A Second-Order-in-Time, Explicit Approach Addressing the Redundancy in the Low-Mach, Variable-Density Navier-Stokes Equations
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Reuter, Bryan William [Sandia National Laboratorie↗
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Polarimetric Radar Variables in Snowfall at Ka- and W-Band Frequency Bands: A Comparative Analysis
Dual-frequency millimeter-wavelength radar observations in snowfall are analyzed in order to evaluate differences in conventional polarimetric radar variables such as differential reflectivity (ZDR) specific differential phase shift (K DP ) and linear depolarization ratio (LDR) at traditional cloud radar frequencies at Ka and W bands (~35 and ~94 GHz, correspondingly). Low radar beam elevation (~5°) measurements were performed at Oliktok Point, Alaska, with a scanning fully polarimetric radar operating in the horizontal–vertical polarization basis. This radar has the same gate spacing and very close beam widths at both frequencies, which largely alleviates uncertainties associated with spatial and temporal data matching. It is shown that observed Ka- and W-band Z DR differences are, on average, less than about 0.5 dB and do not have a pronounced trend as a function of snowfall reflectivity. The observed Z DR differences agree well with modeling results obtained using integration over nonspherical ice particle size distributions. For higher signal-to-noise ratios, KDP data derived from differential phase measurements are approximately scaled as reciprocals of corresponding radar frequencies indicating that the influence of non-Rayleigh scattering effects on this variable is rather limited. This result is also in satisfactory agreement with data obtained by modeling using realistic particle size distributions. Observed Ka- and W-band LDR differences are strongly affected by the radar hardware system polarization “leak” and are generally less than 4 dB. Smaller differences are observed for higher depolarizations, where the polarization “leak” is less pronounced. Realistic assumptions about particle canting and the system polarization isolation lead to modeling results that satisfactorily agree with observational dual-frequency LDR data.
42 ENGINEERING↗
Charge Recombination with Fractional Reaction Orders in Water-Splitting Dye-sensitized Photoelectrochemical Cells
In water-splitting dye-sensitized photoelectrochemical cells (WS-DSPECs), charge recombination competes with catalytic water oxidation to determine the overall efficiency of the system. The kinetics of these processes have been difficult to understand because transient absorbance (TA) experiments typically show nearly complete charge recombination on the sub-millisecond timescale; in contrast, electrochemical measurements such as open circuit photovoltage decay suggest a charge recombination timescale that is 2-3 orders of magnitude longer. Here we explore these processes with dye-sensitized nanocrystalline TiO 2 and TiO 2 /Ta 2 O 5 core-shell photoanodes in aqueous electrolytes using TA spectroscopy, intensity-modulated photovoltage spectroscopy (IMVS), and photoelectrochemical impedance spectroscopy (PEIS). The fast recombination rates measured by TA result from strong laser excitation that leads to high electron occupancy in TiO 2 , whereas IMVS modulates the concentration of charge-separated states near solar irradiance levels. The recombination processes measured by electrochemical methods such as IMVS, PEIS, and transient photovoltage are the discharging of injected electrons in TiO 2 , as evidenced by the close agreement betweeen the nearly first-order recombination rates probed by IMVS and the RC time constants derived from PEIS data. However, IMVS measurements at variable probe light intensity reveal that the reaction orders for the recombination of injected electrons with oxidized sensitizer molecules are far from unity. In conclusion, this kinetic analysis is relevant to understanding steady-state recombination rates in full WS-DSPECs in which molecular and nanoparticle catalysts are used to oxidize water.
14 SOLAR ENERGY↗
An in-silico NMR laboratory for nuclear magnetic shieldings computed via finite fields: Exploring nucleus-specific renormalizations of MP2 and MP3
Here we developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics
We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10 -5 , which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM + -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.
97 MATHEMATICS AND COMPUTING↗
Stochastic simulations of temporally and spatially variable Fe cycling within a floodplain aquifer
This data package contains model input and output files for local and global sensitivity analysis (SA) of a reactive transport model simulating redox cycling within a floodplain aquifer. The reaction network is implemented in CrunchFlow and focuses on spatially and temporally heterogeneous Fe cycling, though it contains several other species and redox pathways (37 aqueous species and 7 minerals in total). The package contains data from 600 Monte Carlo simulations (for global SA) and 104 one-at-a-time simulations (for local SA). It includes all input files required to run the CrunchFlow model, as well as limited model output – .csv files containing time series of primary species concentrations at 21 grid cells within the domain. These time series files contain the following species: H+, CO32-, SO42-, Cl-, Ca2+, Mg2+, Na+, K+, Fe(II), Fe(III), HS-, CH3COO-, O2(aq), S(aq), and Br-.These data were used to demonstrate the application of a novel form of global SA, distance-based generalized sensitivity analysis (DGSA) to a reactive transport model. The 2D model simulates the export of reduced species from pockets of fine-grained, organic-rich sediments embedded in a coarse sand aquifer. Stochastic simulations jointly varied 17 key model input parameters across several orders of magnitude, including the spatial variability of each parameter. DGSA on the model results reveal that the amplitude and variability of exported Fe(II) are most sensitive to the interaction between sand permeability and individual reaction rates. By contrast, the propagation of reducing conditions downgradient from the fine-grained lenses depends most heavily on the rate of dissolved organic carbon and sulfate release from the fines.
54 ENVIRONMENTAL SCIENCES↗
Ground-Active Arthropod Diversity Under Energycane and Biomass Sorghum Production
Energycane and biomass sorghum are two of the most promising cellulosic energy crops in the southeastern US. Research on these two energy crops has focused mainly on biomass production, and there is a lack of knowledge on their ability to promote biodiversity and ecosystem services. This paper presents results from a comprehensive study on ground-active arthropod diversity in seven sites across five states in the southeastern US (Florida, Georgia, Louisiana, Mississippi, and Texas). Pitfall traps were deployed four times during each crop season for energycane, biomass sorghum, and a local reference conventional crop from 2020 to 2022. Arthropod abundance (individuals/(trap × day)) values were 4.9 ± 0.46, 3.7 ± 0.18, and 2.6 ± 0.16 (mean ± stderr) for conventional crops, biomass sorghum, and energycane, respectively, with a significant difference found only between conventional crops and energycane. Individuals were identified to arthropod orders, and Hill’s diversity indices were calculated based on the number of individuals in each arthropod order instead of the number of individuals in each arthropod species. Order-based arthropod richness values were 5.3, 5.2, and 4.8 for biomass sorghum, conventional crops, and energycane, with significant difference found only between biomass sorghum and energycane. There was no significant difference in the order-based Shannon diversity and Simpson diversity between the three crop types. The effective number of arthropod orders for the two energy crops decreased from 5.0 to 3.4 to 2.9 with increasing order of diversity from arthropod richness to Shannon diversity to Simpson diversity. The explained variability by environmental factors also decreased with increasing Hill’s order of diversity. The results from this study indicate no significant advantage in order-based arthropod diversity in growing biomass sorghum and energycane. This research fills a critical knowledge gap in understanding the impacts of cellulosic energy crop production on biodiversity and ecosystem services.
Yang, Yubin↗
Hydrodynamics and Load Shedding Behavior of a Variable-Geometry Oscillating Surge Wave Energy Converter (OSWEC)
In order to improve their long-term viability, wave energy converters (WECs) need to be able to shed loads when a threshold wave condition is exceeded. As shown by Tom et al. (2016) [1], provision of adjustable flaps within the body of an oscillating surge wave energy converter (OSWEC) allows wave energy to pass through the device. A control system may then be able to open and close the flaps when waves approaching the device exceed preset thresholds. The variable-geometry OSWEC (VG-OSWEC) concept studied in this paper is a bottom-hinged, rectangular wave paddle with five flaps of elliptical cross-section embedded into the face of the paddle. System ID tests were conducted on this VG-OSWEC device at a 1:14 scale in a wave basin. Free decay tests showed that the damping was distinctly nonlinear when the flaps were fully open, and the natural frequency increased by 40% when compared with the flaps in a fully closed configuration. Tests with regular wave conditions were used to develop the response amplitude operator for the rotational motion about the hinge. These response amplitude operator results when compared with numerical simulations run using WEC-Sim/WAMIT and ANSYS AQWA, show strong agreement with the flap open and closed conditions. The regular-wave condition measurements also show that the wave excitation moment about the hinge was reduced by up to 60% when the flaps were fully open. The experiments serve to demonstrate the potential of the variable geometry design to shed loads and survive harsh ocean environments.
load shedding↗
A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Scaling exponents for ordered maxima
We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences and investigate the probability S N that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability S N is universal: it does not depend on the distribution from which the random variables are drawn. For two sequences, S N ~N –1/2 , and in general, the decay is algebraic, S N ~N –σm , for large N. We analytically obtain the exponent σ 3 ≅1.302931 as root of a transcendental equation. Moreover, the exponents σ m grow with m, and we show that σ m ~m for large m.
97 MATHEMATICS AND COMPUTING↗
Model Predictive Control of GTAW Weld Pool Penetration
Weld pool penetration is a major implication of weld integrity but it is not directly measurable. The key to solving this issue is to find or create observable phenomena that can be used to derive the penetration. An innovative method has recently been proposed/developed to derive the penetration from the reflection of projected laser from an oscillating weld pool surface. Yet, in addition to the penetration, the oscillation, thus the reflection determined by it, also depends on the pulse amplitude of the current, which needs to be adjusted as the control variable to feedback control the penetration as the output. This dependence imposes a constraint on the control algorithm such that the adjustment of the control variable must be relatively slow to minimize additional sources that affect the oscillation/sensor. This restriction on the control variable adjustment also brings challenges to the identification of the dynamic model of the weld process to be controlled, which has to apply a varying control signal to stimulate the dynamics. To solve these issues, this letter proposes using a low order model to catch the dominant dynamics such that a high speed variation in the control signal can be avoided when choosing the model predictive control algorithm. This allows use of relatively poor models to determine the adjustment on the pulsing amplitude, and still achieves relatively accurate control. Experimental results verified the effectiveness of the resultant penetration control system despite the restrictions imposed by the penetration sensor, which affect the identification of high order dynamics and free adjustments of control variables.
42 ENGINEERING↗
Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A well-posed and stable stochastic Galerkin formulation of the incompressible Navier–Stokes equations with random data
We present a well-posed stochastic Galerkin formulation of the incompressible Navier–Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimate for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Accurate models of the added mass force of a uniform random distribution of spherical particles or bubbles
The added mass force resulting from the acceleration of a body in a fluid is of fundamental and practical interest in dispersed multiphase flows. Euler–Lagrange (EL) and Euler–Euler (EE) simulations require closure terms for the added mass force in order to accurately couple the conserved variables between phases. Presently, a more thorough understanding of the added mass force in a multi-particle system is developed based on potential flow resulting in a resistance matrix formulation analogous to Stokesian dynamics. This formulation is then used to generate a dataset of added mass resistance matrices for large systems of randomly generated particles. This methodology is used to create a volume fraction corrected binary model for predicting the added mass force in large systems as well as generate statistics of the added mass force in such systems. This work provides clarification to the theory of the added mass force for particle clouds, and modelling options that may be implemented in existing EL and EE codes.
42 ENGINEERING↗
Material Characterization of Hierarchical Tunable Pore Size Polymer Foams Used in the MARBLE Mix Morphology Experiment
One of the great challenges of inertial confinement fusion and high energy density experiments is understanding the effects of mix on thermonuclear burn. The MARBLE campaign, conceived at Los Alamos National Laboratory, aims to gather new insights into this issue by utilizing unique target capsules containing polymer foams of variable pore sizes, tunable over an order of magnitude. Such capsules allow the degree of initial heterogeneity to be controlled experimentally for the first time. Here, we describe the various characterization efforts used to gain understanding of the chemical structure and behavior of the foam. Previous experiments were not sensitive to foam physical properties, and the MARBLE platform has aided in the development of techniques to measure foam properties such as deuterium content, density variation, hydrogen adsorption, and pore size and volume distribution.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Spherically symmetric Einstein-aether perfect fluid models
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.
79 ASTRONOMY AND ASTROPHYSICS↗
Snowflake: A Lightweight Portable Stencil DSL
Stencil computations are not well optimized by general-purpose production compilers and the increased use of multicore, manycore, and accelerator-based systems makes the optimization problem even more challenging. In this paper we present Snowflake, a Domain Specific Language (DSL) for stencils that uses a 'micro-compiler' approach, i.e., small, focused, domain-specific code generators. The approach is similar to that used in image processing stencils, but Snowflake handles the much more complex stencils that arise in scientific computing, including complex boundary conditions, higher-order operators (larger stencils), higher dimensions, variable coefficients, non-unit-stride iteration spaces, and multiple input or output meshes. Snowflake is embedded in the Python language, allowing it to interoperate with popular scientific tools like SciPy and iPython; it also takes advantage of built-in Python libraries for powerful dependence analysis as part of a just-in-time compiler. We demonstrate the power of the Snowflake language and the micro-compiler approach with a complex scientific benchmark, HPGMG, that exercises the generality of stencil support in Snowflake. By generating OpenMP comparable to, and OpenCL within a factor of 2x of hand-optimized HPGMG, Snowflake demonstrates that a micro-compiler can support diverse processor architectures and is performance-competitive whilst preserving a high-level Python implementation.
97 MATHEMATICS AND COMPUTING↗
ODD (Version 0.X)
The Orthogonal Diffusion Discretizations (ODD) library is a collection of low order (Diffusion, P1, Ray Tracing, and Variable Eddington Factor (VEF)) thermal radiation solvers for orthogonal structured grids driven by an application programing interface (API).
Cleveland, Mathew↗