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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 253 records · Page 14

Can general circulation models (GCMs) represent cloud liquid water path adjustments to aerosol–cloud interactions?

Abstract. General circulation models (GCMs), unlike other lines of evidence, indicate that anthropogenic aerosols cause a global-mean increase in cloud liquid water path (ℒ) and thus a negative adjustment to radiative forcing of the climate by aerosol–cloud interactions. In part 1 of this series of papers, we showed that this is true even in models that reproduce the negative correlation observed in present-day internal variability in ℒ and cloud droplet number concentration (Nd). We studied several possible confounding mechanisms that could explain the noncausal cloud–aerosol correlations in GCMs and that possibly contaminate observational estimates of radiative adjustments. Here, we perform single-column and full-atmosphere GCM experiments to investigate the causal model-physics mechanisms underlying the model radiative adjustment estimate. We find that both aerosol–cloud interaction mechanisms thought to be operating in real clouds – precipitation suppression and entrainment evaporation enhancement – are active in GCMs and behave qualitatively in agreement with physical process understanding. However, the modeled entrainment enhancement has a negligible global-mean effect. This raises the question of whether the GCM estimate is incorrect due to parametric or base-state representation errors or whether the process understanding gleaned from a limited set of canonical cloud cases is insufficiently representative of the diversity of clouds in the real climate. Regardless, even at limited resolution, the GCM physics appears able to parameterize the small-scale microphysics–turbulence interplay responsible for the entrainment enhancement mechanism. We suggest ways to resolve tension between current and future (storm-resolving) global modeling systems and other lines of evidence in synthesis climate projections.

54 ENVIRONMENTAL SCIENCES↗

Leveraging transfer learning and leaf spectroscopy for leaf trait prediction with broad spatial, species, and temporal applicability

Accurate and reliable prediction of leaf traits is crucial for understanding plant adaptations to environmental variation, monitoring terrestrial ecosystems, and enhancing comprehension of functional diversity and ecosystem functioning. Currently, various approaches (e.g., statistical, physical models) have been developed to estimate leaf traits through hyperspectral remote sensing and leaf spectroscopy. However, the absence of high-performing, transferable, and stable models across various domains of space, plant functional types (PFTs) and seasons hinder our ability to quantify and comprehend spatiotemporal variations in leaf traits. This study proposes robust and highly transferable models for better predicting leaf traits with hyperspectral reflectance. Initially, three datasets were assembled, pairing common leaf traits — chlorophyll (Chla+b), carotenoids (Ccar), leaf mass per area (LAM), equivalent water thickness (EWT) — with leaf spectra measurements collected across diverse geographic locations in the U.S. and Europe, PFTs, and seasons. Measurements were acquired using spectroradiometers (e.g., ASD FieldSpec 3/4/Pro and SVC HR-1024i) with integrating spheres, leaf clips, and contact probes. Here, we then developed transfer learning-based hybrid models that incorporated the domain knowledge of radiative transfer models (RTMs) through pretraining processes and were well-constrained by fine-tuning with field measurements. Through comparison with other state-of-the-art statistical models, including partial-least squares regression (PLSR) and Gaussian Process Regression (GPR), as well as pure physical models, we found that the proposed transfer learning models achieved better predictive performance and higher transferability. Specifically, compared to other statistical models and pure RTMs, the transfer learning model exhibited higher coefficient of determination (R 2 ) values with range of 0.01 to 0.79, lower normalized root mean square error (NRMSE) with range of 0.06 % to 33.25 % in model performance. Additionally, the models exhibited improved transferability, with higher R 2 values range from 0.04 to 0.32, lower NRMSE range from 0.08 % to 30.81 %. The findings underscore that transfer learning models through integrating domain knowledge from RTMs and limited observations, can harness the advantages of both RTMs and statistical models and serve as a promising approach for effectively predicting leaf traits.

59 BASIC BIOLOGICAL SCIENCES↗

Model Forecast Skill and Sensitivity to Initial Conditions in the Seasonal Sea Ice Outlook

We explore the skill of predictions of September Arctic sea ice extent from dynamical models participating in the Sea Ice Outlook (SIO). Forecasts submitted in August, at roughly 2 month lead times, are skillful. However, skill is lower in forecasts submitted to SIO, which began in 2008, than in hindcasts (retrospective forecasts) of the last few decades. The multimodel mean SIO predictions offer slightly higher skill than the single-model SIO predictions, but neither beats a damped persistence forecast at longer than 2 month lead times. The models are largely unsuccessful at predicting each other, indicating a large difference in model physics and/or initial conditions. Motivated by this, we perform an initial condition sensitivity experiment with four SIO models, applying a fixed −1 m perturbation to the initial sea ice thickness. The significant range of the response among the models suggests that different model physics make a significant contribution to forecast uncertainty.

Arctic Sea↗

Introduction to Analysis Methods for Big Earth Data

Big Earth Data are too big to be tractable to simple data inspection. Thus, they typically require models to make sense of all the data. Useful models for Big Earth Data may be physical, statistical, or machine learning based. While physical models are ideal for understanding the data, they are not always feasible, particularly when our ability to observe at finer scales exceeds our ability to incorporate the physics. Statistical models are more generalized, but computationally intensive for many Earth Observation datasets. Machine Learning models generally scale well but are sometimes limited in the physical understanding they can offer. Hybrid models combine attributes—and advantages—of two or more of these types.

Christopher Lynnes↗

Modelling of physical influences in sea level records for vertical crustal movement detection

Attempts to specify and evaluate such physical influences are reviewed with the intention of identifying problem areas and promising approaches. An example of linear modelling based on air/water temperatures, atmospheric pressure, river discharges, geostrophic and/or local wind velocities, and including forced period terms to allow for the long period tides and Chandlerian polar motion is evaluated and applied to monthly mean sea levels recorded in Atlantic Canada. Refinement of the model to admit phase lag in the response to some of the driving phenomena is demonstrated. Spectral analysis of the residuals is employed to assess the model performance. The results and associated statistical parameters are discussed with emphasis on elucidating the sensitivity of the technique for detection of local episodic and secular vertical crustal movements, the problem areas most critical to the type of approach, and possible further developments.

Anderson, E. G.↗

Physics-Based Modeling of Meteor Entry and Breakup

A new research effort at NASA Ames Research Center has been initiated in Planetary Defense, which integrates the disciplines of planetary science, atmospheric entry physics, and physics-based risk assessment. This paper describes work within the new program and is focused on meteor entry and breakup.Over the last six decades significant effort was expended in the US and in Europe to understand meteor entry including ablation, fragmentation and airburst (if any) for various types of meteors ranging from stony to iron spectral types. These efforts have produced primarily empirical mathematical models based on observations. Weaknesses of these models, apart from their empiricism, are reliance on idealized shapes (spheres, cylinders, etc.) and simplified models for thermal response of meteoritic materials to aerodynamic and radiative heating. Furthermore, the fragmentation and energy release of meteors (airburst) is poorly understood.On the other hand, flight of human-made atmospheric entry capsules is well understood. The capsules and their requisite heatshields are designed and margined to survive entry. However, the highest speed Earth entry for capsules is 13 kms (Stardust). Furthermore, Earth entry capsules have never exceeded diameters of 5 m, nor have their peak aerothermal environments exceeded 0.3 atm and 1 kW/sq cm. The aims of the current work are: (i) to define the aerothermal environments for objects with entry velocities from 13 to 20 kms; (ii) to explore various hypotheses of fragmentation and airburst of stony meteors in the near term; (iii) to explore the possibility of performing relevant ground-based tests to verify candidate hypotheses; and (iv) to quantify the energy released in airbursts. The results of the new simulations will be used to anchor said risk assessment analyses. With these aims in mind, state-of-the-art entry capsule design tools are being extended for meteor entries. We describe: (i) applications of current simulation tools to spherical geometries of diameters ranging from 1 to 100 m for an entry velocity of 20 kms and stagnation pressures ranging from 1 to 100 atm; (ii) the influence of shape and departure of heating environment predictions from those for a simple spherical geometry; (iii) assessment of thermal response models for silica subject to intense radiation; and (iv) results for porosity-driven gross fragmentation of meteors, idealized as a collection of smaller objects. Lessons learned from these simulations will be used to help understand the Chelyabinsk meteor entry up to its first point of fragmentation.

Near-Earth Asteroids↗

Physics-Based Modeling of Meteor Entry and Breakup

A new research effort at NASA Ames Research Center has been initiated in Planetary Defense, which integrates the disciplines of planetary science, atmospheric entry physics, and physics-based risk assessment. This paper describes work within the new program and is focused on meteor entry and breakup. Over the last six decades significant effort was expended in the US and in Europe to understand meteor entry including ablation, fragmentation and airburst (if any) for various types of meteors ranging from stony to iron spectral types. These efforts have produced primarily empirical mathematical models based on observations. Weaknesses of these models, apart from their empiricism, are reliance on idealized shapes (spheres, cylinders, etc.) and simplified models for thermal response of meteoritic materials to aerodynamic and radiative heating. Furthermore, the fragmentation and energy release of meteors (airburst) is poorly understood. On the other hand, flight of human-made atmospheric entry capsules is well understood. The capsules and their requisite heatshields are designed and margined to survive entry. However, the highest speed Earth entry for capsules is less than 13 km/s (Stardust). Furthermore, Earth entry capsules have never exceeded diameters of 5 m, nor have their peak aerothermal environments exceeded 0.3 atm and 1 kW/cm2. The aims of the current work are: (i) to define the aerothermal environments for objects with entry velocities from 13 to greater than 20 km/s; (ii) to explore various hypotheses of fragmentation and airburst of stony meteors in the near term; (iii) to explore the possibility of performing relevant ground-based tests to verify candidate hypotheses; and (iv) to quantify the energy released in airbursts. The results of the new simulations will be used to anchor said risk assessment analyses. With these aims in mind, state-of-the-art entry capsule design tools are being extended for meteor entries. We describe: (i) applications of current simulation tools to spherical geometries of diameters ranging from 1 to 100 m for an entry velocity of 20 km/s and stagnation pressures ranging from 1 to 100 atm; (ii) the influence of shape and departure of heating environment predictions from those for a simple spherical geometry; (iii) assessment of thermal response models for silica subject to intense radiation; and (iv) results for porosity-driven gross fragmentation of meteors, idealized as a collection of smaller objects. Lessons learned from these simulations will be used to help understand the Chelyabinsk meteor entry up to its first point of fragmentation.

Aerothermodynamics↗

Physics-Based Modeling of Meteor Entry and Breakup

A new research effort at NASA Ames Research Center has been initiated in Planetary Defense, which integrates the disciplines of planetary science, atmospheric entry physics, and physics-based risk assessment. This paper describes work within the new program and is focused on meteor entry and breakup. Over the last six decades significant effort was expended in the US and in Europe to understand meteor entry including ablation, fragmentation and airburst (if any) for various types of meteors ranging from stony to iron spectral types. These efforts have produced primarily empirical mathematical models based on observations. Weaknesses of these models, apart from their empiricism, are reliance on idealized shapes (spheres, cylinders, etc.) and simplified models for thermal response of meteoritic materials to aerodynamic and radiative heating. Furthermore, the fragmentation and energy release of meteors (airburst) is poorly understood. On the other hand, flight of human-made atmospheric entry capsules is well understood. The capsules and their requisite heat shields are designed and margined to survive entry. However, the highest speed Earth entry for capsules is 13 kms (Stardust). Furthermore, Earth entry capsules have never exceeded diameters of 5 m, nor have their peak aerothermal environments exceeded 0.3 atm and 1 kWcm2. The aims of the current work are: (i) to define the aerothermal environments for objects with entry velocities from 13 to 20 kms; (ii) to explore various hypotheses of fragmentation and airburst of stony meteors in the near term; (iii) to explore the possibility of performing relevant ground-based tests to verify candidate hypotheses; and (iv) to quantify the energy released in airbursts. The results of the new simulations will be used to anchor said risk assessment analyses.With these aims in mind, state-of-the-art entry capsule design tools are being extended for meteor entries. We describe: (i) applications of current simulation tools to spherical geometries of diameters ranging from 1 to 100 m for an entry velocity of 20 kms and stagnation pressures ranging from 1 to 100 atm; (ii) the influence of shape and departure of heating environment predictions from those for a simple spherical geometry; (iii) assessment of thermal response models for silica subject to intense radiation; and (iv) results for porosity-driven gross fragmentation of meteors, idealized as a collection of smaller objects. Lessons learned from these simulations will be used to help understand the Chelyabinsk meteor entry up to its first point of fragmentation.

Atmospheric Entry↗

Astrophysical tests for radiative decay of neutrinos and fundamental physics implications

The radiative lifetime tau for the decay of massious neutrinos was calculated using various physical models for neutrino decay. The results were then related to the astrophysical problem of the detectability of the decay photons from cosmic neutrinos. Conversely, the astrophysical data were used to place lower limits on tau. These limits are all well below predicted values. However, an observed feature at approximately 1700 A in the ultraviolet background radiation at high galactic latitudes may be from the decay of neutrinos with mass approximately 14 eV. This would require a decay rate much larger than the predictions of standard models but could be indicative of a decay rate possible in composite models or other new physics. Thus an important test for substructure in leptons and quarks or other physics beyond the standard electroweak model may have been found.

Stecker, F. W.↗

Reaction Wheel Disturbance Model Extraction Software - RWDMES

The RWDMES is a tool for modeling the disturbances imparted on spacecraft by spinning reaction wheels. Reaction wheels are usually the largest disturbance source on a precision pointing spacecraft, and can be the dominating source of pointing error. Accurate knowledge of the disturbance environment is critical to accurate prediction of the pointing performance. In the past, it has been difficult to extract an accurate wheel disturbance model since the forcing mechanisms are difficult to model physically, and the forcing amplitudes are filtered by the dynamics of the reaction wheel. RWDMES captures the wheel-induced disturbances using a hybrid physical/empirical model that is extracted directly from measured forcing data. The empirical models capture the tonal forces that occur at harmonics of the spin rate, and the broadband forces that arise from random effects. The empirical forcing functions are filtered by a physical model of the wheel structure that includes spin-rate-dependent moments (gyroscopic terms). The resulting hybrid model creates a highly accurate prediction of wheel-induced forces. It accounts for variation in disturbance frequency, as well as the shifts in structural amplification by the whirl modes, as the spin rate changes. This software provides a point-and-click environment for producing accurate models with minimal user effort. Where conventional approaches may take weeks to produce a model of variable quality, RWDMES can create a demonstrably high accuracy model in two hours. The software consists of a graphical user interface (GUI) that enables the user to specify all analysis parameters, to evaluate analysis results and to iteratively refine the model. Underlying algorithms automatically extract disturbance harmonics, initialize and tune harmonic models, and initialize and tune broadband noise models. The component steps are described in the RWDMES user s guide and include: converting time domain data to waterfall PSDs (power spectral densities); converting PSDs to order analysis data; extracting harmonics; initializing and simultaneously tuning a harmonic model and a wheel structural model; initializing and tuning a broadband model; and verifying the harmonic/broadband/structural model against the measurement data. Functional operation is through a MATLAB GUI that loads test data, performs the various analyses, plots evaluation data for assessment and refinement of analysis parameters, and exports the data to documentation or downstream analysis code. The harmonic models are defined as specified functions of frequency, typically speed-squared. The reaction wheel structural model is realized as mass, damping, and stiffness matrices (typically from a finite element analysis package) with the addition of a gyroscopic forcing matrix. The broadband noise model is realized as a set of speed-dependent filters. The tuning of the combined model is performed using nonlinear least squares techniques. RWDMES is implemented as a MATLAB toolbox comprising the Fit Manager for performing the model extraction, Data Manager for managing input data and output models, the Gyro Manager for modifying wheel structural models, and the Harmonic Editor for evaluating and tuning harmonic models. This software was validated using data from Goodrich E wheels, and from GSFC Lunar Reconnaissance Orbiter (LRO) wheels. The validation testing proved that RWDMES has the capability to extract accurate disturbance models from flight reaction wheels with minimal user effort.

Blaurock, Carl↗

MPD Thruster Performance Analytic Models

Magnetoplasmadynamic (MPD) thrusters are capable of accelerating quasi-neutral plasmas to high exhaust velocities using Megawatts (MW) of electric power. These characteristics make such devices worthy of consideration for demanding, far-term missions such as the human exploration of Mars or beyond. Assessment of MPD thrusters at the system and mission level is often difficult due to their status as ongoing experimental research topics rather than developed thrusters. However, in order to assess MPD thrusters utility in later missions, some adequate characterization of performance, or more exactly, projected performance, and system level definition are required for use in analyses. The most recent physical models of self-field MPD thrusters have been examined, assessed, and reconfigured for use by systems and mission analysts. The physical models allow for rational projections of thruster performance based on physical parameters that can be measured in the laboratory. The models and their implications for the design of future MPD thrusters are presented.

Gilland, James↗

MPD Thruster Performance Analytic Models

Magnetoplasmadynamic (MPD) thrusters are capable of accelerating quasi-neutral plasmas to high exhaust velocities using Megawatts (MW) of electric power. These characteristics make such devices worthy of consideration for demanding, far-term missions such as the human exploration of Mars or beyond. Assessment of MPD thrusters at the system and mission level is often difficult due to their status as ongoing experimental research topics rather than developed thrusters. However, in order to assess MPD thrusters utility in later missions, some adequate characterization of performance, or more exactly, projected performance, and system level definition are required for use in analyses. The most recent physical models of self-field MPD thrusters have been examined, assessed, and reconfigured for use by systems and mission analysts. The physical models allow for rational projections of thruster performance based on physical parameters that can be measured in the laboratory. The models and their implications for the design of future MPD thrusters are presented.

Gilland, James↗

Computational and Experimental Fluid-Structure Interaction Analysis of a High-Lift Wing with a Slat-Cove Filler for Noise Reduction

Airframe noise is a significant component of overall noise produced by transport aircraft during landing and approach (low speed maneuvers). A significant source for this noise is the cove of the leading-edge slat. The slat-cove filler (SCF) has been shown to be effective at mitigating slat noise. The objective of this work is to understand the fluid-structure interaction (FSI) behavior of a superelastic shape memory alloy (SMA) SCF in flow using both computational and physical models of a high-lift wing. Initial understanding of flow around the SCF and wing is obtained using computational fluid dynamics (CFD) analysis at various angles of attack. A framework compatible with an SMA constitutive model (implemented as a user material subroutine) is used to perform FSI analysis for multiple flow and configuration cases. A scaled physical model of the high-lift wing is constructed and tested in the Texas A&M 3 ft-by-4-foot wind tunnel. Initial validation of both CFD and FSI analysis is conducted by comparing lift, drag and pressure distributions with experimental results.

Scholten, William D.↗

Improved Systematic Pointing Error Model for the DSN Antennas

New pointing models have been developed for large reflector antennas whose construction is founded on elevation over azimuth mount. At JPL, the new models were applied to the Deep Space Network (DSN) 34-meter antenna s subnet for corrections of their systematic pointing errors; it achieved significant improvement in performance at Ka-band (32-GHz) and X-band (8.4-GHz). The new models provide pointing improvements relative to the traditional models by a factor of two to three, which translate to approximately 3-dB performance improvement at Ka-band. For radio science experiments where blind pointing performance is critical, the new innovation provides a new enabling technology. The model extends the traditional physical models with higher-order mathematical terms, thereby increasing the resolution of the model for a better fit to the underlying systematic imperfections that are the cause of antenna pointing errors. The philosophy of the traditional model was that all mathematical terms in the model must be traced to a physical phenomenon causing antenna pointing errors. The traditional physical terms are: antenna axis tilts, gravitational flexure, azimuth collimation, azimuth encoder fixed offset, azimuth and elevation skew, elevation encoder fixed offset, residual refraction, azimuth encoder scale error, and antenna pointing de-rotation terms for beam waveguide (BWG) antennas. Besides the addition of spherical harmonics terms, the new models differ from the traditional ones in that the coefficients for the cross-elevation and elevation corrections are completely independent and may be different, while in the traditional model, some of the terms are identical. In addition, the new software allows for all-sky or mission-specific model development, and can utilize the previously used model as an a priori estimate for the development of the updated models.

Rochblatt, David J.↗

A roadmap toward scaling, reasoning and self-evolving foundation models for nuclear and particle physics

Foundation models have revolutionized artificial intelligence, with Large Language Models demonstrating unprecedented capabilities in multimodal understanding, reasoning and tool use. Nuclear and particle physics stands at a critical juncture where similar transformative potential awaits realization. The field generates exabytes of experimental data, exascale simulations, and decades of theoretical insights — yet these remain largely disconnected from modern Artifical Intelligence (AI) capabilities, with most physics AI applications confined to narrow, task-specific models that suffer from domain shifting when applied to real experimental data. We present a roadmap for FM4NPP (Foundation Model for Nuclear and Particle Physics), systematically scaling from current proof-of-concept models to trillion-parameter architectures capable of autonomous discovery. Our approach advances three critical frontiers: unified data infrastructure integrating detector data, scientific knowledge and computational tools across global facilities; multi-facility foundation models enabling cross-experiment knowledge transfer and accelerated discovery; and agentic AI capabilities for reasoning and autonomous tool use. The resulting self-evolving FM4NPP will transform physics research by converting time-intensive data analysis, theory derivation and computational bottlenecks into rapid AI–human collaborative discovery. This paradigm shift promises to fundamentally accelerate scientific progress in nuclear and particle physics, enabling researchers to focus on high-level insights while AI handles routine analysis and explores vast parameter spaces beyond human capacity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Study of Magnetic Damping Effect on Convection and Solidification Under G-Jitter Conditions

As shown in space flight experiments, g-jitter is a critical issue affecting solidification processing of materials in microgravity. This study aims to provide, through extensive numerical simulations and ground based experiments, an assessment of the use of magnetic fields in combination with microgravity to reduce the g-jitter induced convective flows in space processing systems. Analytical solutions and 2-D and 3-D numerical models for g-jitter driven flows in simple solidification systems with and without the presence of an applied magnetic field have been developed and extensive analyses were carried out. A physical model was also constructed and PIV measurements compared reasonably well with predictions from numerical models. Some key points may be summarized as follows: (1) the amplitude of the oscillating velocity decreases at a rate inversely proportional to the g-jitter frequency and with an increase in the applied magnetic field; (2) the induced flow oscillates at approximately the same frequency as the affecting g-jitter, but out of a phase angle; (3) the phase angle is a complicated function of geometry, applied magnetic field, temperature gradient and frequency; (4) g-jitter driven flows exhibit a complex fluid flow pattern evolving in time; (5) the damping effect is more effective for low frequency flows; and (6) the applied magnetic field helps to reduce the variation of solutal distribution along the solid-liquid interface. Work in progress includes developing numerical models for solidification phenomena with the presence of both g-jitter and magnetic fields and developing a ground-based physical model to verify numerical predictions.

Li, Ben Q.↗

Numerical modeling of physical vapor transport under microgravity conditions: Effect of thermal creep and stress

One of the most promising applications of microgravity (micro-g) environments is the manufacture of exotic and high-quality crystals in closed cylindrical ampoules using physical vapor transport (PVT) processes. The quality enhancements are believed to be due to the absence of buoyant convection in the weightless environment - resulting in diffusion-limited transport of the vapor. In a typical experiment, solid-phase sample material is initially contained at one end of the ampoule. The sample is made to sublime into the vapor phase and deposit onto the opposite end by maintaining the source at an elevated temperature with respect to the deposit. Identification of the physical factors governing both the rates and uniformity of crystal growth, and the optimization of the micro-g technology, will require an accurate modeling of the vapor transport within the ampoule. Previous micro-g modeling efforts have approached the problem from a 'classical' convective/diffusion formulation, in which convection is driven by the action of buoyancy on thermal and solutal density differences. The general conclusion of these works have been that in low gravity environments the effect of buoyancy on vapor transport is negligible, and vapor transport occurs in a diffusion-limited mode. However, it has been recently recognized than in the non-isothermal (and often low total pressure) conditions encountered in ampoules, the commonly-assumed no-slip boundary condition to the differential equations governing fluid motion can be grossly unrepresentative of the actual situation. Specifically, the temperature gradients can give rise to thermal creep flows at the ampoule side walls. In addition, temperature gradients in the vapor itself can, through the action of thermal stress, lead to bulk fluid convection.

Mackowski, Daniel W.↗

A physically consistent model for artificial dissipation in transonic potential flow computations

The effect that artificial dissipation has on numerical solutions of the transonic Full Potential Equation (FPE) are investigated by comparing the artificially dissipative FPE to a Physically Dissipative Potential (PDP) equation. Analytic expressions were derived from the variables C and M sub c that are used in the artificial density formulation. It was shown that these new values generate artificial dissipation which is equivalent to the physical dissipation existing in the PDP equation. The new expression for the variables C and M sub c can easily be incorporated into the existing full potential codes which are based either on the artificial density or on the artificial viscosity formulation. A comparison of Physically Dissipative Potential (PDP), Artificial Density or Viscosity (ADV), Artificial Mass Flux (AMF), and ADV with variable C and M sub c formulation (MCC) is also presented.

Dulikravich, George S.↗