure |$A_\kappa$|⁠, the amplitude of the observed lensing signal relative to the simulation template, obtaining |$A_\kappa = 1.03 \pm 0.22$| (⁠|$4.6\sigma$| significance) for Voxel and |$A_\kappa = 1.02 \pm 0.17$| (⁠|$5.9\sigma$| significance) for 2D voids, both consistent with Lambda cold dark matter expectations. We additionally invert the 2D void-finding process to identify superclusters in the projected density field, for which we measure |$A_\kappa = 0.87 \pm 0.15$| (⁠|$5.9\sigma$| significance). The leading source of noise in our measurements is Planck noise, implying that data from the Atacama Cosmology Telescope, South Pole Telescope and CMB-S4 will increase sensitivity and allow for more precise measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

QCD analysis of Δ S = 0 hadronic parity violation

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging (ΔS = 0) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the W to the O(2 GeV) energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators that enter below the W mass scale from QCD operator mixing effects form a closed set, and they result in a 12 x 12 anomalous dimension matrix. Computing the resulting effective Hamiltonian and comparing to earlier results, we affirm the importance of operator mixing effects and find, as an example, that the parity-violating pion-nucleon coupling constant, using the factorization Ansatz and an assessment of the pertinent quark charge of the nucleon in lattice QCD at the 2 GeV scale, is in better agreement with recent experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗
DOE OSTI2022

Constraining the baryonic feedback with cosmic shear using the DES Year-3 small-scale measurements

ABSTRACT We use the small scales of the Dark Energy Survey (DES) Year-3 cosmic shear measurements, which are excluded from the DES Year-3 cosmological analysis, to constrain the baryonic feedback. To model the baryonic feedback, we adopt a baryonic correction model and use the numerical package baccoemu to accelerate the evaluation of the baryonic non-linear matter power spectrum. We design our analysis pipeline to focus on the constraints of the baryonic suppression effects, utilizing the implication given by a principal component analysis on the Fisher forecasts. Our constraint on the baryonic effects can then be used to better model and ameliorate the effects of baryons in producing cosmological constraints from the next-generation large-scale structure surveys. We detect the baryonic suppression on the cosmic shear measurements with a ∼2σ significance. The characteristic halo mass for which half of the gas is ejected by baryonic feedback is constrained to be $M_c \gt 10^{13.2} \, h^{-1} \, \mathrm{M}_{\odot }$ (95 per cent C.L.). The best-fitting baryonic suppression is $\sim 5{{\ \rm per\ cent}}$ at $k=1.0 \, {\rm Mpc}\ h^{-1}$ and $\sim 15{{\ \rm per\ cent}}$ at $k=5.0 \, {\rm Mpc} \ h^{-1}$. Our findings are robust with respect to the assumptions about the cosmological parameters, specifics of the baryonic model, and intrinsic alignments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence

A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. Furthermore, these simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗