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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Enhancing 2D hydrodynamic flood models through machine learning and urban drainage integration

Two-dimensional hydrodynamic flood models are commonly employed for simulating flood extent and inundation depth. However, the influence of urban drainage network (UDN) is frequently overlooked in these models, potentially compromising their accuracy. Furthermore, the expensive computational costs and longer processing times make them challenging for large-scale hydrodynamic simulation. To address these challenges, this paper develops a machine learning (ML)-driven emulator for an open-source flood model, the Two-dimensional Runoff Inundation Toolkit for Operational Needs (TRITON). A TRITON-ML Emulator (TR-Emulator) that utilizes Convolutional Long Short-Term Memory is developed to capture the spatiotemporal features of flood events based on the outputs from TRITON. We further enhance the emulator by integrating UDN parameters (TR-UDN), such as the flow capacity of drainage pipes, pipe size, and pipe length, via an ML stacking technique to improve the water surface elevation (WSE) simulation. Hurricane Harvey 2017 in Houston, TX is used as the case study. We compare WSE results from TRITON, TR-Emulator, TR-UDN, and the United States Geological Survey (USGS) observations to evaluate the performance of these models. The results indicate that the TR-Emulator effectively replicates the WSE simulated by TRITON. Additionally, TR-UDN performs well in capturing WSE patterns and peak flows, aligning more closely with USGS observations, except in areas with milder slopes where conveyance discrepancies are observed. We further test the generalizability of our ML-based models using another smaller event. This paper shows that the TR-Emulator is effective for users and engineers to emulate a 2D hydrodynamic model, and the enhanced version of the TR-Emulator, TR-UDN, can be an efficient tool for predicting WSEs during urban flooding.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Assessing climate-change-induced flood risk in the Conasauga River watershed: an application of ensemble hydrodynamic inundation modeling

Abstract. This study evaluates the impact of potential future climate change on flood regimes, floodplain protection, and electricity infrastructures across the Conasauga River watershed in the southeastern United States through ensemble hydrodynamic inundation modeling. The ensemble streamflow scenarios were simulated by the Distributed Hydrology Soil Vegetation Model (DHSVM) driven by (1) 1981–2012 Daymet meteorological observations and (2) 11 sets of downscaled global climate models (GCMs) during the 1966–2005 historical and 2011–2050 future periods. Surface inundation was simulated using a GPU-accelerated Two-dimensional Runoff Inundation Toolkit for Operational Needs (TRITON) hydrodynamic model. A total of 9 out of the 11 GCMs exhibit an increase in the mean ensemble flood inundation areas. Moreover, at the 1 % annual exceedance probability level, the flood inundation frequency curves indicate a ∼ 16 km2 increase in floodplain area. The assessment also shows that even after flood-proofing, four of the substations could still be affected in the projected future period. The increase in floodplain area and substation vulnerability highlights the need to account for climate change in floodplain management. Overall, this study provides a proof-of-concept demonstration of how the computationally intensive hydrodynamic inundation modeling can be used to enhance flood frequency maps and vulnerability assessment under the changing climatic conditions.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially non-oscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗
NASA NTRS1991

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially nonoscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗
DOE OSTI2023

Higher-order cumulants and correlation functions of proton multiplicity distributions in s N N = 3 GeV Au + Au collisions at the RHIC STAR experiment

Here, we report a measurement of cumulants and correlation functions of event-by-event proton multiplicity distributions from fixed-target Au+Au collisions at $\sqrt{s_\text{NN}}$ = 3 GeV measured by the STAR experiment. Protons are identified within the rapidity (y) and transverse momentum ($p_T$) region –0:9 < $\textit{y}$ < 0 and 0:4 < pT < 2:0 GeV/c in the center-of-mass frame. A systematic analysis of the proton cumulants and correlation functions up to sixth-order as well as the corresponding ratios as a function of the collision centrality, $p_T$, and $\textit{y}$ are presented. The effect of pileup and initial volume fluctuations on these observables and the respective corrections are discussed in detail. The results are compared to calculations from the hadronic transport UrQMD model as well as a hydrodynamic model. In the most central 5% collisions, the value of proton cumulant ratio $C_4 = C_2$ is negative, drastically different from the values observed in Au+Au collisions at higher energies. Compared to model calculations including Lattice QCD, a hadronic transport model, and a hydrodynamic model, the strong suppression in the ratio of $C_4/C_2$ at 3 GeV Au+Au collisions indicates an energy regime dominated by hadronic interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Fluctuating hydrodynamics and the Rayleigh–Plateau instability

The Rayleigh–Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation–based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh–Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension–driven phenomena.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Hydrodynamic description of D meson production in high-energy heavy-ion collisions *

The large values and constituent-quark-number scaling of the elliptic flow of low-p T D mesons imply that charm quarks, initially produced through hard processes, might be partially thermalized through strong interactions with quark-gluon plasma (QGP) in high-energy heavy-ion collisions. To quantify the degree of thermalization of low-p T charm quarks, we compare the D 0 meson spectra and elliptic flow from a hydrodynamic model to experimental data as well as transport model simulations. We use an effective charm chemical potential at the freeze-out temperature to account for the initial charm quark production from hard processes and assume that they are thermalized in the local comoving frame of the medium before freeze-out. D 0 mesons are sampled statistically from the freeze-out hyper-surface of the expanding QGP as described by the event-by-event (3+1)D viscous hydrodynamic model CLVisc. Both the hydrodynamic and transport models can describe the elliptic flow of D 0 mesons at P T < 3 GeV/c as measured in Au+Au collisions at $sqrts_{NN} = 200$ GeV. Though the experimental data on spectra are consistent with the hydrodynamic result at small p T ~ 1 GeV/c, they deviate from the hydrodynamic model at high transverse momentum, GeV/c. The diffusion and parton energy loss mechanisms in the transport model can describe the measured spectra reasonably well within the theoretical uncertainty. Finally, our comparative study indicates that charm quarks only approach local thermal equilibrium at small p T , even though they acquire sizable elliptic flow comparable to light-quark hadrons at both small and intermediate p T .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2012

Calibration of Two-dimensional Floodplain Modeling in the Atchafalaya River Basin Using SAR Interferometry

Two-dimensional (2D) satellite imagery has been increasingly employed to improve prediction of floodplain inundation models. However, most focus has been on validation of inundation extent, with little attention on the 2D spatial variations of water elevation and slope. The availability of high resolution Interferometric Synthetic Aperture Radar (InSAR) imagery offers unprecedented opportunity for quantitative validation of surface water heights and slopes derived from 2D hydrodynamic models. In this study, the LISFLOOD-ACC hydrodynamic model is applied to the central Atchafalaya River Basin, Louisiana, during high flows typical of spring floods in the Mississippi Delta region, for the purpose of demonstrating the utility of InSAR in coupled 1D/2D model calibration. Two calibration schemes focusing on Manning s roughness are compared. First, the model is calibrated in terms of water elevations at a single in situ gage during a 62 day simulation period from 1 April 2008 to 1 June 2008. Second, the model is calibrated in terms of water elevation changes calculated from ALOS PALSAR interferometry during 46 days of the image acquisition interval from 16 April 2008 to 1 June 2009. The best-fit models show that the mean absolute errors are 3.8 cm for a single in situ gage calibration and 5.7 cm/46 days for InSAR water level calibration. The optimum values of Manning's roughness coefficients are 0.024/0.10 for the channel/floodplain, respectively, using a single in situ gage, and 0.028/0.10 for channel/floodplain the using SAR. Based on the calibrated water elevation changes, daily storage changes within the size of approx 230 sq km of the model area are also calculated to be of the order of 107 cubic m/day during high water of the modeled period. This study demonstrates the feasibility of SAR interferometry to support 2D hydrodynamic model calibration and as a tool for improved understanding of complex floodplain hydrodynamics

Hahn Chul Jung↗
NASA NTRS1996

Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

Smith, A. W.↗
NASA NTRS1995

Non-parabolic hydrodynamic formulations for the simulation of inhomogeneous semiconductor devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models can not fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations of the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship (hk)(exp 2)/2m = W(1 + alpha(W)). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(sup y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships: parabolic, Kane dispersion, and power low dispersion.

Smith, Arlynn W.↗
DOE OSTI2026

OC7 phase I: CFD investigation of viscous forces on rectangular members of semisubmersibles

In Phase I of the Offshore Code Comparison Collaboration 7 (OC7) project, we aim to address key questions related to the modeling of viscous hydrodynamic loads on floating platforms. Here, this paper presents results from a collaborative effort within Phase I of the OC7 project. We investigate viscous forces acting on the rectangular members of semisubmersible platforms using high-fidelity computational fluid dynamics (CFD) simulations. The parametric CFD analyses include two-and-a-half-dimensional (2.5D) simulations of pontoon sections of two different semisubmersible platform designs (the VolturnUS-S and the INO WINDMOOR) and full three-dimensional (3D) structure simulations of the VolturnUS-S platform. We extract both the added mass and drag coefficients that are typically used in engineering-level hydrodynamic models from the 2.5D forced oscillation simulations with various Keulegan-Carpenter numbers and compare them to the coefficients from the 3D forced oscillation simulations. We observe consistent variation of the coefficients along the pontoon legs due to 3D platform and free-surface effects. With the breadth of the simulations and component-level detailed analyses, this work establishes a useful database and several empirical formulas for selecting hydrodynamic coefficients when modeling semisubmersible platforms in engineering tools.

13 HYDRO ENERGY↗
DOE OSTI2023

Coupled wave-current modeling for hydrodynamic load analysis of macroalgae cultivation farms

Large-scale cultivation of macroalgae is one of the most promising biofuel sources that could reduce our consumption of fossil fuels and would be particularly economically competitive when grown for the co-production of additional goods such as food and textiles. Current production of biofuel from algal biomass is limited by labor costs and lack of data on potential impacts of cultivation and harvesting on marine and coastal environments as well as a comprehensive characterization of the impact of environmental conditions on macroalgal feedstock and their bioproduct and biofuel yield and quality. Awarded by the United States (U.S.) Department of Energy Advanced Research Projects Agency-Energy (ARPA-E) Macroalgae Research Inspiring Novel Energy Resources (MARINER) program, which seeks to enable the U.S. as a global leader in the production of marine biomass, the Marine Biological Laboratory (MBL) has been developing a test system for tropical seaweed cultivation in the Gulf of Mexico and the Caribbean. An integral step in designing macroalgae cultivation farms is to adequately characterize the hydrodynamic climate at potential growth sites. In regions like the Gulf of Mexico and the Caribbean, which are highly exposed to tropical cyclones, it is critical to not only consider the day-to-day hydrodynamic conditions but to also assess the risk of extreme sea states to ensure the survivability of future macroalgae farms. Under these considerations, the Pacific Northwest National Laboratory (PNNL) is providing modeling support for MBL to inform the design and siting of the farm systems that have been proposed for their ARPA-E MARINER project. This report describes the development of a high-resolution coupled storm surge and wave model to simulate the hydrodynamics and wave climate at proposed macroalgae cultivation sites selected by MBL in Florida and Puerto Rico. Model results, including model validation, water level, current distributions, and sea states, are discussed for both selected sites in Florida and Puerto Rico coast. These simulations provide an accurate insight into the hydrodynamic conditions that a macroalgae farm is likely to experience during its operational lifetime, including current information to support fine-scale hydrodynamic load modeling, risk analysis and system design.

09 BIOMASS FUELS↗
DOE OSTI2020

Possible octupole deformation of 208 Pb and the ultracentral v 2 to v 3 puzzle

Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of nonspherical nuclei. In the case of 129 Xe collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In 208 Pb collisions a discrepancy exists in similar centralities, where either elliptic flow is overpredicted or triangular flow is underpredicted by hydrodynamic models; this is known as the v 2 -to-v 3 puzzle in ultracentral collisions. Motivated by low-energy nuclear structure calculations, we consider the possibility that 208Pb nuclei could have a pear-shape deformation (octupole), which has the effect of increasing triangular flow in central PbPb collisions. Using the recent data from ALICE and ATLAS, we reexamine the v 2 -to-v 3 puzzle in ultracentral collisions, including new constraints from recent measurements of the triangular cumulant ratio v 3 {4}/v 3 {2} and comparing two different hydrodynamic models. We find that while an octupole deformation would slightly improve the ratio between v 2 and v 3 , it is at the expense of a significantly worse triangular flow cumulant ratio. In fact, the latter observable prefers no octupole deformation, with β 3 ≲ 0.0375 for 208 Pb, and is therefore consistent with the expectation for a doubly-magic nucleus even at top collider energies. Furthermore, the v 2 -to-v 3 puzzle remains a challenge for hydrodynamic models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

OC7 phase I: Toward practical sea-state-dependent modeling of hydrodynamic viscous drag and damping

Here, this article presents a collaborative research campaign under the OC7 project on refining the engineering modeling approach for hydrodynamic viscous drag and damping on floating wind platforms, focusing on the adjustment of hydrodynamic drag and damping coefficients for different sea states. The participant simulation results show significant improvements over the previous OC6 project in predicting the low-frequency resonance motion under nonoperational conditions. The improvements are mainly due to enhanced modeling, including the adoption of wave stretching, and directly tuning the coefficients to measured platform motion in waves instead of free decay. For accurate predictions of mean- and slow-drift motion, the better performing models use a decreasing column splash zone drag coefficient and increasing surge damping/drag with increasing wave height. The model tuning for heave and pitch resonance shows less consistency. Generally, both quadratic drag and additional heave or pitch damping are needed for accurate predictions. Alternatively, a quadratic drag formulation with velocity filtering for the rectangular pontoons leads to improved predictions without additional damping. This model is also potentially more predictive, requiring minimal adjustment to its parameters for different conditions.

17 WIND ENERGY↗
DOE OSTI2021

National Opacity Program: Analysis of Opacity-relevant X-ray Emission Spectra (Milestone Report ID 7121)

We have produced high energy density iron plasmas at temperatures above 1 keV and electron densities exceeding 1023 cm -3 (~ 1 g/cm 3 ) using the Orion laser at the Atomic Weapons Establishment. These plasmas were created by irradiating 50 µm diameter layered targets with frequency doubled (λ = 527 nm), 1 ps laser pulses focused to a 100 µm diameter producing an irradiance of ~ 2 x 10 18 W/cm 2 . The buried layer targets consist of 160 nm iron sulfide (FeS), 60 nm potassium chloride (KCl), and 15 nm carbon. The combined layers are tamped on both sides with 3 µm of parylene-N. The x-ray emission from the plasma was measured using two time-resolved, and four time-integrated Bragg crystal spectrometers, as well as one time-integrated imaging system. One time-resolved x-ray spectrometer measured emission from L-shell transitions in highly charged iron, the other from K-shell transitions in helium-like S 14+ and hydrogen-like S 15+ . The time-integrated spectrometers are intensity-calibrated and measured emission from K-shell transitions in sulfur, potassium, chlorine, and both K-shell and L-shell transitions in iron. The density and temperature of the plasma were determined by modeling the x-ray spectra using different spectral and hydrodynamic modeling packages. A brief overview of the uncertainties associated with the measurements and models are presented. We also give an overview of our 1-D HYDRA-DCA radiation-hydrodynamics model and improvements for future work. Our results aid in assessing experimental uncertainties associated with plasma uniformity and with x-ray emission employed as diagnostics in opacity experiments at temperatures and densities not achievable elsewhere and represent a significant step in creating and diagnosing plasmas near LTE. These results are summarized as part of the completion requirements for milestone 7121

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Assessing climate change impacts on live fuel moisture and wildfire risk using a hydrodynamic vegetation model

Abstract. Live fuel moisture content (LFMC) plays a critical role in wildfire dynamics, but little is known about responses of LFMC to multivariate climate change, e.g., warming temperature, CO2 fertilization, and altered precipitation patterns, leading to a limited prediction ability of future wildfire risks. Here, we use a hydrodynamic demographic vegetation model to estimate LFMC dynamics of chaparral shrubs, a dominant vegetation type in fire-prone southern California. We parameterize the model based on observed shrub allometry and hydraulic traits and evaluate the model's accuracy through comparisons between observed and simulated LFMC of three plant functional types (PFTs) under current climate conditions. Moreover, we estimate the number of days per year of LFMC below 79 % (which is a critical threshold for wildfire danger rating of southern California chaparral shrubs) from 1960 to 2099 for each PFT and compare the number of days below the threshold for medium and high greenhouse gas emission scenarios (RCP4.5 and 8.5). We find that climate change could lead to more days per year (5.2 %–14.8 % increase) with LFMC below 79 % between the historical (1960–1999) and future (2080–2099) periods, implying an increase in wildfire danger for chaparral shrubs in southern California. Under the high greenhouse gas emission scenario during the dry season, we find that the future LFMC reductions mainly result from a warming temperature, which leads to 9.1 %–18.6 % reduction in LFMC. Lower precipitation in the spring leads to a 6.3 %–8.1 % reduction in LFMC. The combined impacts of warming and precipitation change on fire season length are equal to the additive impacts of warming and precipitation change individually. Our results show that the CO2 fertilization will mitigate fire risk by causing a 3.5 %–4.8 % increase in LFMC. Our results suggest that multivariate climate change could cause a significant net reduction in LFMC and thus exacerbate future wildfire danger in chaparral shrub systems.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1991

Energy Models for One-Carrier Transport in Semiconductor Devices

Moment models of carrier transport, derived from the Boltzmann equation, made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It was found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime required empirical modification of this law, or nonstandard choices. Simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, are presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms. Some mathematical results are presented and contrasted with the highly developed state of the drift-diffusion model.

Jerome, Joseph W.↗
NASA NTRS2012

Enthalpy-Based Thermal Evolution of Loops: III. Comparison of Zero-Dimensional Models

Zero dimensional (0D) hydrodynamic models, provide a simple and quick way to study the thermal evolution of coronal loops subjected to time-dependent heating. This paper presents a comparison of a number of 0D models that have been published in the past and is intended to provide a guide for those interested in either using the old models or developing new ones. The principal difference between the models is the way the exchange of mass and energy between corona, transition region and chromosphere is treated, as plasma cycles into and out of a loop during a heating-cooling cycle. It is shown that models based on the principles of mass and energy conservation can give satisfactory results at some, or, in the case of the Enthalpy Based Thermal Evolution of Loops (EBTEL) model, all stages of the loop evolution. Empirical models can lead to low coronal densities, spurious delays between the peak density and temperature, and, for short heating pulses, overly short loop lifetimes.

Cargill, P. J.↗