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At least 829 records · Page 46

Entropy Splitting and Numerical Dissipation

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.

Yee, H. C.↗

Extreme Antiscaling Performance of Slippery Omniphobic Covalently Attached Liquids

Scale formation presents an enormous cost to the global economy. Classical nucleation theory dictates that to reduce the heterogeneous nucleation of scale, the surface should have low surface energy and be as smooth as possible. Past approaches have focused on lowering surface energy via the use of hydrophobic coatings and have created atomically smooth interfaces to eliminate nucleation sites, or both, via the infusion of low-surface-energy lubricants into rough superhydrophobic substrates. Although lubricant-based surfaces are promising candidates for antiscaling, lubricant drainage inhibits their utilization. Here, we develop methodologies to deposit slippery omniphobic covalently attached liquids (SOCAL) on arbitrary substrates. Similar to lubricant-based surfaces, SOCAL has ultralow roughness and surface energy, enabling low nucleation rates and eliminating the need to replenish the lubricant. To enable SOCAL coating on metals, we investigated the surface chemistry required to ensure high-quality functionalization as measured by ultralow contact angle hysteresis (<3°). Using a multilayer deposition approach, we first electrophoretically deposit (EPD) silicon dioxide (SiO 2 ) as an intermediate layer between the metallic substrate and SOCAL. The necessity of EPD SiO 2 is to smooth (<10 nm roughness) as well as to enable the proper surface chemistry for SOCAL bonding. To characterize antiscaling performance, we utilized calcium sulfate (CaSO 4 ) scale tests, showing a 20× reduction in scale deposition rate than untreated metallic substrates. Descaling tests revealed that SOCAL dramatically decreases scale adhesion, resulting in rapid removal of scale buildup. Furthermore, our work not only demonstrates a robust methodology for depositing antiscaling SOCAL coatings on metals but also develops design guidelines for the creation of antifouling coatings for alternate applications such as biofouling and high-temperature coking.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multiple relaxation and inhomogeneous broadening in resonance enhanced Raman scattering - Application to tunable infrared generation

The solutions for the imaginary susceptibility of the Raman field transition with arbitrary relaxation rates and field strengths are examined for differing sets of relaxation rates with emphasis on alkali metal vapors which have spontaneous emission dominated relaxation. The model is further expanded to include Doppler broadening and used to predict the peak gain as a function of detuning for a frequency doubled alexandrite laser-pumped cesium vapor gain cell.

Ryan, J. C.↗

Performance Modeling of Urban Air Mobility Vehicles to Support Air Traffic Management Research

The recent emergence of Urban Air Mobility (UAM) vehicles has resulted in a need for flight performance models that enable comprehensive simulation-based research on air traffic management topics such as route structure, scheduling, and separation standards. Successful performance modeling methods exist for a wide range of traditional aircraft designs. However, comparable modeling methods appropriate for UAM vehicles that combine fixed-wing and rotorcraft performance have not yet been established. One challenge to progress has been the lack of available data capturing the performance characteristics and unique flight profiles of these aircraft. This paper describes methods used to generate the required performance data and the development of performance models for UAM vehicles. Included is a review of the energy and power equations often used in developing performance models for traditional aircraft as well as a discussion of their applicability to UAM vehicles. The challenge of generating realistic performance data in over-actuated vehicles transitioning from hover to cruise flight is also addressed through an approach based on objective function optimization. A table-based performance model format adapted to UAM configurations is described, as well as parametric models intended to accompany the performance table to allow detailed modeling of power and fuel consumption during accelerated flight, turning flight, or flight at an arbitrary climb or descent rate. A discussion of future work is also provided, including the need for refinement of UAM performance modeling methods and formats, especially in conjunction with improvements to aerodynamic modeling of vehicles with complex designs where strong interaction effects may dominate important regions of the flight envelope.

Performance Modeling↗

Performance Modeling of Urban Air Mobility Vehicles to Support Air Traffic Management Research

The recent emergence of Urban Air Mobility (UAM) vehicles has resulted in a need for flight performance models that enable comprehensive simulation-based research on air traffic management topics such as route structure, scheduling, and separation standards. Successful performance modeling methods exist for a wide range of traditional aircraft designs. However, comparable modeling methods appropriate for UAM vehicles that combine fixed-wing and rotorcraft performance have not yet been established. One challenge to progress has been the lack of available data capturing the performance characteristics and unique flight profiles of these aircraft. This paper describes methods used to generate the required performance data and the development of performance models for UAM vehicles. Included is a review of the energy and power equations often used in developing performance models for traditional aircraft as well as a discussion of their applicability to UAM vehicles. The challenge of generating realistic performance data in over-actuated vehicles transitioning from hover to cruise flight is also addressed through an approach based on objective function optimization. A table-based performance model format adapted to UAM configurations is described, as well as parametric models intended to accompany the performance table to allow detailed modeling of power and fuel consumption during accelerated flight, turning flight, or flight at an arbitrary climb or descent rate. A discussion of future work is also provided, including the need for refinement of UAM performance modeling methods and formats, especially in conjunction with improvements to aerodynamic modeling of vehicles with complex designs where strong interaction effects may dominate important regions of the flight envelope.

Performance Modeling↗

Imaginary-time correlation function thermometry: A new, high-accuracy and model-free temperature analysis technique for x-ray Thomson scattering data

The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [Dornheim et al., Nat. Commun. 13, 7911 (2022)], we have introduced a formally exact methodology that allows extracting the temperature of arbitrary complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Solution and sensitivity analysis of nonlinear equations using a hypercomplex-variable Newton-Raphson method

Here, the classical Newton-Raphson (NR) method for solving nonlinear equations is enhanced in two ways through the use of hypercomplex variables and algebra. In particular, i) the Jacobian is computed in a highly accurate and automated way, and ii) the derivative of the solution to the nonlinear equations is computed with respect to any parameter contained within the system of equations. These advances provide two significant enhancements in that it is straightforward to provide an accurate Jacobian and to construct a reduced order model (ROM) of arbitrary order with respect to any parameter of the system. The ROM can then be used to approximate the solution for other parameter values without requiring additional solutions of the nonlinear equations. Several case studies are presented including 1D and 2D academic examples with fully functioning Python code provided. Additionally, a case of study of the catenary of an elastic cable subject to its own weight and a vertical point load. Derivatives up to 10th order were computed with respect to material, loading, and geometrical parameters. The derivatives were used to generate reduced order models of the cable deformation and reaction forces at its ends with respect to multiple input parameters. Results show that from a single hypercomplex evaluation of the cable under a single vertical point load, it is possible to generate an accurate reduced order model capable of predicting the cable deformation with 1.5 times the load in the opposite direction and with 3.5 times the load in the same direction without resolving the system of equations.

97 MATHEMATICS AND COMPUTING↗

A global model of the earth's ionosphere for use in space applications

A general expression is derived for the F layer electron density profile as a function of latitude and longitude for that part of the earth which is in direct sunlight including dawn and dusk. Furthermore, the derived model is extended to encompass the night-time ionosphere. The expressions allow determination by standard means of the range correction for arbitrary ray path directions. It is also shown that the naive application of the Chapman ionospheric model entails range correction errors which for low elevation angles (less than 20 deg) and large solar zenith angles (40 deg) cannot be tolerated. Numerical calculations are displayed showing the dependence of the range correction on the pertinent parameters.

Von Roos, O. H.↗

The mirror and ion cyclotron anisotropy instabilities

The linear dispersion equation for fully electromagnetic waves and instabilities at arbitrary directions of propagation relative to a background magnetic field B(0) in a homogeneous Vlasov plasma is solved numerically for bi-Maxwellian particle distributions. For isotropic plasmas the dispersion and damping of the three modes below the proton cyclotron frequency are studied as functions of Beta(i) and T(e)/T(i). The transport ratios of helicity, cross-helicity, Alfven ratio, compressibility, and parallel compressibility are defined. Under the condition that the proton temperature perpendicular to B(0) is greater than the parallel temperature, the growth rates and transport ratios of the mirror instability and the ion cyclotron anisotropy instability are examined and compared. Both the proton parallel compressibility and the proton Alfven ratio are significantly different for the two growing modes.

Gary, S. P.↗

Generic hypersonic vehicle performance model

An integrated computational model of a generic hypersonic vehicle was developed for the purpose of determining the vehicle's performance characteristics, which include the lift, drag, thrust, and moment acting on the vehicle at specified altitude, flight condition, and vehicular configuration. The lift, drag, thrust, and moment are developed for the body fixed coordinate system. These forces and moments arise from both aerodynamic and propulsive sources. SCRAMjet engine performance characteristics, such as fuel flow rate, can also be determined. The vehicle is assumed to be a lifting body with a single aerodynamic control surface. The body shape and control surface location are arbitrary and must be defined. The aerodynamics are calculated using either 2-dimensional Newtonian or modified Newtonian theory and approximate high-Mach-number Prandtl-Meyer expansion theory. Skin-friction drag was also accounted for. The skin-friction drag coefficient is a function of the freestream Mach number. The data for the skin-friction drag coefficient values were taken from NASA Technical Memorandum 102610. The modeling of the vehicle's SCRAMjet engine is based on quasi 1-dimensional gas dynamics for the engine diffuser, nozzle, and the combustor with heat addition. The engine has three variable inputs for control: the engine inlet diffuser area ratio, the total temperature rise through the combustor due to combustion of the fuel, and the engine internal expansion nozzle area ratio. The pressure distribution over the vehicle's lower aft body surface, which acts as an external nozzle, is calculated using a combination of quasi 1-dimensional gas dynamic theory and Newtonian or modified Newtonian theory. The exhaust plume shape is determined by matching the pressure inside the plume, calculated from the gas dynamic equations, with the freestream pressure, calculated from Newtonian or Modified Newtonian theory. In this manner, the pressure distribution along the vehicle after body expansion surface is then determined. The aerodynamic modeling, the engine modeling, and the exhaust plume analysis are described in more detail. A description of the computer code used to perform the above calculations is given and an input/output example is then given. The computer code is available on a Macintosh floppy disk.

Chavez, Frank R.↗

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.

TURBINE COOLING↗

Development of PFLOTRAN Transport Capability for Use in the Waste Isolation Pilot Plant Performance Assessment - 20545

Waste Isolation Pilot Plant (WIPP) performance assessment (PA) calculations estimate the probability of radionuclide release from the repository to the land surface and across the land withdrawal boundary for a regulatory period of 10,000 years after facility closure. Simulations of flow and transport in the repository and the surrounding Salado Formation are foundational to the PA. Because proposed additional waste emplacement panels would result in an asymmetric repository layout, the US Department of Energy (DOE) is preparing to transition to use of a three-dimensional (3-D) model domain for simulation of flow and transport instead of the two-dimensional (2-D) flared grid domain currently used. DOE has charged Sandia National Laboratories with developing the capability necessary to simulate processes affecting flow and transport in the WIPP in PFLOTRAN, an open-source massively parallel multi-phase flow and reactive transport code. The new flow and transport capabilities developed in PFLOTRAN incorporate WIPP-specific process models and will replace the 2-D simulators (BRAGFLO and NUTS) that are currently utilized for Salado flow and transport calculations in WIPP PA. The focus of this paper is on the development of a new Nuclear Waste Transport (NWT) mode in PFLOTRAN that has all of the capabilities necessary for Salado transport simulations, including the ability to handle complete dry-out (100% gas saturation) of arbitrary cells in the model domain, radionuclide mass conservation at step changes in porosity associated with borehole intrusion, and the ability to calculate fluxes on a flared grid. The new PFLOTRAN transport capability and a suite of verification tests were designed around a list of functional requirements for WIPP PA calculations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Recovering non-Maxwellian particle velocity distribution functions from collective Thomson-scattered spectra

Collective optical Thomson scattering (TS) is a diagnostic commonly used to characterize plasma parameters. These parameters are typically extracted by a fitting algorithm that minimizes the difference between a measured scattered spectrum and an analytic spectrum calculated from the velocity distribution function (VDF) of the plasma. However, most existing TS analysis algorithms assume that the VDFs are Maxwellian, and applying an algorithm that makes this assumption does not accurately extract the plasma parameters of a non-Maxwellian plasma due to the effect of non-Maxwellian deviations on the TS spectra. We present new open-source numerical tools for forward modeling analytic spectra from arbitrary VDFs and show that these tools are able to more accurately extract plasma parameters from synthetic TS spectra generated by non-Maxwellian VDFs compared to standard TS algorithms. Estimated posterior probability distributions of fits to synthetic spectra for a variety of example non-Maxwellian VDFs are used to determine uncertainties in the extracted plasma parameters and show that correlations between parameters can significantly affect the accuracy of fits in plasmas with non-Maxwellian VDFs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

Meshes↗

Holographic open quantum systems: toy models and analytic properties of thermal correlators

We present a unified picture of open quantum systems, the theory of a system probing a noisy thermal environment, distilling lessons learnt from previous holographic analyses. Our treatment is applicable both when the system is coupled to short-lived (Markovian), and long-lived (non-Markovian) environmental degrees of freedom. The thermal environment is modeled using an asymptotically AdS black hole, and the systems of interest are simple probe field theories. The effective stochastic dynamics of the system is governed by real-time thermal correlators, which we compute using the gravitational Schwinger-Keldysh (grSK) geometry. We describe the structure of arbitrary tree-level contact and exchange Witten diagrams in the grSK geometry. In particular, we argue, that all such diagrams reduce to integrals supported on a single copy of the exterior of the black hole. The integrand is obtained as a multiple discontinuity of a function comprising ingoing boundary-bulk propagators, monodromy functions which appear as radial Boltzmann weights, and vertex factors. These results allow us to deduce the analytic structure of real-time thermal n-point functions in holographic CFTs. We illustrate the general statements by a two-dimensional toy model, dual to fields in the BTZ background, which we argue captures many of the essential features of generic open holographic QFTs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions

Surveys of cosmological large-scale structure (LSS) are sensitive to the presence of local primordial non-Gaussianity (PNG), and may be used to constrain models of inflation. Local PNG, characterized by f NL ⁠, the amplitude of the quadratic correction to the potential of a Gaussian random field, is traditionally measured from LSS two-point and three-point clustering via the power spectrum and bi-spectrum. We propose a framework to measure f NL using the configuration space two-point correlation function (2pcf) monopole and three-point correlation function (3pcf) monopole of survey tracers. Our model estimates the effect of the scale-dependent bias induced by the presence of PNG on the 2pcf and 3pcf from the clustering of simulated dark matter haloes. We describe how this effect may be scaled to an arbitrary tracer of the cosmological matter density. The 2pcf and 3pcf of this tracer are measured to constrain the value of f NL ⁠. In LSS surveys, the effect of imaging systematics on two-point statistics is often degenerate with the PNG signal. Our proposed model employs three-point statistics primarily to break this degeneracy. Using simulations of luminous red galaxies observed by the Dark Energy Spectroscopic Instrument (DESI), we demonstrate the accuracy and constraining power of our method. Our forecast indicates the ability to constrain f NL to a precision of σf NL ≈ 22 with one year of DESI survey data, as well as the ability to constrain the imaging systematic weights in situ.

early Universe↗