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Results for “BGK approximation”

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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11 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Non-Maxwellian distribution functions in flaring coronal loops - Comparison of Landau-Fokker-Planck and BGK solutions

The high-velocity tail of the electron distribution has been calculated by solving the high-velocity form of the Landau equation for a thermal structure representative of a flaring coronal loop. These calculations show an enhancement of the tail population above Maxwellian for electrons moving down the temperature gradient. The results obtained are used to test the reliability of the BGK approximation. The comparison shows that the BGK technique can estimate contributions to the heat flux from the high-energy tail to within an order of magnitude.

Ljepojevic, N. N.↗
DOE OSTI2021

A Consistent BGK Model with Velocity-Dependent Collision Frequency for Gas Mixtures

Abstract We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entropy under the constraint that the number of particles of each species, total momentum, and total energy are conserved. We prove that this minimization problem admits a unique solution for very general collision frequencies. Moreover, we prove that the model satisfies an H-Theorem and characterize the form of equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation

We report the Boltzmann equation with the Bhatnagar-Gross-Krook collision model (Boltzmann-BGK equation) has been employed to describe multiscale flows, i.e., from the hydrodynamic limit to free molecular flow. In this study we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular, the PINN-BGK is composed of three sub-networks, i.e., the first for approximating the equilibrium distribution function, the second for approximating the non-equilibrium distribution function, and the third one for encoding the Boltzmann-BGK equation as well as the corresponding boundary/initial conditions. By minimizing the residuals of the governing equations and the mismatch between the predicted and provided boundary/initial conditions, we can approximate the Boltzmann-BGK equation for both continuous and rarefied flows. For forward problems, the PINN-BGK is utilized to solve various benchmark flows given boundary/initial conditions, e.g. Kovasznay flow, Taylor-Green flow, cavity flow, and micro Couette flow for Knudsen number up to 5. For inverse problems, we focus on rarefied flows in which accurate boundary conditions are difficult to obtain. We employ the PINN-BGK to infer the flow field in the entire computational domain given a limited number of interior scattered measurements on the velocity without using the (unknown) boundary conditions. Results for the two-dimensional micro Couette and micro cavity flows with Knudsen numbers ranging from 0.1 to 10 indicate that the PINN-BGK can infer the velocity field in the entire domain with good accuracy. Finally, we also present some results on using transfer learning to accelerate the training process. Specifically, we can obtain a three-fold speedup comparted to the standard training process (e.g., Adam plus L-BFG-B) for the two-dimensional flow problems considered in our work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Axisymmetric gyrokinetic simulation of ASDEX-Upgrade scrape-off layer using a conservative implicit BGK collision operator

Collisions play an important role in turbulence and transport of fusion plasmas. For kinetic simulations, as the collisionality increases in the domain of interest, the size of the time step to resolve the collisional physics can become overly restrictive in an explicit time integration scheme, leading to high computational cost. With the aim of overcoming such restriction, we have implemented an implicit Bhatnagar–Gross–Krook (BGK) collision operator for use in the discontinuous Galerkin full-f gyrokinetic solver within the Gkeyll framework, which, when combined with Gkeyll's traditional explicit time integrator for collisionless advection, can significantly increase the time step in gyrokinetic simulations of highly collisional regimes. To ensure conservation of density, momentum, and energy, we utilize an iterative scheme to correct the discretized approximation to the equilibrium Maxwellian distribution to which the BGK collision operator relaxes. We have further generalized the BGK infrastructure, both the implicit scheme and the correction routine, to handle cross-species collisions. This improved implicit and conservative BGK operator is benchmarked against the more accurate but more computationally expensive Lenard–Bernstein–Dougherty (LBD) operator, which has been utilized in prior studies with Gkeyll. The implicit BGK operator enables 2D axisymmetric simulations of the ASDEX-Upgrade scrape-off layer to run 56 times faster to completion than the simulations with the LBD operator, because the BGK operator is more robust and converges at a lower resolution than is required by the LBD operator. Additionally, in this more collisional limit, we demonstrate that the results of our simulations utilizing the implicit BGK operator agreed well with simulations utilizing the more computationally expensive LBD operator.

Gyrokinetic simulations↗
NASA NTRS1989

The diffusion approximation and transport theory for cosmic rays in relativistic flows

Equations describing the transport of cosmic rays in relativistic flows in the diffusion approximation are obtained. The analysis is based on the zeroth, first, and second differential moment equations of the relativistic Boltzmann equation with a BGK collision term. A perturbation solution of the moment equations in the diffusion approximation yields both the co-moving frame particle current and viscous stresses. The resultant cosmic-ray continuity equation contains three readily recognized energy change terms: the adiabatic energy change term; the viscous shear energy change term; and a term proportional to the scalar product of the acceleration vector of the scattering frame and the heat flux.

Webb, G. M.↗
NASA NTRS1976

Spacecraft self-contamination due to back-scattering of outgas products

The back-scattering of outgas contamination near an orbiting spacecraft due to intermolecular collisions was analyzed. Analytical tools were developed for making reasonably accurate quantitative estimates of the outgas contamination return flux, given a knowledge of the pertinent spacecraft and orbit conditions. Two basic collision mechanisms were considered: (1) collisions involving only outgas molecules (self-scattering) and (2) collisions between outgas molecules and molecules in the ambient atmosphere (ambient-scattering). For simplicity, the geometry was idealized to a uniformly outgassing sphere and to a disk oriented normal to the freestream. The method of solution involved an integration of an approximation of the Boltzmann kinetic equation known as the BGK (or Krook) model equation. Results were obtained in the form of simple equations relating outgas return flux to spacecraft and orbit parameters. Results were compared with previous analyses based on more simplistic models of the collision processes.

Robertson, S. J.↗
NASA NTRS1983

Density drift instabilities and weak collisions

A model is developed which describes the effects of weak collisions on the linear kinetic theory of electrostatic density drift instabilities. A dispersion equation valid at all frequencies and wave numbers is derived using the assumptions of a weak, uniform density gradient; a uniform magnetic field; and the BGK collision operator with a modification of the local approximation. The properties of the universal and collisional density drift instabilities at maximum growth rates are examined in detail. The thresholds of the instabilities are examined for an ionospheric model which includes ion-neutral, electron-neutral, and electron-ion collisions, and are compared with the threshold of the lower hybrid density drift instability. It is concluded that the k to the -5th short wavelength density power spectra observed above 280 km in the PLUMEX experiment are due to the effects of the universal density drift instability.

Gary, S. P.↗
NASA NTRS1992

An analytic model of the neutral cloud evolution in the earth's atmosphere

An analytic model for the expansion of a chemically reacting gas in the upper atmosphere is discussed. The spatial-temporal distribution of released particles in the initial regime is described on the basis of self-similar solutions of Euler's equations. In the case of transition to the diffusion regime an approximate solution of the kinetic equation with the collision integral in the form of BGK is performed. Gravitation and the atmospheric inhomogeneity are taken into account, The diffusion regime is described by an analytic solution of the diffusion equation in an exponential atmosphere taking account of possible losses of the gas due to chemical reactions. Some peculiarities of the expansion of various gases as well as the possibility of applying the model for describing ionospheric 'holes' are discussed.

Bruskin, L. G.↗
DOE OSTI2024

Bhatnagar-Gross-Krook subgrid model for neutrino quantum kinetics

Here, we present a new subgrid model for neutrino quantum kinetics, which is primarily designed to incorporate effects of collective neutrino oscillations into neutrino-radiation-hydrodynamic simulations for core-collapse supernovae and mergers of compact objects. We approximate the neutrino oscillation term in a quantum kinetic equation using the Bhatnagar-Gross-Krook (BGK) relaxation-time prescription, and the transport equation is directly applicable for classical neutrino transport schemes. The BGK model is motivated by recent theoretical indications that nonlinear phases of collective neutrino oscillations settle into quasisteady structures. We explicitly provide basic equations of the BGK subgrid model for both multiangle and moment-based neutrino transport to facilitate the implementation of the subgrid model in the existing neutrino transport schemes. We also show the capability of our BGK subgrid model by comparing it to fully quantum kinetic simulations for fast neutrino-flavor conversion. We find that the overall properties can be well reproduced in the subgrid model; the error of angular-averaged survival probability of neutrinos is within ~20%. By identifying the source of error, we also discuss perspectives to improve the accuracy of the subgrid model.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Reactive collision terms for fluid transport theory

A modified Bhatnagar-Gross-Krook (BGK) collision method is used for the derivation of reactive collision terms to allow for complete higher-moment approximations in fluid transport theory. The general reactive collision terms for the 8-, 10- and 13-moment approximation for binary reactions are derived. Then, reactive collision terms for specific chemistry are derived with the assumptions: (1) all reactants and products have 13-moment distribution functions; (2) simple, classical assumptions provide sufficient models for reaction dynamics; and (3) the reaction rate is energy-independent. The derived specific formulas reflect two extremes in reactive collision dynamics: direct and indirect reaction mechanisms. Finally, considerations for correct use of the reactive collision terms are discussed in the context of space plasma environments.

Eccles, J. V.↗
NASA NTRS1986

Nonlinear upper hybrid drift waves for a longitudinal electric field perpendicular to a uniform magnetic field in the Vlasov-Maxwell approximation

Upper hybrid drift waves are found as a special solution to a Vlasov-Maxwell plasma which has a longitudinal electric field and a perpendicular uniform magnetic field. A single-species plasma with a constant-density mobile neutralizing background supports spatially varying disturbances that oscillate at the upper hybrid frequency. The general functional dependences of the electric field, the plasma number density, and the one-particle distribution function for the special case are found from more general Vlasov-Maxwell equations invariant under a Lie group point transformation. The one-particle distribution function for the plasma is a function of the Liouville invariant, which is the energy in the generalized Bernstein-Greene-Kruskal (BGK) reference frame, and the momentum in the drift direction.

Abraham-Shrauner, B.↗