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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Rethinking the ill-posedness of the spectral function reconstruction — Why is it fundamentally hard and how Artificial Neural Networks can help

Reconstructing hadron spectral functions through Euclidean correlation functions are of the important missions in lattice QCD calculations. However, in a Källen–Lehmann (KL) spectral representation, the reconstruction is observed to be ill-posed in practice. It is usually ascribed to the fewer observation points compared to the number of points in the spectral function. In this paper, by solving the eigenvalue problem of continuous KL convolution, we show analytically that the ill-posedness of the inversion is fundamental and it exists even for continuous correlation functions. We discussed how to introduce regulators to alleviate the predicament, in which include the Artificial Neural Networks (ANNs) representations recently proposed by the Authors in another study. The uniqueness of solutions using ANNs representations is manifested analytically and validated numerically. Reconstructed spectral functions using different regularization schemes are also demonstrated, together with their eigen-mode decomposition. We observe that components with large eigenvalues can be reliably reconstructed by all methods, whereas those with low eigenvalues need to be constrained by regulators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

Physics↗
DOE OSTI2022

Process Interactions Can Change Process Ranking in a Coupled Complex System Under Process Model and Parametric Uncertainty

For a complex hydrologic system with multiple processes and process interactions, global sensitivity analysis is often used to identify important or influential parameters for model development and improvement. The identification is complicated by process model uncertainty, when a system process can be represented by multiple process models. This study develops a new total-effect process sensitivity index to identify influential processes under model uncertainty. This is done by extending Sobol's total-effect parameter sensitivity index for one system model to total-effect process sensitivity index for multiple system models to account for uncertainty in process models and model parameters. The total-effect process sensitivity index includes not only the first-order process sensitivity index for measuring the importance of individual processes but also higher-order indices that account for process interactions. The total-effect process sensitivity index can identify an influential process that itself and its interactions with other processes influence a model output. Here, the total-effect process sensitivity index is applied to two numerical examples: (a) Sobol's G*-functions with analytical solutions of first-order and total-effect process sensitivity indices, and (b) groundwater flow models with interactions between recharge, geology, and snowmelt processes. The second evaluation shows that, due to second-order and higher-order process interactions, the first-order and total-effect process sensitivity indices give different process ranking. It is thus necessary to estimate both first-order and total-effect process sensitivity indices to appreciate the difference between the first-order impact of a process alone and the overall total-effect impact of the process itself and its interactions with other processes on a model output.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Analytic quasi-steady evolution of marginally unstable kinetic plasma instabilities in the presence of drag and scattering

The 1D bump-on-tail problem is studied in order to determine the influence of drag on quasi-steady solutions near marginal stability (1-γ d /γ L << 1) when effective collisions are much larger than the instability growth rate (ν>>γ). In this common tokamak regime, it is rigorously shown that the paradigmatic Berk–Breizman cubic equation for the nonlinear mode evolution reduces to a much simpler differential equation, dubbed the time-local cubic equation, which can be solved directly. It is found that in addition to increasing the saturation amplitude, drag introduces a shift in the apparent oscillation frequency by modulating the saturated wave envelope. Furthermore, excellent agreement is found between the analytic solution for the mode evolution and both the numerically integrated Berk–Breizman cubic equation and fully nonlinear 1D Vlasov simulations. Experimentally isolating the contribution of drag to the saturated mode amplitude for verification purposes is explored but complicated by the reality that the amount of drag cannot be varied independently of other key parameters in realistic scenarios. While the influence of drag is modest when the ratio of effective drag to effective scattering α/ν is very small, it can become substantial when α/ν ≳ 0.5, suggesting that drag should be accounted for in quantitative models of fast-ion-driven instabilities in fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Continuum shock mixture models for Ni+Al multilayers: Individual layers and bulk equations of state

Continuum shock mixture models are reviewed and applied to determine the equations of state for five different compositions of Ni x Al y ⁠, as well as bulk Ni+Al reactive multilayers, by combining the fundamental property data for elemental nickel and aluminum. From the literature, we down-select and evaluate two analytical models for the mixture Hugoniot, i.e., the well-known method of kinetic energy averaging (KEA) and a recent model proposed by Jordan and Baer [J. Appl. Phys. 111, 083516 (2012)]. Fundamentally, the former method assumes pressure equilibrium, whereas the latter assumes a common particle velocity and mixture sound speed from compressible two-phase cavitating flows. Additionally, we construct thermodynamically complete equations of state by fitting Einstein oscillator series models for the specific heat at constant volume. Finally, the solid solution approximation is invoked for intermetallic compositions, which are not strictly physical mixtures. Overall, the KEA model provides a better fit to the available Ni x Al y and Ni+Al multilayer shock compression data; however, there are combinations of material properties where the performance of these two models is thought to be reversed. Moreover, the results of this work include the first analytical solution of Jordan–Baer that does not require numerical root finding, as well as proposed modifications to the Einstein oscillator series to incorporate some effects of local pressure–temperature equilibrium and reaction–diffusion. Future work is planned that will use these equations of state in mesoscale simulations to study shock-induced reaction in Ni+Al multilayers, and the intended application is illustrated with a brief 2D hydrocode example.

36 MATERIALS SCIENCE↗
DOE OSTI2022

1D Heat Loss Models Validation Experiment

Contains data from the model validation in the 1D Heat Loss Models to Predict the Aquifer Temperature Profile during Hot/Cold Water Injection Project. The data include two COMSOL models (2D axisymmetric benchmark model and 2D Vinsome model), one python code (1D Vinsome based FEM numerical simulation), one matlab main code (1D Newton analytical solution and all results comparison visualization), and output files generated from the above models.

1D↗
DOE OSTI2021

Computational Evaluation of Thermal Response of Open-Cell Foam With Circular Pore (Computional Evaluation of Thermal Response of Open-Cell Foam with Circular Pore)

The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) critically relevant to a wide spectrum of applications, including nuclear power, electronic packaging, flame retardants, hypersonics, and gas turbine power. The work described in this paper is centered around the numerical assessment of the thermal behavior of porous materials obtained from finite element thermal modeling and simulation. Here, two-dimensional, steady state analyses were performed on unit cells with centered, circular pores using a second order accurate Galerkin finite element method (FEM). The effective thermal conductivities of the porous systems were examined, encompassing a range of porosities from 4.9% to 60.1%. The geometries of the models were generated based on ordered circular pores for each modeled porosity level. The system response quantity (SRQ) under investigation was the dimensionless effective thermal conductivity across the unit cell. The dimensionless effective thermal conductivity was compared across all simulated cases, producing a trend between porosity and effective thermal conductivity. In the presented investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) was employed to estimate discretization uncertainty as solution verification. Code verification concluded an approximately second order accurate Galerkin FEM solver. It was found that the introduction of porosity to the unit cell material structure reduces effective thermal conductivity, as anticipated. Numerical results obtained in this study are compared to an analytical solution and to a sample of empirical data.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Transport Modeling of Kinetically Limited Microscale Extraction Systems: Droplet and Supported Liquid Membrane Separations

Microfluidic droplet extraction devices can be used to efficiently measure solute phase transfer kinetics in liquid–liquid extraction systems. In this work, a droplet extraction apparatus was constructed using off-the-shelf and custom 3D printed parts for less than 110 USD. The interfacial kinetics of the transfer of Pu(IV) between an aqueous nitric acid phase and a 5 v/v% tridodecylamine (TDA) in toluene phase were characterized by determining the extent of Pu(IV) transfer between phases at different flow rates. Forward interfacial rate constants calculated from this data using an analytical model are 5.6 × 10 –3 mm s –1 under extraction (aqueous-to-organic solute transfer) conditions and 3.3 × 10 –3 mm s –1 under stripping (organic-to-aqueous solute transfer) conditions. The analytical model is valid when the rate of solute transfer across the interface between the two liquid phases has pseudo-first-order reversible reaction kinetics and is slow relative to the rate of solute transport to the interface. The change in the outlet concentration with residence time determined using the analytical model was compared with the results of a numerical model accounting for advection/diffusion to the interface in addition to kinetically limited interfacial solute transfer. These calculations revealed that for systems with forward interfacial rate constants greater than approximately 10 –2 mm s –1 , the analytical model must be supplemented with a numerical transport model accounting for an additional advection/diffusion mass transfer resistance. This threshold corresponds to a Damköhler number of one. The measured interfacial kinetic rate constants for Pu(IV)/TDA were used in a supported liquid membrane (SLM) numerical model, which showed that the Pu(IV) phase transfer kinetics are fast enough for use in a practical separation.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

A projection-based analytical Jacobian framework for chemical kinetics applications

A major challenge in simulating complex combustion systems with detailed chemical kinetic models is the cost of integrating the chemical source terms, often done using stiff ODE solvers that require frequent Jacobian evaluations. Using analytically derived Jacobian matrices instead of divided-difference-based numerical Jacobian approximations can significantly reduce the associated computational cost. However, ambiguities arise in the formulation of analytical Jacobians because the chemical state of the system, or state vector, can be expressed in multiple ways, involving variables that are typically not independent from one another. Here, in this work, the consequences of those ambiguities on practical calculations are characterized in detail, and a generalized, projection-based framework is proposed as a mitigation strategy. Performances are assessed in a series of test cases involving a variety of configurations and numerical solution approaches. Results show that with proper treatment, commonly used analytical Jacobian formulations can be considered as equivalent for practical purposes, thereby alleviating concerns that the state vector chosen to express the governing equations and corresponding analytical Jacobian may significantly impact the accuracy of the simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Simulation of Multiphase Flow and Poromechanical Effects Around Injection Wells in CO 2 Storage Sites

In geological CO 2 storage operations, wellbore deformations and leakage pathways formations can occur around injection and abandoned wells subjected to high rates and long-term CO 2 injection. To guide engineering design and prevent CO 2 leakage risks, a full understanding of the underlying physics and robust numerical models is necessary to evaluate the response of underground formations in the near wellbore region and in the reservoir. In this study, a multi-scale and multi-physics open-source simulator (GEOS) is used to simulate multiphase flow and poromechanical deformations over time in three dimensions. The governing equations for mechanical deformations of the rock body and multiphase compositional fluid flow within the rock matrix are solved with a fully coupled finite element and finite volume approach. The Drucker–Prager model with friction hardening is applied to simulate elastoplastic deformation and a multiphase fluid model with power-law correlations for relative permeability is used to model the migration of CO 2 plume, which are coupled with numerical implicit scheme. Simulation results are verified against multiple analytical solutions for multiphase flow and wellbore problems, thus demonstrating the accuracy of this advanced simulator. In two engineering applications, here we highlight the impact of elastoplastic deformation and coupled modeling for assessing induced displacements and stress perturbations, which are more pronounced in the near wellbore regions. This work focuses on short-term processes in the vicinity of injection wells where stress evolutions, rock deformations and multiphase compositional flow and transport are simulated jointly to ensure wellbore stability and prevent damage. This fully coupled geomechanical model can simulate multiphase flow and any associated poromechanical effects within the CO 2 storage site and in the surrounding formations. Such a large-scale, long-term, multi-physics simulation model is useful in many ways: it can guide operational decisions for CO 2 injection, assess the containment potential and risks of a site, and analyze the wellbore stability and integrity during and after CO 2 injection.

58 GEOSCIENCES↗
DOE OSTI2022

Fueling limits in a cylindrical viscosity-limited reactor

Recently, a method to achieve a “natural hot-ion mode” was suggested by utilizing ion viscous heating in a rotating plasma with a fixed boundary. We explore the steady-state solution to the Braginskii equations and find the parameter regime in which a significant temperature difference between ions and electrons can be sustained in a driven steady state. Here, the threshold for this effect occurs at ρ i ≳ 0.1R. An analytic, leading order low flow solution is obtained, and a numerical, moderate Mach number M ≲ 2 is investigated. The limitation is found to be at moderate Mach numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

ZND Verification Tests for Reactive Burn Models in FLAG

The ZND theory, named after Zeldovich, von Neumann, and Doering, provides a simple model for one-dimensional ideal steady-state detonation. It assumes that the detonation wave front starts with a shock that is a discontinuous jump and is followed by a finite-length reaction zone. Reactive burn (also called reactive flow) models are based on ZND theory, as they model the shock initiation and detonation process with a finite reaction rate. The ZND wave propagation test is essentially the only available test case where an analytic solution exists for verification of reactive burn models in numerical codes. However, there are extensions and variants of the ZND test that have been devised for verification of multidimensional flows. The objective of this work is to provide verification of the reactive burn models currently implemented in the Lagrangian hydrocode FLAG and investigate the influence of mesh resolution, artificial viscosity models, and the Arbitrary Lagrangian-Eulerian (ALE) Euler relaxer on the simulation results. The burn models of interest are the Wescott-Stewart-Davis (WSD) model, the Scaled Uniform Reactive Flow (SURF) model (specifically with the SURFplus model extension), and the Arrhenius shock temperature state dependent WSD (AWSD) model. Previously, Ralph Menikoff has used ZND tests for verification of the SURF and SURFplus models in the Eulerian hydrocode xRAGE. The ZND tests here are somewhat different than the approach by Menikoff. In particular, we use a piston-driven ZND detonation wave (via a prescribed constant velocity boundary condition) in a Lagrangian framework whereas Menikoff had a ZND wave followed by a invariant rarefaction wave. The xRAGE simulations were carried out on uniform grids and adaptive mesh refinement (AMR) grids. Although AMR was recently implemented in FLAG and now fully functional for 2D simulations, it will not be evaluated with ZND tests at this time. Some work has been done previously for validating the reactive burn models in FLAG. For example, the validation studies of SURF with shock-to-detonation (SDT) tests, cylinder tests, and gap-stick tests. Further validation of the AWSD, WSD, and SURF models is described in for SDT, multi-shock, cylinder, and corner-turning tests. Recently, a large parameter study with approximately twenty SDT tests was performed to validate the AWSD, WSD, SURF, and SURFplus models while also investigating mesh resolution and artificial viscosity settings. To the best of our knowledge, the current work represents the first documented verification of these burn models in FLAG. The reader should note that many of the tables and figures in this report use units of cm/g/µs, which are the default units for FLAG. However, some lengths and velocities are expressed in µm and mm/µs, respectively, which are typical units for detonation analyses.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

Tree hydrodynamic modelling of the soil–plant–atmosphere continuum using FETCH3

Modelling the water transport along the soil–plant–atmosphere continuum is fundamental to estimating and predicting transpiration fluxes. A Finite-difference Ecosystem-scale Tree Crown Hydrodynamics model (FETCH3) for the water fluxes across the soil–plant–atmosphere continuum is presented here. The model combines the water transport pathways into one vertical dimension, and assumes that the water flow through the soil, roots, and above-ground xylem can be approximated as flow in porous media. This results in a system of three partial differential equations, resembling the Richardson–Richards equation, describing the transport of water through the plant system and with additional terms representing sinks and sources for the transfer of water from the soil to the roots and from the leaves to the atmosphere. The numerical scheme, developed in Python 3, was tested against exact analytical solutions for steady state and transient conditions using simplified but realistic model parameterizations. The model was also used to simulate a previously published case study, where observed transpiration rates were available, to evaluate model performance. With the same model setup as the published case study, FETCH3 results were in agreement with observations. Through a rigorous coupling of soil, root xylem, and stem xylem, FETCH3 can account for variable water capacitance, while conserving mass and the continuity of the water potential between these three layers. FETCH3 provides a ready-to-use open access numerical model for the simulation of water fluxes across the soil–plant–atmosphere continuum.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

The liquid-conduction, vapor-flow heat pipe model in Sockeye

A single-phase heat pipe flow model implemented in the heat pipe application Sockeye is described. This model solves one-dimensional, compressible flow equations for the vapor phase in the center of a heat pipe, which are coupled to the two-dimensional heat conduction equation for the wick, liquid, and cladding, as well as to an ordinary differential equation tracking the working fluid inventory in the evaporator section of the heat pipe. This model is demonstrated with several test problems, including comparisons to analytic solutions for the vapor flow fields, analytic curves for sonic and capillary limitations of heat pipe operation, and some experimental data. The numerical solution gives excellent agreement for verification problems and good agreement with experimental results. Also, demonstrations show that the model is very robust, allowing for full simulations of heat pipe transients, including frozen startup, sonic-limited (supersonic) flow, and heat pipe shutdown.

42 ENGINEERING↗
DOE OSTI2020

Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods

In this paper, we present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Evolution of coupled weakly driven waves in a dissipative plasma

The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved and time delays become unimportant. The system is then shown to be governed by two first-order coupled autonomous differential equations of cubic order for the wave amplitudes and two complementary first-order equations for the evolution of their phases. That system of equations can be decoupled and further simplified to a single second-order differential equation of Liénard's type for each amplitude. Numerical solutions for this equation are obtained in the general case, while analytic solutions are obtained for special cases in terms of parameters related to the spacing of the resonances of the two waves in frequency space, e.g., wave lengths and oscillation frequencies. These parameters are further analyzed to find classes of quasi-steady saturation and pulsating scenarios. To classify equilibrium points, local stability analysis is applied, and bifurcation conditions are determined. When the two waves saturate at similar amplitude levels, their combined signal is shown to invariably exhibit amplitude beating and phase jumps of nearly π. In conclusion, the obtained analytical results can be used to benchmark simulations and to interpret eigenmode amplitude measurements in fusion experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗