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Charged Particle Dynamics in Lunar Environment

Current state-of-the-art (SOA) granular gas dynamics models used to explain rocket plume impingement physics have not taken into account the natural or induced electrostatic environment of the lunar surface, nor the effect of charged regolith grains being present in the plume plasma. This work improved upon the SOA by adding long-range and contact inter-particle electrostatic interactions to a granular mechanics discrete element method (DEM) modeling software package. Experiments have been tentatively selected to fly on a lunar gravity Blue Origin New Shepard flight through the Flight Opportunities Program (FOP). These experiments will directly provide inputs into the models discussed in this report to provide validation from a more relevant environment than may be produced in the lab.

James Phillips↗

Transmantle flux tectonics

Venus, Earth, and Mars have surfaces that display topographic domes and depressions with quasi-circular planimetric shapes, relief of 0 to several km, and large spatial scales (10(exp 2) to 10(exp 4) km). Our morphostructural mapping reveals hierarchical arrangements of these features. They are explained by a model of long-acting mantle convection, as a particular case of convection in a stratified and random inhomogeneous medium, which develops the form of a hierarchy of different convective pattern scales, each arising from different levels in the mantle. The hypothesis of transmantle flux tectonics parsimoniously explains a diversity of seemingly unrelated terrestrial planetary phenomena, including Earth megaplumes, global resurfacing epochs on Venus, and cyclic ocean formation and global climate change for Mars. All these phenomenon are hypothesized to be parsimoniously explained by a process of transmantle flux tectonics in which long-acting mantle convection generates stresses in blocks of planetary lithosphere to produce distinctive quasi-circular global-hierarchical morphostructure (QGM) patterns. Transmantle flux tectonics differs from plume tectonics in that individual plumes are not considered in isolation. Rather, a wholly interactive process is envisioned in which various spatial and temporal scales of convection operate contemporaneously and hierarchically within other scales. This process of continual change by hierarchical convective cells affects the surface at varying temporal and spatial scales, and its effects are discernable through their relic geological manifestations, the QGM patterns.

Finn, V. J.↗

Stereoscopic Retrieval of Smoke Plume Heights and Motion from Space-Based Multi-Angle Imaging, Using the MISR INteractive eXplorer(MINX)

Airborne particles desert dust, wildfire smoke, volcanic effluent, urban pollution affect Earth's climate as well as air quality and health. They are found in the atmosphere all over the planet, but vary immensely in amount and properties with season and location. Most aerosol particles are injected into the near-surface boundary layer, but some, especially wildfire smoke, desert dust and volcanic ash, can be injected higher into the atmosphere, where they can stay aloft longer, travel farther, produce larger climate effects, and possibly affect human and ecosystem health far downwind. So monitoring aerosol injection height globally can make important contributions to climate science and air quality studies. The Multi-angle Imaging Spectro-Radiometer (MISR) is a space borne instrument designed to study Earths clouds, aerosols, and surface. Since late February 2000 it has been retrieving aerosol particle amount and properties, as well as cloud height and wind data, globally, about once per week. The MINX visualization and analysis tool complements the operational MISR data products, enabling users to retrieve heights and winds locally for detailed studies of smoke plumes, at higher spatial resolution and with greater precision than the operational product and other space-based, passive remote sensing techniques. MINX software is being used to provide plume height statistics for climatological studies as well as to investigate the dynamics of individual plumes, and to provide parameterizations for climate modeling.

aerosols↗

Supersonic jet plume interaction with a flat plate

Supersonic jet plume interaction with a flat plate was studied using a model scaled test apparatus designed to simulate plume/aircraft structure interaction for the cruise configuration. The generic configuration consisted of a rectangular supersonic nozzle of aspect ratio 7, and a large flat plate located beneath the nozzle at various nozzle plate distances; the plate was instrumented to measure surface dynamic pressure and mean wall temperature, with provisions for measurements of acceleration and strain on coupon size panels that could be inserted in the plate. Phase-averaged schlieren measurements revealed the presence of high-intensity acoustic emission from the supersonic plume above the plate, directed upstream; this radiation could be associated with the shock noise generation. Narrow band spectra of surface dynamic pressure show spectral peaks with amplitude levels reaching 1 psi, related to the screech tones. Temperature measurements indicated elevated surface temperatures in regions of high turbulence intensity.

Seiner, John M.↗

LANDSAT-4 image data quality analysis for energy related applications

No useable LANDSAT 4 TM data were obtained for the Hanford site in the Columbia Plateau region, but TM simulator data for a Virginia Electric Company nuclear power plant was used to test image processing algorithms. Principal component analyses of this data set clearly indicated that thermal plumes in surface waters used for reactor cooling would be discrenible. Image processing and analysis programs were successfully testing using the 7 band Arkansas test scene and preliminary analysis of TM data for the Savanah River Plant shows that current interactive, image enhancement, analysis and integration techniques can be effectively used for LANDSAT 4 data. Thermal band data appear adequate for gross estimates of thermal changes occurring near operating nuclear facilities especially in surface water bodies being used for reactor cooling purposes. Additional image processing software was written and tested which provides for more rapid and effective analysis of the 7 band TM data.

Wukelic, G. E.↗

Cratering Soil by Impinging Jets of Gas, with Application to Landing Rockets on Planetary Surfaces

Several physical mechanisms are involved in excavating granular materials beneath a vertical jet of gas. These occur, for example, beneath the exhaust plume of a rocket landing on the soil of the Moon or Mars. A series of experiments and simulations have been performed to provide a detailed view of the complex gas/soil interactions. Measurements have also been taken from the Apollo lunar landing videos and from photographs of the resulting terrain, and these help to demonstrate how the interactions extrapolate into the lunar environment. It is important to understand these processes at a fundamental level to support the ongoing design of higher-fidelity numerical simulations and larger-scale experiments. These are needed to enable future lunar exploration wherein multiple hardware assets will be placed on the Moon within short distances of one another. The high-velocity spray of soil from landing spacecraft must be accurately predicted and controlled lest it erosively damage the surrounding hardware.

Metzger, Philip T.↗

Predicting the Seawater Chemistry of an Ocean World Using Machine Learning on Isotopic Measurements of Volatile CO2

Introduction: Given the long time intervals required for data transmission to and from ocean worlds targets, low bandwidth for data transmission, time required for data processing and analysis, and potentially extreme radiation environments (e.g., Europa), it is clear that ocean worlds missions will need more autonomous flight instruments and software in order to achieve established science goals. Protracted time intervals for data analysis (e.g., Europa Lander) strongly motivates the development of rapid, consistent and streamlined methods for interpreting data from flight mass spectrometers to e.g., determine how mass spectra from a plume or surface liquid/ice relates to the surface/subsurface. Since mass spectrometry also has the potential to correctly identify biosignatures[1], it is imperative that such methods for interpreting data are consistent and accurate. We used 848 isotope ratio mass spectra from laboratory analyses of CO2 that interacted with ocean worlds-relevant seawaters as a ‘training’ dataset for ‘unsupervised’ machine learning. In unsupervised learning, characteristics of the data are not labeled or linked, and any similarities found only result from the neural network. CO2 isotopologues analyzed for this dataset mimic the remote measurements of CO2 by a flight mass spectrometer, and are detailed in Theiling [2]. From this dataset, we used measured features of the spectra, such as retention time, intensity, and (isotopologue) mass ratios as inputs for our autoencoder neural network. Our neural network was trained to find similarities in these and other spectral features for seawaters of a particular composition and amount of initial CO2. Successful training then created an output of these similarities for various seawaters, which included MgSO4, Na2SO4, NaCl, MgCl2, KCl, and NaHCO3, and combinations of these salts. We then applied dimensionality reduction techniques such as Principal Component Analysis (PCA), T-Distributed Stochastic Neighbor Embedding (TSNE), and Uniform Manifold Approximation and Projection (UMAP) to demonstrate latent data features as a two-dimensional projection in a unitless, high-dimensional space. In this projection, a data point represents the combined effect of spectral features such as intensity, retention time, and isotope ratio. Our initial UMAP demonstrates data clustering (organization of the data by the neural network) based on the amount of CO2 that had initially interacted with each seawater. Further training using more ‘supervised’ learning techniques demonstrate strong clustering of preliminary data based on initial CO2 concentration, seawater chemical composition, and ionic strength (salinity). Our preliminary work therefore suggests that machine learning has the potential to identify compositional variants of an ocean world seawater based on mass spectra from volatile CO2 measurements. Acknowledgments: This work was funded through a Strategic Task Group at NASA Goddard Space Flight Center. The training dataset was collected through funding from the Oklahoma Space Grant Consortium. References: [1] Pappalardo, R. et al. (2013) Astrobiology, 13, 740–773. [2] Theiling (2020) Icarus, 114216.

Europa↗

Jet Surface Interaction Scrubbing Noise from High Aspect-Ratio Rectangular Jets

Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity of the airframe. Distributed propulsion system with exhaust configurations that resemble a high aspect ratio rectangular jet are among geometries of interest. Nearby solid surfaces could provide noise shielding for the purpose of reduced community noise. Interaction of high-speed jet exhaust with structure could also generate new sources of sound as a result of flow scrubbing past the structure, and or scattered noise from sharp edges. The present study provides a theoretical framework to predict the scrubbing noise component from a high aspect ratio rectangular exhaust in proximity of a solid surface. The analysis uses the Greens function (GF) to the variable density Pridmore-Brown equation in a transversely sheared mean flow. Sources of sound are defined as the auto-covariance function of second-rank velocity fluctuations in the jet plume, and are modeled using a RANS-based acoustic analogy approach. Acoustic predictions are presented in an 8:1 aspect ratio rectangular exhaust at three subsonic Mach numbers. The effect of nearby surface on the scrubbing noise component is shown on both reflected and shielded sides of the plate.

Propulsion Noise↗

Analytical study of viscous effects on transonic flow over boattail nozzles

An analytical study has been made of the effects of viscous/inviscid interactions on the transonic flow over boattail nozzles. The theoretical method couples a relaxation solution of the full potential transonic flow equations with a conventional boundary-layer solution to account for displacement-thickness effects. Surface pressures calculated on circular-arc boattails with solid jet-plume simulators show good agreement with experiment for free-stream Mach numbers less than 0.90. For separated flows, an empirical discriminating streamline model of the separation bubble gives good results until the onset of shock-induced separation, which occurs typically at a Mach number of about 0.90.

Wilmoth, R. G.↗

Flight-Determined Subsonic Longitudinal Stability and Control Derivatives of the F-18 High Angle of Attack Research Vehicle (HARV) with Thrust Vectoring

The subsonic longitudinal stability and control derivatives of the F-18 High Angle of Attack Research Vehicle (HARV) are extracted from dynamic flight data using a maximum likelihood parameter identification technique. The technique uses the linearized aircraft equations of motion in their continuous/discrete form and accounts for state and measurement noise as well as thrust-vectoring effects. State noise is used to model the uncommanded forcing function caused by unsteady aerodynamics over the aircraft, particularly at high angles of attack. Thrust vectoring was implemented using electrohydraulically-actuated nozzle postexit vanes and a specialized research flight control system. During maneuvers, a control system feature provided independent aerodynamic control surface inputs and independent thrust-vectoring vane inputs, thereby eliminating correlations between the aircraft states and controls. Substantial variations in control excitation and dynamic response were exhibited for maneuvers conducted at different angles of attack. Opposing vane interactions caused most thrust-vectoring inputs to experience some exhaust plume interference and thus reduced effectiveness. The estimated stability and control derivatives are plotted, and a discussion relates them to predicted values and maneuver quality.

Iliff, Kenneth W.↗

Exhaust Simulation Testing of a Hypersonic Airbreathing Model at Transonic Speeds

An experimental study was performed to examine jet-effects for an airframe-integrated, scramjet-rocket combined-cycle vehicle configuration at transonic test conditions. This investigation was performed by testing an existing exhaust simulation wind tunnel model, known as Model 5B, in the NASA Langley 16-Ft. Transonic Tunnel. Tests were conducted at freestream Mach numbers from 0.7 to 1.2, at angles of attack from 2 to +14 degrees, and at up to seven nozzle static pressure ratio values for a set of horizontal-tail and body-flap deflections. The model aftbody, horizontal tails, and body flaps were extensively pressure instrumented to provide an understanding of jet-effects and control-surface/plume interactions, as well as for the development of analytical methodologies and calibration of computational fluid dynamic codes to predict this type of flow phenomenon. At all transonic test conditions examined, the exhaust flow at the exit of the internal nozzle was over-expanded, generating an exhaust plume that turned toward the aftbody. Pressure contour plots for the aftbody of Model 5B are presented for freestream transonic Mach numbers of 0.70, 0.95, and 1.20. These pressure data, along with shadowgraph images, indicated the impingement of an internal plume shock and at least one reflected shock onto the aftbody for all transonic conditions tested. These results also provided evidence of the highly three-dimensional nature of the aftbody exhaust flowfield. Parametric testing showed that angle-of-attack, static nozzle pressure ratio, and freestream Mach number all affected the exhaust-plume size, exhaust-flowfield shock structure, and the aftbody-pressure distribution, with Mach number having the largest effect. Integration of the aftbody pressure data showed large variations in the pitching moment throughout the transonic regime.

Huebner, Lawrence D.↗

The Summer 1997 Eruption at Pillan Patera on Io: Implications for Ultrabasic Lava Flow Emplacement

Galileo data and numerical modeling were used to investigate the summer 1997 eruption at Pillan Patera on Io. This event, now defined as 'Pillanian' eruption style, included a high-temperature (greater than 1600 C), possibly ultrabasic, 140-km-high plume eruption that deposited dark, orthopyroxene-rich pyroclastic material over greater than 125,000 sq km, followed by emplacement of dark flow-like material over greater than 3100 sq km to the north of the caldera. We estimate that the high-temperature, energetic episode of this eruption had a duration of 52- 167 days between May and September 1997, with peak eruption temperatures around June 28, 1997. Galileo 20 m/pixel images of part of the Pillan flow field show a widespread, rough, pitted surface that is unlike any flow surface we have seen before. We suggest that th.s surface may have resulted from (1) a fractured lava crust formed during rapid, low-viscosity lava surging, perhaps including turbulent flow emplacement; (2) disruption of the lava flow by explosive interaction with a volatile-rich substrate: or (3) a combination of 1 and 2 with or without accumulation of pyroclastic materials on the surface. Well-developed flow lobes are observed, suggesting that this is a relatively distal part of the flow field. Shadow measurements at flow margins indicate a thickness of approx. 8-10 m. We have modeled the emplacement of putative ultrabasic flows from the summer 1997 Pillan eruption using constraints from new Galileo data. Results suggest that either laminar sheet flows or turbulent channelized flows could have traveled 50-150 km on a flat. unobstructed surface, which is consistent with the estimated length of the Pillan flow field (approx. 60 km). Our modeling suggests low thermal erosion rates (less than 0.1 m/d), and that the formation of deep (greater than 20 m) erosion channels was unlikely, especially distal to the source. We calculate a volumetric flow rate of approx. 2-7 x l0(exp 3) cu m/s, which is greater than those for typical Mauna Loa/Kilauea flows but comparable to those for the (1783) Laki eruption and the inferred flow rates of the Roza flows in the Columbia River flood basalts. The differences in ultrabasic eruption styles on Earth and Io appear to be controlled by the different eruption environments: Plumes at sites of ultrabasic eruptions on Io suggest strong magma-volatile: interactions on a low-gravity body lacking an atmosphere, whereas the geology at sites of komatiite eruptions on Earth suggest mostly submarine emplacement of thick flows with a pronounced lack of subaerial explosive activity.

Williams, David A.↗

The Summer 1997 Eruption at Pillan Patera on Io: Implications for Ultrabasic Lava Flow Emplacement

Galileo data and numerical modeling were used to investigate the summer 1977 eruption at Pillan Patera on Io. This event, now defined as "Pillanian" eruption style, included a high-temperature (greater than 1600 C), possible ultrabasic , 140-km-high plume eruption that deposited dark, orthopyroxene-rich pyroclastic material over greater than 125,000 sq km, followed by emplacement of dark flow-like material over greater than 3100 sq km to the north of the caldera. We estimate that the high-temperature, energetic episode of this eruption had a duration of 52 - 167 days between May and September 1997, with peak eruption temperatures around June 28, 1997. Galileo 20 m/pixel images of part of the Pillan flow field show a wide-spread, rough, pitted surface that is unlike any flow surface we have seen before. We suggest that this surface may have resulted from: 1. A fractured lava crust formed during rapid, low-viscosity lava surging, perhaps including turbulent flow emplacement. 2. Disruption of the lava flow by explosive interaction with a volatile-rich substrate. or 3. A combination of 1 and 2 with or without accumulation of pyroclastic material on the surface. Well-developed flow lobes are observed, suggesting that this is a relatively distant part of the flow field.Shadow measurements at flow margins indicate a thickness of-8 - 10 m. We have modeled the emplacement of putative ultrabasic flow from the summer 1997 Pillan eruption using constraints from new Galileo data. Results suggest that either laminar sheet flows or turbulent channelized flows could have traveled 50 - 150 km on a flat, unobstructed surface, which is consistent with the estimated length of the Pillan flow field (approx. 60 km). Our modeling suggests low thermal erosion rates (less than 4.1 m/d), and that the formation of deep (greater than 20 m) erosion channels was unlikely, especially distal to the source. We calculate a volumetric flow rate of approx. 2 - 7 x 10(exp 3)cu m/s, which is greater than those for typical Mauna Loa/Kilaueaq flows but comparable to those for the (1783) Laki eruption and the inferred flow rates of the Roza flows in the Columbia River flood basalts. The differences in ultrabasic eruption styles on Earth and Io appear to be controlled by the different eruption environments; Plumes at sites of ultrabasic eruptions on Io suggest strong magma-volatile interactions on a low-gravity body lacking an atmosphere, whereas the geology at sites of komatiite eruptions on Earth suggest mostly submarine emplacement of thick flows with a pronounced lack of subaerial explosive activity.

Williams, David A.↗

Electric propulsion produced environments and possible interactions with the SP-100 power system

An examination of a conceptual SP-100 type power system has been conducted to assess the effect of possible electric thruster induced contamination. The operating characteristics and known exhaust plume properties of various electric thrusters are summarized along with the natural environment and its effects to provide background for the contamination discussion. Charge buildup on nonconducting surfaces, differential charging of surfaces and arcing should be moderated by the operation of an electric thruster system. Thin film deposition of eroded thruster materials is a possible contamination mechanism. Electric thruster field efflux and propellant condensation should have only a minor contaminating effect upon a nuclear power system.

Deininger, W. D.↗

Exploring the Elevated Water Vapor Signal Associated With the Free Tropospheric Biomass Burning Plume Over the Southeast Atlantic Ocean

In southern Africa, widespread agricultural fires produce substantial biomass burning (BB) emissions over the region. The seasonal smoke plumes associated with these emissions are then advected westward over the persistent stratocumulus cloud deck in the southeast Atlantic (SEA) Ocean, resulting in aerosol effects which vary with time and location. Much work has focused on the effects of these aerosol plumes, but previous studies have also described an elevated free tropospheric water vapor signal over the SEA. Water vapor influences climate in its own right, and it is especially important to consider atmospheric water vapor when quantifying aerosol–cloud interactions and aerosol radiative effects. Here we present airborne observations made during the NASA ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) campaign over the SEA Ocean. In observations collected from multiple independent instruments on the NASA P-3 aircraft (from near-surface to 6–7 km), we observe a strongly linear correlation between pollution indicators (carbon monoxide (CO) and aerosol loading) and atmospheric water vapor content, seen at all altitudes above the boundary layer. The focus of the current study is on the especially strong correlation observed during the ORACLES-2016 deployment (out of Walvis Bay, Namibia), but a similar relationship is also observed in the August 2017 and October 2018 ORACLES deployments. Using reanalyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) and Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), and specialized WRF-Chem simulations, we trace the plume–vapor relationship to an initial humid, smoky continental source region, where it mixes with clean, dry upper tropospheric air and then is subjected to conditions of strong westward advection, namely the southern African easterly jet (AEJ-S). Our analysis indicates that air masses likely left the continent with the same relationship between water vapor and carbon monoxide as was observed by aircraft. This linear relationship developed over the continent due to daytime convection within a deep continental boundary layer (up to ∼5–6 km) and mixing with higher-altitude air, which resulted in fairly consistent vertical gradients in CO and water vapor, decreasing with altitude and varying in time, but this water vapor does not originate as a product of the BB combustion itself. Due to a combination of conditions and mixing between the smoky, moist continental boundary layer and the dry and fairly clean upper-troposphere air above (∼6 km), the smoky, humid air is transported by strong zonal winds and then advected over the SEA (to the ORACLES flight region) following largely isentropic trajectories. Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT) back trajectories support this interpretation. This work thus gives insights into the conditions and processes which cause water vapor to covary with plume strength. Better understanding of this relationship, including how it varies spatially and temporally, is important to accurately quantify direct, semi-direct, and indirect aerosol effects over this region.

Kristina Pistone↗

Numerical and experimental investigations of rarefied nozzle and plume flows of nitrogen

Numerical and experimental investigations are performed for the rarefied flow of nitrogen through a small nozzle which is expanded into near-vacuum conditions. Two different numerical studies are undertaken: the first employs a continuum approach in solving the Navier-Stokes equations, and the second employs a particle approach through use of the direct simulation Monte Carlo method (DSMC). The experimental investigation concerns the measurement of pressure, using a Pitot tube, in the nozzle exit plane and near-field of the plume. Comparison of the experimental and numerical data at the nozzle exit reveals that the DSMC technique provides the more accurate description of the expanding flow. It is discovered that the DSMC solutions are quite sensitive to the model employed to simulate the interaction between the gas and the nozzle wall surface. It is concluded that the simplistic fully diffuse model is quite satisfactory for the present application.

Boyd, Iain D.↗

Spatial Distributions of Metal Atoms During Carbon SWNTs Formation: Measurements and Modelling

Experiments and modelling have been undertaken to clarify the role of metal catalysts during single-wall carbon nanotube formation. For instance, we wonder whether the metal catalyst is active as an atom, a cluster, a liquid or solid nanoparticle [1]. A reactor has been developed for synthesis by continuous CO2-laser vaporisation of a carbon-nickel-cobalt target in laminar helium flow. The laser induced fluorescence technique [2] is applied for local probing of gaseous Ni, Co and CZ species throughout the hot carbon flow of the target heated up to 3500 K. A rapid depletion of C2 in contrast to the spatial extent of metal atoms is observed in the plume (Fig. 1). This asserts that C2 condenses earlier than Ni and Co atoms.[3, 4]. The depletion is even faster when catalysts are present. It may indicate that an interaction between metal atoms and carbon dimers takes place in the gas as soon as they are expelled from the target surface. Two methods of modelling are used: a spatially I-D calculation developed originally for the arc process [5], and a zero-D time dependent calculation, solving the chemical kinetics along the streamlines [6]. The latter includes Ni cluster formation. The peak of C2 density is calculated close to the target surface where the temperature is the highest. In the hot region, C; is dominant. As the carbon products move away from the target and mix with the ambient helium, they recombine into larger clusters, as demonstrated by the peak of C5 density around 1 mm. The profile of Ni-atom density compares fairly well with the measured one (Fig. 2). The early increase is due to the drop of temperature, and the final decrease beyond 6 mm results from Ni cluster formation at the eutectic temperature (approx.1600 K).

Cau, M.↗

Large Eddy Simulation (LES) of Particle-Laden Temporal Mixing Layers

High-fidelity models of plume-regolith interaction are difficult to develop because of the widely disparate flow conditions that exist in this process. The gas in the core of a rocket plume can often be modeled as a time-dependent, high-temperature, turbulent, reacting continuum flow. However, due to the vacuum conditions on the lunar surface, the mean molecular path in the outer parts of the plume is too long for the continuum assumption to remain valid. Molecular methods are better suited to model this region of the flow. Finally, granular and multiphase flow models must be employed to describe the dust and debris that are displaced from the surface, as well as how a crater is formed in the regolith. At present, standard commercial CFD (computational fluid dynamics) software is not capable of coupling each of these flow regimes to provide an accurate representation of this flow process, necessitating the development of custom software. This software solves the fluid-flow-governing equations in an Eulerian framework, coupled with the particle transport equations that are solved in a Lagrangian framework. It uses a fourth-order explicit Runge-Kutta scheme for temporal integration, an eighth-order central finite differencing scheme for spatial discretization. The non-linear terms in the governing equations are recast in cubic skew symmetric form to reduce aliasing error. The second derivative viscous terms are computed using eighth-order narrow stencils that provide better diffusion for the highest resolved wave numbers. A fourth-order Lagrange interpolation procedure is used to obtain gas-phase variable values at the particle locations.

Bellan, Josette↗