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Utah State University's contribution to Enhancing Understanding of High Energy Density Plasmas from Wire Array and Solid Liner Implosions Using Fluid Modeling with Kinetic Closures (Final Report)
This final report pertains to work performed at Utah State University (USU) on the subject of kinetic closures for fluid simulations of high-energy-density (HED) plasmas. This report was written following the end date of the three year grant that started August 1, 2016, and ended July 31, 2019. The key aspect of the work at USU was to develop and implement kinetic closures for fluid simulations of more strongly coupled plasmas. Funds for this project provided some summer salary for the PI at USU, Dr. Eric Held, but mainly provided a robust stipend for his graduate student, David Hansen, who has worked on the project since the start date. Mr. Hansen is nearing completion of his PhD thesis which he will defend either in December of 2019 or the spring of 2020. With this award Dr. Eric Held and his PhD student David Hansen developed a computer code called {\bf X-section} that can be used to generate collisional scattering cross sections which summarize particle interactions in high-energy-density plasmas.
Robust Data-Driven Turbulence Modeling for RANS Closures Using a SciML Approach for Validation
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Independent Evaluation and Verification of Data-Driven RANS Closures in Turbulence Modeling
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Enhancing Turbulence Modeling for RANS Closures through Explainable Machine Learning Using SHAP Analysis
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Learning turbulence with machines: data-driven closures and generative models
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Current collection and current closure in the Tethered Satellite System
Current collection and closure-path modeling are examined analytically with respect to the Tethered Satellite System (TSS). A particle-in cell code is compared with a one-dimensional unmagnetized fluid code to model the behavior of a positively charged satellite in the ionosphere. The morphology of the sheath and the sheath-region processes are thus examined, and the influence of ions leaving the sheath region is found to cause the attraction of an electron current that is 40 times greater than the steady state value. The enhancement is transient and enhances the acceleration of the electrons in the sheath. A set of modified MHD equations, including those for ion inertia, quasineutrality, and electron drift, is employed to model TSS current closure. Whistler modes are found to exist and can be excited as the TSS passes through the ionosphere. Important conclusions include a significant fluctuation level in the steady state sheath, an ion void which affects the electron population, and some long-lived electrons trapped in the settled sheath with respect to two directions.
Execution of an Alternative Modeling Strategy for Closure of the Rainier Mesa Corrective Action Unit at the Nevada National Security Site
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Evaluating and Improving Scale–Awareness of a Convective Parameterization Closure Using Cloud–Resolving Model Simulations of Convection
This study aims to evaluate a revised closure of the Zhang-McFarlane (ZM) scheme for deep convection and to further improve its scale awareness. Output from two cloud-resolving model (CRM) simulations of both midlatitude organized (MC3E) and tropical unorganized (TWP-ICE) convection are used for the evaluation. By averaging the CRM output over different subdomain sizes from 64 km to 4 km, convection-associated fields are obtained to represent the fields at different horizontal resolutions of global climate models (GCMs). The convection parameterization closure is then tested using these fields. Results show that the cloud base mass flux M b determined from the closure has a relatively good relationship with CRM-simulated convection at coarse resolutions for both MC3E and TWP-ICE, but their correlation degrades at higher resolutions, especially when approaching the gray zone scale under 10 km. The fluctuation of CAPE consumption rate per unit cloud base mass flux for different convective events is found to be an important factor affecting the correlation. When averaged over the base domain, the cloud base mass flux determined by the closure is found to increase with decreasing subdomain size, implying that the closure is not scale-aware. To improve its scale-awareness, a modified closure is designed to alleviate the overprediction of convection at high GCM resolutions. Furthermore, results show that the modified closure has the scale-aware ability to suppress the overprediction problem at high GCM resolutions for both MC3E and TWP-ICE.
Toward Realistic Simulation of low-Level Clouds Using a Multiscale Modeling Framework With a Third-Order Turbulence Closure in its Cloud-Resolving Model Component
This study presents preliminary results from a multiscale modeling framework (MMF) with an advanced third-order turbulence closure in its cloud-resolving model (CRM) component. In the original MMF, the Community Atmosphere Model (CAM3.5) is used as the host general circulation model (GCM), and the System for Atmospheric Modeling with a first-order turbulence closure is used as the CRM for representing cloud processes in each grid box of the GCM. The results of annual and seasonal means and diurnal variability are compared between the modified and original MMFs and the CAM3.5. The global distributions of low-level cloud amounts and precipitation and the amounts of low-level clouds in the subtropics and middle-level clouds in mid-latitude storm track regions in the modified MMF show substantial improvement relative to the original MMF when both are compared to observations. Some improvements can also be seen in the diurnal variability of precipitation.
Communication: Fragment-based Hamiltonian model of electronic charge-excitation gaps and gap closure
Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) model uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transfer hopping integrals T and on-fragment parameters U{sup (FH)}. The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. We demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U{sup (FH)}, thus providing new insight into the nature of metal-insulator transitions. This result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.
Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows
In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.
On closures for reduced order models - A spectrum of first-principle to machine-learned avenues
For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex models, of which the von Karman vortex street is one of the most prominent. Subsequent ROMs typically relied on first principles, like mathematical Galerkin models, weakly nonlinear stability theory, and two- and three-dimensional vortex models pioneered the data-driven proper orthogonal decomposition (POD) modeling. In early POD modeling, available data were used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM, but data have made a profound impact on ROMs beyond the Galerkin expansion. In this paper, we take a modest step and illustrate the impact of data-driven modeling on one significant ROM area. Specifically, we focus on ROM closures, which are correction terms that are added to the classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations. Through simple examples, we illustrate the main modeling principles used to construct the classical ROMs, motivate and introduce modern ROM closures, and show how data-driven modeling, artificial intelligence, and machine learning have changed the standard ROM methodology over the last two decades. Finally, we outline our vision on how the state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.
A weak form equation learning approach for identifying closures in optically thin thermal radiation transport
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A mapping closure for turbulent scalar mixing using a time-evolving reference field
A general mapping-closure approach for modeling scalar mixing in homogeneous turbulence is developed. This approach is different from the previous methods in that the reference field also evolves according to the same equations as the physical scalar field. The use of a time-evolving Gaussian reference field results in a model that is similar to the mapping closure model of Pope (1991), which is based on the methodology of Chen et al. (1989). Both models yield identical relationships between the scalar variance and higher-order moments, which are in good agreement with heat conduction simulation data and can be consistent with any type of epsilon(phi) evolution. The present methodology can be extended to any reference field whose behavior is known. The possibility of a beta-pdf reference field is explored. The shortcomings of the mapping closure methods are discussed, and the limit at which the mapping becomes invalid is identified.
Reynolds stress closure in jet flows using wave models
Ways of implementing the turbulence closure scheme based on modeling the large scale coherent structures as instability waves were sought. The computational tools necessary to apply this scheme to jets of arbitrary geometry were developed. The model, developed earlier, was extended to the shock structure of supersonic jets of arbitrary geometry and multiple jets. It was found that though the qualititate features of the unsteady flow field could be predicted there were always difficulties with some of the quantitative features. This led to the new formation of the closure scheme. The schemes for computations tools which were developed are efficient and represent the application of the very powerful mathematical tools to the problems of practical significance.
488-1D Ash basin closure cap help modeling-Microdrain® liner option
At the request of Area Completion Engineering and in support of the 488-1D Ash Basin closure, the Savannah River National Laboratory (SRNL) performed hydrologic simulations of the revised 488-1D Ash Basin closure cap design using the Hydrologic Evaluation of Landfill Performance (HELP) model. The revised design substitutes a MicroDrain Liner®—50-mil linear low-density polyethylene geomembrane structurally integrated with 130-mil drainage layer—for the previously planned drainage/barrier system—300-mil geosynthetic drainage layer (GDL), 300-mil geosynthetic clay liner (GCL), and 6-inch common fill soil layer. For a 25-year, 24-hour storm event, HELP model v3.07 was employed to (1) predict the peak maximum daily hydraulic head for the geomembrane layer, and (2) ensure that South Carolina Department of Health and Environmental Control (SCDHEC) requirements for the barrier layer (i.e., ≤ 12 inches hydraulic head on top of a barrier having a saturated hydraulic conductivity ≤ 1.0E-05 cm/s) will not be exceeded. A 25-year, 24-hour storm event at the Savannah River Site (SRS) is 6.1 inches rainfall (Weber 1998). HELP model v3.07 results based upon the new planned cap design suggest that the peak maximum daily hydraulic head on the geomembrane barrier layer will be 0.179 inches for a minimum slope equal to 3%, which is approximately two orders of magnitude below the SCDHEC upper limit of 12 inches.
A comparison of three algebraic stress closures for combustor flow calculations
A comparison is made of the performance of two locally nonequilibrium and one equilibrium algebraic stress closures in calculating combustor flows. Effects of four different pressure-strain models on these closure models are also analyzed. The results show that the pressure-strain models have a much greater influence on the calculated mean velocity and turbulence field than the algebraic stress closures, and that the best mean strain model for the pressure-strain terms is that proposed by Launder, Reece and Rodi (1975). However, the equilibrium algebraic stress closure with the Rotta return-to-isotropy model (1951) for the pressure-strain terms gives as good a correlation with measurements as when the Launder et al. mean strain model is included in the pressure-strain model. Finally, comparison of the calculations with the standard k-epsilon closure results show that the algebraic stress closures are better suited for simple turbulent flow calculations.