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At least 253 records · Page 14
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NASA NTRS1987

Beaming of Uranian kilometric radiation and implications for the planetary magnetic field

Radio waves from Uranus at 481.2 kHz detected by Voyager 2 show a strong beaming effect. When the data are analyzed according to the magnetic latitude of the observer in an offset tilted dipole field model, a sharply defined emission beam extending from 25 to 55 deg latitude is evident consistent with a source over the south magnetic pole. The lack of prominent emission from the north magnetic pole can be attributed to the large spatial offset of the magnetic dipole resulting in much lower source frequencies. For proper alignment of the beam, an advance of the dipole axis longitude by 23 deg from the standard model is required. This phase shift is interpreted as the result of higher order magnetic moments producing a skew of the field lines at low altitudes in the polar source region. This conclusion further substantiates models of the interior of Uranus which predict a complex intrinsic field with significant nondipolar contributions to the surface magnetic field.

Barbosa, D. D.↗
NASA NTRSDate not supplied

ADVANCES IN PLUME-SURFACE INTERACTION SIMULATION CAPABILITY UNDER LUNAR LANDING CONDITIONS

The Fluid Dynamics Branch at theNASA Marshall Space Flight Center has assembled a portfolio of simulation tools to predict Plume-SurfaceInteraction (PSI) environments during extra-terrestrial propulsive landings. Particular focus is on engineering support for lunar landers such as robotic CommercialLunar Payload Services (CLPS) and the HumanLander System (HLS). Extension of existing PSI simulation capabilities are required to accurately capture the complex plume flow conditions and surface soil particle composition effects that arise in the lunar environment. The required model development and implementation, and extensive verification and validation of the key simulation tools, Loci/Chem [1]and Loci/Boltzmann [2], and Loci/GGFS [3] are now performed under a NASA Space Technology MissionDirectorate (STMD) funded multi-year GameChanging Development (GCD) project. The project will implement and mature these new modeling features and verify and validate them for the Mars andMoon environments with the aid of existing and new experiments to be performed under this project

Plume Surface Interaction↗
NASA NTRS2013

Atmospheric Dissolved Iron Depostiion to the Global Oceans: Effects of Oxalate-Promoted Fe Dissolution, Photochemical Redox Cycling, and Dust Mineralogy

Mineral dust deposition is suggested to be a significant atmospheric supply pathway of bioavailable iron (Fe) to Fe-depleted surface oceans. In this study, mineral dust and dissolved Fe (Fed) deposition rates are predicted for March 2009 to February 2010 using the 3-D chemical transport model GEOS-Chem implemented with a comprehensive dust-Fe dissolution scheme. The model simulates Fed production during the atmospheric transport of mineral dust taking into account inorganic and organic (oxalate)-promoted Fe dissolution processes, photochemical redox cycling between ferric (Fe(III)) and ferrous (Fe(II)) forms of Fe, dissolution of three different Fe-containing minerals (hematite, goethite, and aluminosilicates), and detailed mineralogy of windblown dust from the major desert regions. Our calculations suggest that during the yearlong simulation is approximately 0.26 Tg (1 Tg = 1012 g) of Fed was deposited to global oceanic regions. Compared to simulations only taking into account proton-promoted Fe dissolution, the addition of oxalate to the dust-Fe mobilization scheme increased total annual model-predicted Fed deposition to global oceanic regions by approximately 75%. The implementation of Fe(II)/Fe(III) photochemical redox cycling in the model allows for the distinction between different oxidation states of deposited Fed. Our calculations suggest that during the daytime, large fractions of Fed deposited to the global oceans is likely to be in Fe(II) form, while nocturnal fluxes of Fed are largely in Fe(III) form. Model simulations also show that atmospheric fluxes of Fed can be strongly influenced by the mineralogy of Fe-containing compounds. This study shows that Fed deposition to the oceans is controlled by total dust-Fe mass concentrations, mineralogy, the surface area of dust particles, atmospheric chemical composition, cloud processing, and meteorological parameters and exhibits complex and spatiotemporally variable patterns. Our study suggests that the explicit model representation of individual processes leading to Fed production within mineral dust are needed to improve the understanding of the atmospheric Fe cycle, and quantify the effect of dust-Fe on ocean biological productivity, carbon cycle, and climate.

Johnson, M. S.↗
NASA NTRSDate not supplied

The Aguas Zarcas Breccia - Similarities to Surface Features of C-Complex Asteroids Ryugu and Bennu

Knowledge of the materials originally present in the proto-solar nebula is one of the most significant constraints for models concerning the formation of our solar system. The physicochemical properties of these original materials can be determined through two distinct and complementary approaches: astronomical observations of nascent stellar systems and the dense clouds from which they originated; and laboratory studies of available astromaterials such as meteorites, interplanetary dust particles, comets, as well as returned mission samples (e.g., from Hayabusa -1 -2;OSIRIS -Rex). Laboratory study of these extraterrestrial materials provides valuable information about the first solids portion of the early solar system and their evolution. Here, we present petrographic and mineralogical characteristics of the polymic beccias Aguas Zarcas based on the research results of [1].On April 23, 2019, at 21:07 local time, a meteorite fall occurred in Aguas Zarcas, San Carlos County, Alajuela province, Costa Rica. The rapid recovery of this brecciated carbonaceous chondrite after its fall provides an opportunity to study a freshly fallen, relatively uncontaminated, and highly brecciated meteorite to compare with samples returned by theHayabusa2 and OSIRIS-REx spacecraft from C-group asteroids. The study includes several pre-rain fragments [1].The X-ray Computed Tomography (XCT) results show many different lithologies. We describe the petrography and mineralogy of five different lithologies of the Aguas Zarcas meteorite. We also present data on bulk oxygen isotopes. We describe all fragments in detail and attempt to classify each lithology in order to understand the origin and formation history of the Aguas Zarcas parent body. Our results show that some lithologies of Aguas Zarcas are similar to those in CM chondrites, but others are unique. The different lithologies [1] also represent different degrees of hydration and heating, which are good analogues for the types of materials returned by the Bennu and Ryugu asteroids. Spectroscopic observations of the Ryugu and Bennu asteroids compared to laboratory measurements of meteorites suggest that the asteroids have some similarities to heated CM, heated CI, or CI chondrites[2-5]. Both asteroids are thought to be composed of materials altered by aqueous alteration (e.g., [5]) and formed by reaccretion after destruction by impacts and brecciation (e.g., [6-7]). Considering the different lithologies in Aguas Zarcas [2] and other CM chondrites [8-9], these types of carbonaceous chondrites can be considered good analogues for samples from the Ryugu and Bennu asteroids. The presence of unique and rare lithologies in the Aguas Zarcas, different from the typical CM chondrite lithologies, suggests complex mixing of different materials in a highly dynamic environment.

Imene Kerraouch↗
NASA NTRS1991

Frame Shift/warp Compensation for the ARID Robot System

The Automatic Radiator Inspection Device (ARID) is a system aimed at automating the tedious task of inspecting orbiter radiator panels. The ARID must have the ability to aim a camera accurately at the desired inspection points, which are in the order of 13,000. The ideal inspection points are known; however, the panel may be relocated due to inaccurate parking and warpage. A method of determining the mathematical description of a translated as well as a warped surface by accurate measurement of only a few points on this surface is developed here. The method uses a linear warp model whose effect is superimposed on the rigid body translation. Due to the angles involved, small angle approximations are possible, which greatly reduces the computational complexity. Given an accurate linear warp model, all the desired translation and warp parameters can be obtained by knowledge of the ideal locations of four fiducial points and the corresponding measurements of these points on the actual radiator surface. The method uses three of the fiducials to define a plane and the fourth to define the warp. Given this information, it is possible to determine a transformation that will enable the ARID system to translate any desired inspection point on the ideal surface to its corresponding value on the actual surface.

Latino, Carl D.↗
NASA NTRS2016

Pluto's Global Surface Composition Through Pixel-by-Pixel Hapke Modeling of New Horizons Ralph LEISA Data

On July 14th 2015, NASA's New Horizons mission gave us an unprecedented detailed view of the Pluto system. The complex compositional diversity of Pluto's encounter hemisphere was revealed by the Ralph/LEISA infrared spectrometer on board of New Horizons. We present compositional maps of Pluto defining the spatial distribution of the abundance and textural properties of the volatiles methane and nitrogen ices and non-volatiles water ice and tholin. These results are obtained by applying a pixel-by-pixel Hapke radiative transfer model to the LEISA scans. Our analysis focuses mainly on the large scale latitudinal variations of methane and nitrogen ices and aims at setting observational constraints to volatile transport models. Specifically, we find three latitudinal bands: the first, enriched in methane, extends from the pole to 55degN, the second dominated by nitrogen, continues south to 35 degN, and the third, com- posed again mainly of methane, reaches 20 degN. We demonstrate that the distribution of volatiles across these surface units can be explained by differences in insolation over the past few decades. The latitudinal pattern is broken by Sputnik Planitia, a large reservoir of volatiles, with nitrogen playing the most important role. The physical properties of methane and nitrogen in this region are suggestive of the presence of a cold trap or possible volatile stratification. Furthermore our modeling results point to a possible sublimation transport of nitrogen from the northwest edge of Sputnik Planitia toward the south.

Protopapa, S.↗
NASA NTRS2001

Simulation of MEMS for the Next Generation Space Telescope

The NASA Goddard Space Flight Center (GSFC) is developing optical micro-electromechanical system (MEMS) components for potential application in Next Generation Space Telescope (NGST) science instruments. In this work, we present an overview of the electro-mechanical simulation of three MEMS components for NGST, which include a reflective micro-mirror array and transmissive microshutter array for aperture control for a near infrared (NIR) multi-object spectrometer and a large aperture MEMS Fabry-Perot tunable filter for a NIR wide field camera. In all cases the device must operate at cryogenic temperatures with low power consumption and low, complementary metal oxide semiconductor (CMOS) compatible, voltages. The goal of our simulation efforts is to adequately predict both the performance and the reliability of the devices during ground handling, launch, and operation to prevent failures late in the development process and during flight. This goal requires detailed modeling and validation of complex electro-thermal-mechanical interactions and very large non-linear deformations, often involving surface contact. Various parameters such as spatial dimensions and device response are often difficult to measure reliably at these small scales. In addition, these devices are fabricated from a wide variety of materials including surface micro-machined aluminum, reactive ion etched (RIE) silicon nitride, and deep reactive ion etched (DRIE) bulk single crystal silicon. The above broad set of conditions combine to be a formidable challenge for space flight qualification analysis. These simulations represent NASA/GSFC's first attempts at implementing a comprehensive strategy to address complex MEMS structures.

Mott, Brent↗
NASA NTRS2010

CFD Fuel Slosh Modeling of Fluid-Structure Interaction in Spacecraft Propellant Tanks with Diaphragms

Liquid sloshing within spacecraft propellant tanks causes rapid energy dissipation at resonant modes, which can result in attitude destabilization of the vehicle. Identifying resonant slosh modes currently requires experimental testing and mechanical pendulum analogs to characterize the slosh dynamics. Computational Fluid Dynamics (CFD) techniques have recently been validated as an effective tool for simulating fuel slosh within free-surface propellant tanks. Propellant tanks often incorporate an internal flexible diaphragm to separate ullage and propellant which increases modeling complexity. A coupled fluid-structure CFD model is required to capture the damping effects of a flexible diaphragm on the propellant. ANSYS multidisciplinary engineering software employs a coupled solver for analyzing two-way Fluid Structure Interaction (FSI) cases such as the diaphragm propellant tank system. Slosh models generated by ANSYS software are validated by experimental lateral slosh test results. Accurate data correlation would produce an innovative technique for modeling fuel slosh within diaphragm tanks and provide an accurate and efficient tool for identifying resonant modes and the slosh dynamic response.

Sances, Dillon J.↗
NASA NTRS2010

Temperature Responses to Spectral Solar Variability on Decadal Time Scales

Two scenarios of spectral solar forcing, namely Spectral Irradiance Monitor (SIM)-based out-of-phase variations and conventional in-phase variations, are input to a time-dependent radiative-convective model (RCM), and to the GISS modelE. Both scenarios and models give maximum temperature responses in the upper stratosphere, decreasing to the surface. Upper stratospheric peak-to-peak responses to out-of-phase forcing are approx.0.6 K and approx.0.9 K in RCM and modelE, approx.5 times larger than responses to in-phase forcing. Stratospheric responses are in-phase with TSI and UV variations, and resemble HALOE observed 11-year temperature variations. For in-phase forcing, ocean mixed layer response lags surface air response by approx.2 years, and is approx.0.06 K compared to approx.0.14 K for atmosphere. For out-of-phase forcing, lags are similar, but surface responses are significantly smaller. For both scenarios, modelE surface responses are less than 0.1 K in the tropics, and display similar patterns over oceanic regions, but complex responses over land.

Cahalan, Robert F.↗
NASA NTRS1983

A novel algorithm for sea surface height estimation using complex SAR data

A method of extracting sea height information from Synthetic Aperture Radar (SAR) complex data was studied. A fundamental SAR ocean imaging model for gravity waves showed that information about the long wave is present in the SAR complex data, especially its phase. Phase demodulation algorithm followed by linear regression and filtering was employed. Only the latter two steps incorporated a priori information that might be available. A relatively simplified simulation indicated that the finite bandwidth of the SAR system imposed the apparently most serious limitation. A preliminary application to SEASAT-SAR complex imagery was encouraging. Information about the long wave, if incorporated into a more sophisticated phase demodulation structure, i.e., at an earlier point in the algorithm, could conceivably mitigate this bandwidth limitation.

Harger, R. O.↗
NASA NTRS1993

New concepts for Reynolds stress transport equation modeling of inhomogeneous flows

The ability to model turbulence near solid walls and other types of boundaries is important in predicting complex engineering flows. Most turbulence modeling has concentrated either on flows which are nearly homogeneous or isotropic, or on turbulent boundary layers. Boundary layer models usually rely very heavily on the presence of mean shear and the production of turbulence due to that mean shear. Most other turbulence models are based on the assumption of quasi-homogeneity. However, there are many situations of engineering interest which do not involve large shear rates and which are not quasi-homogeneous or isotropic. Shear-free turbulent boundary layers are the prototypical example of such flows, with practical situations being separation and reattachment, bluff body flow, high free-stream turbulence, and free surface flows. Although these situations are not as common as the variants of the flat plate turbulent boundary layer, they tend to be critical factors in complex engineering situations. The models developed are intended to extend classical quasi-homogeneous models into regions of large inhomogeneity. These models do not rely on the presence of mean shear or production, but are still applicable when those additional effects are included. Although the focus is on shear-free boundary layers as tests for these models, results for standard shearing boundary layers are also shown.

Perot, J. Blair↗
NASA NTRS2015

Airborne Lidar-Based Estimates of Tropical Forest Structure in Complex Terrain: Opportunities and Trade-Offs for REDD+

Background: Carbon stocks and fluxes in tropical forests remain large sources of uncertainty in the global carbon budget. Airborne lidar remote sensing is a powerful tool for estimating aboveground biomass, provided that lidar measurements penetrate dense forest vegetation to generate accurate estimates of surface topography and canopy heights. Tropical forest areas with complex topography present a challenge for lidar remote sensing. Results: We compared digital terrain models (DTM) derived from airborne lidar data from a mountainous region of the Atlantic Forest in Brazil to 35 ground control points measured with survey grade GNSS receivers. The terrain model generated from full-density (approx. 20 returns/sq m) data was highly accurate (mean signed error of 0.19 +/-0.97 m), while those derived from reduced-density datasets (8/sq m, 4/sq m, 2/sq m and 1/sq m) were increasingly less accurate. Canopy heights calculated from reduced-density lidar data declined as data density decreased due to the inability to accurately model the terrain surface. For lidar return densities below 4/sq m, the bias in height estimates translated into errors of 80-125 Mg/ha in predicted aboveground biomass. Conclusions: Given the growing emphasis on the use of airborne lidar for forest management, carbon monitoring, and conservation efforts, the results of this study highlight the importance of careful survey planning and consistent sampling for accurate quantification of aboveground biomass stocks and dynamics. Approaches that rely primarily on canopy height to estimate aboveground biomass are sensitive to DTM errors from variability in lidar sampling density.

Airborne lidar↗
NASA NTRS2014

Hypersonic Separated Flows About "Tick" Configurations With Sensitivity to Model Design

This paper presents computational results obtained by applying the direct simulation Monte Carlo (DSMC) method for hypersonic nonequilibrium flow about "tick-shaped" model configurations. These test models produces a complex flow where the nonequilibrium and rarefied aspects of the flow are initially enhanced as the flow passes over an expansion surface, and then the flow encounters a compression surface that can induce flow separation. The resulting flow is such that meaningful numerical simulations must have the capability to account for a significant range of rarefaction effects; hence the application of the DSMC method in the current study as the flow spans several flow regimes, including transitional, slip, and continuum. The current focus is to examine the sensitivity of both the model surface response (heating, friction and pressure) and flowfield structure to assumptions regarding surface boundary conditions and more extensively the impact of model design as influenced by leading edge configuration as well as the geometrical features of the expansion and compression surfaces. Numerical results indicate a strong sensitivity to both the extent of the leading edge sharpness and the magnitude of the leading edge bevel angle. Also, the length of the expansion surface for a fixed compression surface has a significant impact on the extent of separated flow.

Moss, J. N.↗
NASA NTRS2002

Impact Cratering Calculations

Many Martian craters are surrounded by ejecta blankets which appear to have been fluidized forming lobate and layered deposits terminated by one or more continuous distal scarps, or ramparts. One of the first hypotheses for the formation of so-called rampart ejecta features was shock-melting of subsurface ice, entrainment of liquid water into the ejecta blanket, and subsequent fluidized flow. Our work quantifies this concept. Rampart ejecta found on all but the youngest volcanic and polar regions, and the different rampart ejecta morphologies are correlated with crater size and terrain. In addition, the minimum diameter of craters with rampart features decreases with increasing latitude indicating that ice laden crust resides closer to the surface as one goes poleward on Mars. Our second goal in was to determine what strength model(s) reproduce the faults and complex features found in large scale gravity driven craters. Collapse features found in large scale craters require that the rock strength weaken as a result of the shock processing of rock and the later cratering shear flows. In addition to the presence of molten silicate in the intensely shocked region, the presence of water, either ambient, or the result of shock melting of ice weakens rock. There are several other mechanisms for the reduction of strength in geologic materials including dynamic tensile and shear induced fracturing. Fracturing is a mechanism for large reductions in strength. We found that by incorporating damage into the models that we could in a single integrated impact calculation, starting in the atmosphere produce final crater profiles having the major features found in the field measurements (central uplifts, inner ring, terracing and faulting). This was accomplished with undamaged surface strengths (0.1 GPa) and in depth strengths (1.0 GPa).

Ahrens, Thomas J.↗
NASA NTRS2022

STITCH: A Subgrid-Scale Model for Energy Buildup in the Solar Corona

The solar corona routinely exhibits explosive activity, in particular coronal mass ejections and their accompanying eruptive ares, that have global-scale consequences. These events and their smaller counterparts, coronal jets, originate in narrow, sinuous lament channels. The key processes that form and evolve the channels operate on still smaller spatial scales and much longer time scales, culminating in a vast separation of characteristic lengths and times that govern these explosive phenomena. In this article, we describe implementation and tests of an efficient subgrid-scale model for generating eruptive structures in magnetohydrodynamics (MHD) coronal simulations. STITCH {STatistical InjecTion of Condensed Helicity { is a physics-based, reduced representation of helicity condensation: a process wherein small-scale vortical surface convection forms ubiquitous current sheets, and pervasive reconnection across the sheets mediates an inverse cascade of magnetic helicity and free energy, thereby forming the lament channels. We have developed a formalism, STITCH, that abstracts these complex processes into a single term in Ohm's law and the induction equation that directly injects tangential magnetic flux into the low corona. We show that our approach is in very good agreement with a full helicity-condensation calculation that treats all of the dynamics explicitly, while enabling substantial reductions in temporal duration and spatial resolution. In addition, we illustrate the flexibility of STITCH at forming localized lament channels and at energizing complex surface flux distributions that have sinuous boundaries. STITCH is simple to implement and computationally ecient, making it a powerful technique for physics-based modeling of solar eruptive events.

J T Dahlin↗
NASA NTRS2016

An Efficient Ray-Tracing Method for Determining Terrain Intercepts in EDL Simulations

The calculation of a ray's intercept from an arbitrary point in space to a prescribed surface is a common task in computer simulations. The arbitrary point often represents an object that is moving according to the simulation, while the prescribed surface is fixed in a defined frame. For detailed simulations, this surface becomes complex, taking the form of real-world objects such as mountains, craters or valleys which require more advanced methods to accurately calculate a ray's intercept location. Incorporation of these complex surfaces has commonly been implemented in graphics systems that utilize highly optimized graphics processing units to analyze such features. This paper proposes a simplified method that does not require computationally intensive graphics solutions, but rather an optimized ray-tracing method for an assumed terrain dataset. This approach was developed for the Mars Science Laboratory mission which landed on the complex terrain of Gale Crater. First, this paper begins with a discussion of the simulation used to implement the model and the applicability of finding surface intercepts with respect to atmosphere modeling, altitude determination, radar modeling, and contact forces influencing vehicle dynamics. Next, the derivation and assumptions of the intercept finding method are presented. Key assumptions are noted making the routines specific to only certain types of surface data sets that are equidistantly spaced in longitude and latitude. The derivation of the method relies on ray-tracing, requiring discussion on the formulation of the ray with respect to the terrain datasets. Further discussion includes techniques for ray initialization in order to optimize the intercept search. Then, the model implementation for various new applications in the simulation are demonstrated. Finally, a validation of the accuracy is presented along with the corresponding data sets used in the validation. A performance summary of the method will be shown using the analysis from the Mars Science Laboratory's terminal descent sensing model. Alternate uses will also be shown for determining horizon maps and orbiter set times.

Shidner, Jeremy D.↗
NASA NTRS2012

Surface and Flow Field Measurements on the FAITH Hill Model

A series of experimental tests, using both qualitative and quantitative techniques, were conducted to characterize both surface and off-surface flow characteristics of an axisymmetric, modified-cosine-shaped, wall-mounted hill named "FAITH" (Fundamental Aero Investigates The Hill). Two separate models were employed: a 6" high, 18" base diameter machined aluminum model that was used for wind tunnel tests and a smaller scale (2" high, 6" base diameter) sintered nylon version that was used in the water channel facility. Wind tunnel and water channel tests were conducted at mean test section speeds of 165 fps (Reynolds Number based on height = 500,000) and 0.1 fps (Reynolds Number of 1000), respectively. The ratio of model height to boundary later height was approximately 3 for both tests. Qualitative techniques that were employed to characterize the complex flow included surface oil flow visualization for the wind tunnel tests, and dye injection for the water channel tests. Quantitative techniques that were employed to characterize the flow included Cobra Probe to determine point-wise steady and unsteady 3D velocities, Particle Image Velocimetry (PIV) to determine 3D velocities and turbulence statistics along specified planes, Pressure Sensitive Paint (PSP) to determine mean surface pressures, and Fringe Imaging Skin Friction (FISF) to determine surface skin friction (magnitude and direction). This initial report summarizes the experimental set-up, techniques used, data acquired and describes some details of the dataset that is being constructed for use by other researchers, especially the CFD community. Subsequent reports will discuss the data and their interpretation in more detail

Bell, James H.↗
NASA NTRS2022

Coupling Carbon Oxidation and Surface Recession in Direct-Simulation Monte Carlo Code, SPARTA

Ablative thermal protection system (TPS) materials for spacecraft are composites that are often made out of carbon-based reinforcement and a polymeric matrix. They endure high-temperature oxidation and surface recession when re-entering Earth’s atmosphere. Ablation is the result of many coupled and competing thermal, mechanical, and chemical phenomena, and it is difficult to isolate the role of each on the overall degradation of the TPS. Here we develop an ablation model for material recession coupled explicitly to finite rate carbon oxidation in complex microstructures. In this work, Stochastic PArallel Rarified-gas Time-accurate Analyzer (SPARTA), a direct-simulation Monte Carlo (DSMC) code, is modified to allow oxidation-driven ablation of implicitly defined carbon surfaces. In SPARTA, implicit surfaces are generated from the grid corner point values via a marching cubes algorithm, therefore creating a new set of surface elements every time ablation is performed. The finite-rate oxidation model developed by Gopalan et. al, was adapted to tally surface reactions and other surface data on a per-grid cell basis. The ablation functionality was also adjusted so once the reactions have occurred, the number of reactions leading to CO formation can be converted to corner point reduction values; therefore, carbon removal is directly proportional to surface recession. We also develop robust algorithms which handle the evolution of the flow cells and solid material regions, including split cells (flow cell divided in two by a solid surface). Finally, we demonstrate our implicit chemistry model for 2D and 3D geometries by producing reaction statistics and detailed visualization of oxidation-induced material recession at the microscale.

V Arias↗