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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Effect of Computational Schemes on Coupled Flow and Geo-Mechanical Modeling of CO 2 Leakage through a Compromised Well

Carbon capture, utilization, and storage (CCUS) describes a set of technically viable processes to separate carbon dioxide (CO 2 ) from industrial byproduct streams and inject it into deep geologic formations for long-term storage. Legacy wells located within the spatial domain of new injection and production activities represent potential pathways for fluids (i.e., CO 2 and aqueous phase) to leak through compromised components (e.g., through fractures or micro-annulus pathways). The finite element (FE) method is a well-established numerical approach to simulate the coupling between multi-phase fluid flow and solid phase deformation interactions that occur in a compromised well system. We assumed the spatial domain consists of a three-phases system: a solid, liquid, and gas phase. For flow in the two fluids phases, we considered two sets of primary variables: the first considering capillary pressure and gas pressure (PP) scheme, and the second considering liquid pressure and gas saturation (PS) scheme. Fluid phases were coupled with the solid phase using the full coupling (i.e., monolithic coupling) and iterative coupling (i.e., sequential coupling) approaches. The challenge of achieving numerical stability in the coupled formulation in heterogeneous media was addressed using the mass lumping and the upwinding techniques. Numerical results were compared with three benchmark problems to assess the performance of coupled FE solutions: 1D Terzaghi’s consolidation, Liakopoulos experiments, and the Kueper and Frind experiments. We found good agreement between our results and the three benchmark problems. For the Kueper and Frind test, the PP scheme successfully captured the observed experimental response of the non-aqueous phase infiltration, in contrast to the PS scheme. These exercises demonstrate the importance of fluid phase primary variable selection for heterogeneous porous media. We then applied the developed model to the hypothetical case of leakage along a compromised well representing a heterogeneous media. Considering the mass lumping and the upwinding techniques, both the monotonic and the sequential coupling provided identical results, but mass lumping was needed to avoid numerical instabilities in the sequential coupling. Additionally, in the monolithic coupling, the magnitude of primary variables in the coupled solution without mass lumping and the upwinding is higher, which is essential for the risk-based analyses.

deformation flow↗
DOE OSTI2025

The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can serve as a mini-review of PMC. In a recently published article, P. M. Stevenson has claimed that “the PMC is ineffective and does nothing to resolve the renormalization-scheme-dependence problem”, concluding incorrectly that the success of PMC predictions is due to the PMC being a “laborious, ad hoc, and back-door” version of the Principle of Minimal Sensitivity (PMS). We show that such conclusions are incorrect, deriving from a misinterpretation of the PMC and an overestimation of the applicability of the PMS. The purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization schemes and scale ambiguities. We demonstrate that the PMC predictions satisfy all the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations, which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann–Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization-group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 1: Dust budget analyses and the impacts of a revised coupling scheme

Abstract. An earlier study evaluating dust life cycle in the Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 (EAMv1) has revealed that the simulated global mean dust lifetime is substantially shorter when higher vertical resolution is used, primarily due to significant strengthening of dust dry removal in source regions. This paper demonstrates that the sequential splitting of aerosol emissions, dry removal, and turbulent mixing in the model's time integration loop, especially the calculation of dry removal after surface emissions and before turbulent mixing, is the primary reason for the vertical resolution sensitivity reported in that earlier study. Based on this reasoning, we propose a revised numerical process coupling scheme that requires the least amount of code changes, in which the surface emissions are applied before turbulent mixing instead of before dry removal. The revised scheme allows newly emitted particles to be transported aloft by turbulence before being removed from the atmosphere, and hence better resembles the dust life cycle in the real world. Sensitivity experiments show that the revised process coupling substantially weakens dry removal and strengthens vertical mixing in dust source regions. It also strengthens the large-scale transport from source to non-source regions, strengthens dry removal outside the source regions, and strengthens wet removal and activation globally. In transient simulations of the years 2000–2009 conducted using 1∘ horizontal grid spacing, 72 vertical layers, and unchanged tuning parameters of emission strength, the revised process coupling leads to a 40 % increase in the global total dust burden and an increase of dust lifetime from 1.8 to 2.5 d in terms of 10-year averages. Weakened dry removal and increased mixing ratios are also seen for other aerosol species that have substantial surface emissions, although the changes in mixing ratio are considerably smaller for the submicron species than for dust and sea salt. Numerical experiments confirm that the revised coupling scheme significantly reduces the strong and non-physical sensitivities of model results to vertical resolution in the original EAMv1. This provides a motivation for adopting the revised scheme in EAM as well as for further improvements on the simple revision presented in this paper.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes

Abstract. Part 1 (Wan et al., 2024) of this study discusses the motivation and empirical evaluation of a revision to the aerosol-related numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The framework distinguishes the error due to numerical splitting from the error due to the time integration method(s) used for each individual process. Such a distinction results in a framework that provides an intuitive understanding of the causes of the splitting error. The application of this framework to the dust life cycle in EAMv1 confirms (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes and (ii) that the revised splitting reduces that artificial strengthening. While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and time step size for the isolated integration of processes. Such a perspective has the potential for the rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.

58 GEOSCIENCES↗
DOE OSTI2023

A Novel Multi-Agent Deep Reinforcement Learning-enabled Distributed Power Allocation Scheme for mmWave Cellular Networks

We consider the power allocation problem over shared spectrum for millimeter-Wave (mmWave) cellular downlink. Existing approaches usually find sub-optimal solutions by solving a non-convex optimization which leads to scalability issues due to centralized control. Therefore, distributed and adaptive approaches are desirable. Recently, model-free Deep Reinforcement Learning (DRL) has achieved success in such wireless resource management tasks. By modeling the radio environment as a Markov Decision Process (MDP) with the base stations (BSs) being the agents, power allocation can be automated at the agent level with comparable throughput performance to conventional centralized schemes. The multi-agent setting presents new challenges as the radio environment is impacted by the joint actions of the agents and is no longer stationary from any individual agent’s perspective. Existing literature bypasses this non-stationarity violation by ignoring it which may cause performance degradation. To tackle this issue, we propose a distributed continuous power allocation scheme based on a modified version of multi-agent Deep Deterministic Policy Gradient (MADDPG) that is tailored for the distributed multiple-agent setting. The proposed scheme employs a centralized-training distributed-execution framework where Q-functions are trained over subsets of BSs while each BS determines its transmit power based only on its own local observation. It admits constant per-BS communication and computation complexity and is thus scalable to large networks. Numerical evaluation shows that the proposed scheme adapts well to a wide range of interference conditions and can achieve comparable or better performance than several state-of-the-art non-learning approaches.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2026

A sweeping positivity-preserving high-order finite difference WENO scheme for Euler equations

We develop a simple, high-order, conservative and robust positivity-preserving sweeping procedure for the density and the nonlinear pressure function in the compressible Euler equations. Using the scaling limiter in Zhang and Shu (J Comput Phys 229:3091–3120, 2010), we obtain a non-trivial extension of the scalar sweeping technique in Liu et al. (J Sci Comput 73:1028–1071, 2017) for the positivity of pressure. The sweeping procedure developed in this paper is a post-processing technique, which can be applied to any concave functions of the conserved variables in hyperbolic conservation law systems. Thus, it has applications beyond the Euler equations. This procedure preserves positivity and conservation of physical quantities without destroying the accuracy of the underlying scheme. The algorithm works for general schemes including finite difference, finite volume and discontinuous Galerkin methods; however, in this paper we focus on finite difference weighted essentially non-oscillatory (WENO) methods. As a result, we provide numerical tests of the fifth-order finite difference WENO scheme to demonstrate the accuracy and robustness of the technique.

Compressible Euler equations↗
DOE OSTI2020

Effect of the numerical discretization scheme in Shock-Driven turbulent mixing simulations

In this work, we evaluate the effects of distinct numerical strategies in simulations of shock-driven turbulent mixing. An air-SF 6 -air gas curtain subjected to Mach 1.2 shock-waves is computed with Implicit Large-Eddy Simulation based on three numerical schemes: directional-split with Harten-Lax-van Leer (HLL) solver; directional-unsplit using HLL-Contact (HLLC) solver; and directional-unsplit with HLLC solver and a Low Mach number Correction (LMC). The results illustrate the importance of the numerical strategy to the accuracy of the predictions. Whereas both split and unsplit schemes result in a similar spatial development of the initial shock-driven instability, only the unsplit schemes can predict the turbulent mixing transition after reshock observed by the laboratory experiments. Such feature increases the mixing rate of the two fluids, this being particularly pronounced when the LMC is active due to i) the reduced flow Mach number, and ii) the larger effective Reynolds number. Since the selected mixing problem is driven by the deposition of vorticity at the fluids’ interface, the resultant flow physics is analyzed by investigating the contribution of distinct inviscid mechanisms to the production of vorticity: baroclinicity, stretching, and dilatation. As expected, it is observed that the production of vorticity is initially dominated by the baroclinicity mechanism. Yet, the relevance of the remainder mechanisms is enhanced after the reshock and may even surpass the baroclinicity term.

42 ENGINEERING↗
DOE OSTI2025

Fabrication of α-Fe 2 O 3 Nanoparticles/g-C 3 N 4 Direct Z-Scheme Heterojunction of Durable Photocatalytic Activity

The fabrication of a nanohybrid photocatalyst that combines α-Fe 2 O 3 nanoparticles with graphitic carbon nitride (g-C 3 N 4 ) is reported. The ensuing direct Z-scheme heterojunction greatly boosts the photocatalytic activity of the α-Fe 2 O 3 /g-C 3 N 4 nanohybrids. This results in organic dye degradation rates more than two times higher than its individual components, promoted by the efficient charge separation and transfer of the Z-scheme heterojunction mechanism of the nanohybrid photocatalyst. In addition, recyclability tests show an outstanding stability of the nanohybrids spanning five consecutive dye degradation experiments, during which the degradation rate is slightly improved. The origin of the improved photocatalytic performance of the nanohybrid lies in the intimate interaction between α-Fe 2 O 3 and g-C 3 N 4 afforded by the two-step fabrication process, which enables the direct and controlled growth of α-Fe 2 O 3 nanoparticles on g-C 3 N 4 . A first ultrasound impregnation step promotes the effective anchoring of stable Fe species via Fe–N and C–N/C–O bonding, while a second microwave phase conversion step induces the subsequent growth of α-Fe 2 O 3 nanoparticles on the g-C 3 N 4 sheets. Careful control of the FeCl 3 precursor concentration up to a threshold value of 0.25 M during impregnation enables complete control over their size and phase. This approach clearly highlights the benefits of microwave reactor systems in the fabrication of hematite-based Z-scheme photocatalytic, overcoming the limitations of conventional thermal treatment technology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Unexpected Changes of Aerosol Burdens With Decreased Convection in the Context of Scale-Aware Convection Schemes

Atmospheric aerosols in global climate models (GCMs) can be removed by both large-scale and convective precipitation. As the horizontal resolution of GCMs increases, it is expected that large-scale precipitation increases and convective precipitation decreases if scale-aware convection schemes are well developed. Here, to explore its impact on aerosol burdens, this study develops a novel method and applies it to the National Center for Atmospheric Research Community Atmosphere Model version 5.3 to mimic the behavior of scale-aware convective schemes. Surprisingly, it is found that aerosol burden increases globally as convective precipitation decreases and large-scale precipitation increases, which can be attributed to the reduced light rain. In the light-rain intensity category, the decreased frequency of convective precipitation is not offset by the increased frequency of large-scale precipitation. Therefore, for aerosol simulations in high-resolution GCMs using scale-aware convection schemes, subgrid convection and large-scale condensation should be coordinated to assure light rain stays the same.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Quantifying the Resolution Sensitivity of the Kain–Fritsch Scheme Across the Gray Zone by Isolating Interactions: A TWP‐ICE Case Study

The resolution sensitivity of the Kain–Fritsch (KF) convection scheme and the role of interactions between the physics and dynamics within the gray zone (<10 km) were investigated using the Separate Physics and Dynamics Experiment (SPADE) framework. Two groups of experiments were conducted using the Weather Research and Forecasting (WRF) model via traditional (Tradition) runs and SPADE runs with resolutions of 1, 2, 4, and 8 km during the wet period of the Tropical Warm Pool–International Cloud Experiment (TWP‐ICE). Results show that the KF scheme simulates the weakened convective processes well as the resolution increases in both groups, and the changes in the convective variables with resolution in SPADE are smaller than in the Tradition group. This indicates the important effects of interactions between model components on convection parameterizations as the resolution changes. Additionally, the microphysics variables remain nearly unchanged with resolution in SPADE and weaken slightly in Tradition as the resolution decreases, suggesting the relatively weaker influences of model interactions for the resolved‐cloud parameterization. Therefore, the scale‐aware behavior of KF scheme is further strengthened in Tradition runs, primarily through inhibiting the strength of stratiform processes through physics–dynamics interactions and physical components.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Numerical integration in the virtual element method with the scaled boundary cubature scheme

Abstract The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.

Chin, Eric B.↗
DOE OSTI2021

Photodepositing CdS on the Active Cyano Groups Decorated g‐C 3 N 4 in Z‐Scheme Manner Promotes Visible‐Light‐Driven Hydrogen Evolution

Abstract g‐C 3 N 4 /CdS heterojunctions are potential photocatalysts for hydrogen production but their traditional type‐II configuration generally leads to weak oxidative and reductive activity. How to construct the novel Z‐scheme g‐C 3 N 4 /CdS counterparts to address this issue remains a great challenge in this field. In this work, a new direct Z‐scheme heterojunction of defective g‐C 3 N 4 /CdS is designed by introducing cyano groups (NC‐) as the active bridge sites. Experimental observations in combination with density functional theory (DFT) calculations reveal that the unique electron‐withdrawing feature of cyano groups in the defective g‐C 3 N 4 /CdS heterostructure can endow this photocatalyst with numerous advantageous properties including high light absorption ability, strong redox performance, satisfactory charge separation efficiency, and long lifetime of charge carriers. Consequently, the resultant photocatalytic system exhibits more active performance than CdS and g‐C 3 N 4 under visible light and reaches an excellent hydrogen evolution rate of 1809.07 µmol h −1 g −1 , which is 6.09 times higher than pristine g‐C 3 N 4 . Moreover, the defective g‐C 3 N 4 /CdS photocatalyst maintains good stability after 40 h continuous test. This work provides new insights into design and construction of Z‐scheme heterojunctions for regulating the visible‐light‐induced photocatalytic activity for H 2 evolution.

Wang, Zhipeng↗
DOE OSTI2023

Effects of Anionic Polymer Modification of Dye‐Sensitized Niobate Photocatalysts on Solar‐Driven Z‐Scheme Overall Water Splitting

Pt‐intercalated calcium niobate nanosheets (Pt/HCa 2 Nb 3 O 10 ) sensitized by a Ru(II) complex dye are good photocatalysts for producing H 2 from aqueous solutions containing I − as a reversible electron donor. These materials are applicable to Z‐scheme overall water splitting in combination with a WO 3 ‐based O 2 ‐evolving photocatalyst under simulated sunlight. In this work, the effects of anionic polymer modification of the dye‐sensitized nanosheets are examined by adsorbing sodium poly(styrenesulfonate) (PSS), sodium polyacrylate, sodium polymethacrylate (PMA), or sodium poly(4‐styrenesulfonic‐ co ‐maleic acid) onto the dye‐sensitized nanosheet surface. For half‐cell H 2 ‐evolution reaction in the presence of NaI, all of the polymers have a positive impact on the activity under visible light at lower light intensity, whereas only PMA is effective under high light‐intensity condition. For Z‐scheme overall water splitting with PtO x /H‐Cs‐WO 3 , PSS and PMA give almost the same solar‐to‐hydrogen energy conversion efficiencies (0.12% ± 0.01%) under optimized conditions. However, PMA operates better than PSS at relatively low and high NaI concentrations, which are in general disadvantageous for the H 2 ‐ and O 2 ‐evolving components of the Z‐scheme, respectively.

Energy & Fuels↗
DOE OSTI2020

Protection Scheme for Multiterminal HVDC System Based on Wavelet Transform Modulus Maxima

Fault protection is a major issue in the development of multiterminal high‐voltage direct current (HVDC) system based on voltage‐source converter. Owing to the rapid increase in fault current under DC faults, protection requires a fast fault detection method to isolate the fault current. However, the selectivity and reliability of the fast protection scheme should be primarily guaranteed. Therefore, a new protection strategy based on modulus maximum under wavelet transform is proposed in this paper. Fault detection and discrimination are achieved using single‐end signals of fault current. The external and internal faults can be discriminated via local information. The reliability and robustness of the proposed scheme against potential factors are verified. Numerous simulation cases are performed in PSCAD/EMTDC under different fault scenarios, and signal data are analyzed in MATLAB to demonstrate the effectiveness of the proposed fault protection scheme. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Huai, Qing↗
DOE OSTI2020

Non-perturbative renormalization scheme for the C P -odd three-gluon operator

We define a regularization-independent momentum-subtraction scheme for the C P -odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of C P -violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to \( \overline{\mathrm{MS}} \) at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Uncertainty quantification and optimization of precipitating hydrometeor parameters for winter precipitation in a cloud microphysics scheme

The precipitating hydrometeor parameters used in cloud microphysics schemes carry inherent uncertainties. The quantification of these uncertainties, together with parameter optimization, can significantly improve precipitation forecasts. This study investigates the effects of 13 parameters in the Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) microphysics scheme, which define the hydrometeor characteristics such as fall velocity–diameter and mass–diameter relationships, as well as the shape parameter of the drop size distribution for precipitating particles such as rain, snow, and graupel on simulated winter precipitation. A comparison between the model's pre-defined parameters and observations from the International Collaborative Experiments for the PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign reveals that the fall velocity–diameter relationship for rain, the mass–diameter relationships for snow and graupel, and the shape parameters for all precipitating particles in the WDM6 scheme deviate from the median values observed by the two-dimensional video disdrometer (2DVD). To quantify parameter sensitivities, a perturbed parameter ensemble (PPE) of 256 simulations was conducted within parameter ranges constrained by 2DVD observations for three winter precipitation cases. Bayesian optimization was then applied to identify parameter sets that minimized the root mean square error (RMSE) for each case, achieving reductions of up to 30.2 %. These results demonstrate that ensemble-based uncertainty quantification and parameter optimization can help identify key parameters and provide a pathway to improving precipitation simulation performance. In addition, measurement sites can be strategically selected based on regions that show high sensitivity to variations in hydrometeor characteristic parameters.

Bayesian optimization↗
DOE OSTI2021

An embedded variable step IMEX scheme for the incompressible Navier–Stokes equations

This report presents a series of implicit–explicit (IMEX) variable stepsize algorithms for the incompressible Navier–Stokes equations (NSE). Here, IMEX means the nonlinear term is treated fully explicitly while the remaining terms are treated implicitly. With the advent of new computer architectures there has been growing demand for low memory solvers of this type. The addition of time adaptivity improves the accuracy and greatly enhances the efficiency of the algorithm. We prove energy stability of an embedded first–second order IMEX pair. For the first order member of the pair, we prove stability for variable stepsizes, and analyze convergence. We believe this to be the first proof of this type for a variable stepsize IMEX scheme for the incompressible NSE. We then define and test a variable stepsize, variable order IMEX scheme using these methods. Our work contributes several firsts for IMEX NSE schemes, including an energy argument and error analysis of a two-step, variable stepsize method, and embedded error estimation for an IMEX multi-step method.

42 ENGINEERING↗
DOE OSTI2020

An explicit scheme to enforce charge conservation in transient Particle-in-Cell simulations with Maxwell-Boltzmann electrons

The Maxwell-Boltzmann electron model is a very popular approximation of the electronic behavior in electrostatic plasmas, adopted in all cases where the electron dynamics is governed only by a balance between electric and pressure forces. In such a model, the electron dynamics is reduced to solving for a nonlinear Poisson problem together with an additional expression enforcing charge conservation. In this work we derive an expression of charge conservation which can be conveniently applied to explicit schemes to update the reference Boltzmann density, particularly useful when simulating plasma sheaths. The scheme can be equally applied to both steady-state and transient problems. Two examples are shown, a steady-state plasma sheath, and a radio-frequency magnetic presheath. Our proposed scheme allows to enforce global charge conservation locally in time, and can thus be applied to the simulation of transient phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗