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At least 109 records · Page 6

Dataset from: Improved multispecies Dougherty collisions

The Dougherty model Fokker-Planck operator is extended to describe nonlinear full-f collisions between multiple species in plasmas. Simple relations for cross-species primitive moments are developed which obey conservation laws, and reproduce familiar velocity and temperature relaxation rates. This treatment of multispecies Dougherty collisions, valid for arbitrary mass ratios, avoids unphysical temperatures and satisfies the H-theorem unlike an analogous Bhatnagar-Gross-Krook operator. Formulas for both a Cartesian velocity-space and a gyroaveraged operator are provided for use in Vlasov as well as long-wavelength gyrokinetic models. We present an algorithm for the discontinuous Galerkin discretization of this operator, and provide results from relaxation and Landau damping benchmarks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Vectorizable implicit algorithms for the flux-difference split, three-dimensional Navier-Stokes equations

The computational efficiency of four vectorizable implicit algorithms is assessed when applied to calculate steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in general coordinates. Two of these algorithms are characterized as hybrid schemes; that is, they combine some approximate factorization in two coordinate directions with relaxation in the remaining spatial direction. The other two algorithms utilize an approximate factorization approach which yields two-factor algorithms for three-dimensional systems. All four algorithms are implemented in identical high-resolution upwind schemes for the flux-difference split Navier-Stokes equations. These highly nonlinear schemes are obtained by extending an implicit Total Variation Diminishing (TVD) scheme recently developed for linear one-dimensional systems of hyperbolic conservation laws to the three-dimensional Navier-Stokes equations. The computation of vortical flow over a sharp-edged, thin delta wing has been chosen as a common numerical test case. The convergence of the algorithms is discussed and the accuracy of the computed flow-field results is assessed. The validity of the present results are demonstrated by a comparison with experimental data.

Hartwich, P. M.↗

An Astronomical Test of CCD Photometric Precision

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Koch, David↗

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Larson, Mats G.↗

Polarized Bidirectional Reflectance of Optically Thick Sparse Particulate Layers: an Efficient Numerically Exact Radiative-Transfer Solution

We describe a simple yet efficient numerical algorithm for computing polarized bidirectional reflectance of an optically thick (semi-infinite), macroscopically flat layer composed of statistically isotropic and mirror symmetric random particles. The spatial distribution of the particles is assumed to be sparse, random, and statistically uniform. The 44 Stokes reflection matrix is calculated by iterating the Ambartsumian's vector nonlinear integral equation. The result is a numerically exact solution of the vector radiative transfer equation and as such fully satisfies the energy conservation law and the fundamental reciprocity relation. Since this technique bypasses the computation of the internal radiation field, it is very fast and highly accurate. The FORTRAN implementation of the technique is publicly available on the World Wide Web at http://www.giss.nasa.gov/staff/ mmishchenko/brf. It can be combined with several existing computer programs providing the requisite single-scattering properties of spherical or morphologically complex particles and applied to a wide range of optical characterization problems. Benchmark results obtained with this program can be used for testing alternative solvers of the vector radiative transfer equation.

radiative transfer↗

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

Loh, Ching Y.↗

Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces

We describe a simple and highly efficient and accurate radiative transfer technique for computing bidirectional reflectance of a macroscopically flat scattering layer composed of nonabsorbing or weakly absorbing, arbitrarily shaped, randomly oriented and randomly distributed particles. The layer is assumed to be homogeneous and optically semi-infinite, and the bidirectional reflection function (BRF) is found by a simple iterative solution of the Ambartsumian's nonlinear integral equation. As an exact Solution of the radiative transfer equation, the reflection function thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. Since this technique bypasses the computation of the internal radiation field, it is by far the fastest numerical approach available and can be used as an ideal input for Monte Carlo procedures calculating BRFs of scattering layers with macroscopically rough surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web at http://ww,,v.giss.nasa.gov/-crmim/brf.html and can be applied to a wide range of remote sensing, engineering, and biophysical problems. We also examine the potential effect of ice crystal shape on the bidirectional reflectance of flat snow surfaces and the applicability of the Henyey-Greenstein phase function and the 6-Eddington approximation in calculations for soil surfaces.

Mishchenko, Michael I.↗

Dynamics of Vapour Bubbles in Nucleate Boiling: Basic Equations of Bubble Evolution - 1

We consider the behaviour of a vapour bubble formed at a nucleation site on a heated horizontal wall. There is no forced convection of an ambient liquid, and the bubble is presumably separated from the wall by a thin liquid microlayer. The energy conservation law results in a variational equation for the mechanical energy of the whole system consisting of the bubble and liquid. It leads to a set of two strongly nonlinear equations which govern bubble expansion and motion of its centre of mass. A supplementary equation to find out the vapour temperature follows from consideration of heat transfer to the bubble, both from the bulk of surrounding liquid and through the microlayer. The average thickness of the microlayer is shown to increase monotonously with time as the bubble meniscus spreads along the wall. Bubble expansion is driven by the pressure head between vapour inside and liquid far away from the bubble, with due allowance for surface tension and gravity effects. It is resisted by inertia of liquid being placed into motion as the bubble grows. The inertia originates also a force that presses the bubble to the wall. This force is counteracted by the buoyancy and an effective surface tension force that tends to transform the bubble into a sphere. The analysis brings about quite a new formulation of the familiar problem of bubble growth and detachment under conditions of nucleate pool boiling.

Buyevich, Yu A.↗

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

79 ASTRONOMY AND ASTROPHYSICS↗

Bidirectional Reflectance of a Macroscopically Flat, High-Albedo Particulate Surface: An Efficient Radiative Transfer Solution and Applications to Regoliths

Many remote sensing applications rely on accurate knowledge of the bidirectional reflection function (BRF) of surfaces composed of discrete, randomly positioned scattering particles. Theoretical computations of BRFs for plane-parallel particulate layers are usually reduced to solving the radiative transfer equation (RTE) using one of existing exact or approximate techniques. Since semi-empirical approximate approaches are notorious for their low accuracy, violation of the energy conservation law, and ability to produce unphysical results, the use of numerically exact solutions of RTE has gained justified popularity. For example, the computation of BRFs for macroscopically flat particulate surfaces in many geophysical publications is based on the adding-doubling (AD) and discrete ordinate (DO) methods. A further saving of computer resources can be achieved by using a more efficient technique to solve the plane-parallel RTE than the AD and DO methods. Since many natural particulate surfaces can be well represented by the model of an optically semi-infinite, homogeneous scattering layer, one can find the BRF directly by solving the Ambartsumian's nonlinear integral equation using a simple iterative technique. In this way, the computation of the internal radiation field is avoided and the computer code becomes highly efficient and very accurate and compact. Furthermore, the BRF thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. In this paper, we discuss numerical aspects and the computer implementation of this technique, examine the applicability of the Henyey-Greenstein phase function and the sigma-Eddington approximation in BRF and flux calculations, and describe sample applications demonstrating the potential effect of particle shape on the bidirectional reflectance of flat regolith surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web, and can be applied to a wide range of remote sensing problems. BRF computations for undulated (macroscopically rough) surfaces are more complicated and often rely on time consuming Monte Carlo procedures. This approach is especially inefficient for optically thick, weakly absorbing media (e.g., snow and desert surfaces at visible wavelengths since a photon may undergo many internal scattering events before it exists the medium or is absorbed. However, undulated surfaces can often be represented as collections of locally flat tilted facets characterized by the BRF found from the traditional plane parallel RTE. In this way the MOnte Carlo procedure could be used only to evaluate the effects of surface shadowing and multiple surface reflections, thereby bypassing the time-consuming ray tracing inside the medium and providing a great savings of CPU time.

Mishchenko, Michael I.↗

Computer Program For Variable-Conductance Heat Pipes

VCHPDA provides accurate mathematical models of transient as well as steady-state performance of variable-conductance heat pipes over wide range of operating conditions. Applies to heat pipes with either cold, wicked or hot, nonwicked gas reservoirs and uses ideal-gas law and "flat-front" (negligible vapor diffusion) gas theory. Calculates length of gas-blocked region and temperature of vapor in active portion of heat pipe by solving set of nonlinear equations for conservation of energy and mass. Written in FORTRAN 77.

Antoniuk, D.↗

High resolution numerical simulation of the linearized Euler equations in conservation law form

A linearized Euler solver based on a high resolution numerical scheme is presented. The approach is to linearize the flux vector as opposed to carrying through the complete linearization analysis with the dependent variable vector written as a sum of the mean and the perturbed flow. This allows the linearized equations to be maintained in conservation law form. The linearized equations are used to compute unsteady flows in turbomachinery blade rows arising due to blade vibrations. Numerical solutions are compared to theoretical results (where available) and to numerical solutions of the nonlinear Euler equations.

Sreenivas, Kidambi↗

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Ols- son & Oliger (1994), Gerritsen & Olsson (1996), and Yee et al. (2000) is revisited. The entropy splitting is a form of skew-symmetric splitting of the nonlinear Euler flux derivatives. Central differencing applied to the entropy splitting form of the Euler flux derivatives together with SBP difference operators will, hereafter, be referred to as entropy split schemes. This study is prompted by the recent growing interest in numerical methods for which a discrete entropy conservation law holds, a discrete global entropy conservation can be proved and/or the numerical method possesses a stable entropy in the framework of SBP difference operators and L2-energy norm estimate. The objective of this paper is to recast the entropy split scheme as the re- cent definition of an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for non- linear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grub- ber splitting.

Sjogreen, Bjorn↗

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

Shu, Chi-Wang↗

A fast semidirect method for computing transonic aerodynamic flows

A fast, semidirect, iterative computational method, previously introduced for finite-difference solution of subsonic and slightly supercritical flow over airfoils, is extended both to apply to strongly supercritical conditions and to include full second-order accuracy in computing inviscid flows over airfoils. The nonlinear small-disturbance equations are solved iteratively by a direct, linear, elliptic solver. General, fully conservative, type-dependent difference equations are formulated, including parabolic- and shock-point transition operators that provide consistency with the integral conservation laws. These equations specialize to either first-order or to fully second-order-accurate equations. Various free parameters are evaluated for rapid convergence of the first-order scheme. Resulting pressure distributions and computing times are compared with the improved Murman-Cole line-relaxation method.

Martin, E. D.↗

One-dimensional antilocalization of electrons from spin disorder probed by nonlinear Hall effect

In recent years, nonreciprocal transport measurement has emerged as a probe of spin orbit interaction, spin texture, superconductivity, and other fundamental properties of materials. Here, we study the nonlinear Hall effect (NLHE) in Bi 2 Se 3 /CoFeB heterostructures measured by second harmonic voltage method. Magneto-optical Kerr effect measurements demonstrate the origin of the NLHE to be the asymmetric magnon scattering mechanism. Moreover, a linear relation between the nonlinear Hall resistance and the electron phase coherence length of Bi 2 Se 3 is observed between 5 and 50 K. In this work, we propose a phenomenological model that explains the enhancement of the NLHE below 50 K as a result of one-dimensional antilocalization of electrons from spin disorder, enabled by spin-momentum locking and conservation of angular momentum.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Photon–photon chemical thermodynamics of frequency conversion processes in highly multimode systems

Abstract Frequency generation in highly multimode nonlinear optical systems is inherently a complex process, giving rise to an exceedingly convoluted landscape of evolution dynamics. While predicting and controlling the global conversion efficiencies in such nonlinear environments has long been considered impossible, here, we formally address this challenge even in scenarios involving a very large number of spatial modes. By utilizing fundamental notions from optical statistical mechanics, we develop a universal theoretical framework that effectively treats all frequency components as chemical reactants/products, capable of undergoing optical thermodynamic reactions facilitated by a variety of multi-wave mixing effects. These photon–photon reactions are governed by conservation laws that directly determine the optical temperatures and chemical potentials of the ensued chemical equilibria for each frequency species. In this context, we develop a comprehensive stoichiometric model and formally derive an expression that relates the chemical potentials to the optical stoichiometric coefficients, in a manner akin to atomic/molecular chemical reactions. This advancement unlocks new predictive capabilities that can facilitate the optimization of frequency generation in highly multimode photonic arrangements, surpassing the limitations of conventional schemes that rely exclusively on nonlinear optical dynamics. Notably, we identify a universal regime of Rayleigh–Jeans thermalization where an optical reaction at near-zero optical temperatures can promote the complete and entropically irreversible conversion of light to the fundamental mode at a target frequency. Our theoretical results are corroborated by numerical simulations in settings where second-harmonic generation, sum-frequency generation and four-wave mixing processes can manifest.

Optics↗