Search NASA⌕ Search

SEARCH · Search NASA

Results for “hydrodynamic simulation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

The Role of a Neutron Component in the Photospheric Emission of Long Duration Gamma-Ray Burst Jets

Long-duration gamma-ray bursts (LGRBs), thought to be produced during core-collapse supernovæ, may have a prominent neutron component in the outflow material. If present, neutrons can change how photons scatter in the outflow by reducing its opacity, thereby allowing the photons to decouple sooner than if there were no neutrons present. Understanding the details of this process could therefore allow us to probe the central engine of LGRBs, which is otherwise hidden. Here, we present results of the photospheric emission from an LGRB jet, using a combination of relativistic hydrodynamic simulations and radiative transfer post-processing using the Monte Carlo Radiation Transfer (MCRaT) code. We control the size of the neutron component in the jet material by varying the equilibrium electron fraction Y e , and we find that the presence of neutrons in the GRB fireball affects the Band parameters α and E 0 , while the picture with the β parameter is less clear. In particular, the break energy E 0 is shifted to higher energies. Additionally, we find that increasing the size of the neutron component also increases the total radiated energy of the outflow across multiple viewing angles. Our results not only shed light on LGRBs, but are also relevant to short-duration gamma-ray bursts associated with binary neutron star mergers, due to the likelihood of a prominent neutron component in such systems.

Gamma-ray bursts↗
DOE OSTI2025

Ab initio equation of state for vanadium

Accurate materials’ equations of state (EOS) are essential for understanding materials properties as well as for use in multiphysics simulations. In particular, hydrodynamics simulations are based on three fundamental conservation laws (mass, momentum and energy) that form an under-determined system of equations. The equation of state serves as an additional closure relation between thermodynamic variables for a given material that enables numerical hydrodynamics simulation. In this report, we focus on the development of an ab initio EOS for the body centered cubic (BCC) phase of Vanadium (V) for eventual integration into a multiphase EOS in the OpenSesame EOS database.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Impact of in situ nuclear networks and atomic opacities on neutron star merger ejecta dynamics, nucleosynthesis, and kilonovae

Context. Binary neutron star merger (BNSM) ejecta are key sites of rapid neutron capture (r-process) nucleosynthesis and they produce kilonovae powered by the radioactive decay of freshly synthesized nuclei. Modeling their evolution requires multi-physics simulations involving hydrodynamics, nuclear reactions, and radiative processes. The impact of nuclear burning and atomic opacity is poorly understood and often treated with simplified prescriptions. Aims. We systematically investigate different treatments of nuclear heating, particle thermalization, and atomic opacities in radiation-hydrodynamics simulations of BNSM ejecta and kilonova light curves. Methods. Ejecta profiles from long-term numerical-relativity simulations of asymmetric neutron star binaries with a massive neutron star remnant were evolved to ∼30 days using a 2D ray-by-ray approach. We compared simplified heating-rate and thermalization prescriptions with in situ Nuclear reaction Network (NN) calculations that track nuclear energy deposition and include a composition-dependent thermalization scheme. We also contrasted various gray opacity models with a frequency-dependent treatment based on atomic calculations. Results. Coupling NN and hydrodynamics significantly affects nucleosynthesis and kilonova emission. Assuming homologous expansion alters abundance evolution and produces a narrower, less populated second r-process peak and a third peak shifted to higher mass numbers. The back-reaction of nuclear heating affects the temperature evolution enough to delay and redden the early (t∼ hours) kilonova peaks. A constant thermalization efficiency underestimates and reddens the early emission while overestimating the late-time luminosity compared to the composition-dependent treatment. Analytical opacity prescriptions yield a more extended, colder photosphere, resulting in dimmer, redder kilonovae at early times (t≲ hour), while the delayed recession of the photosphere prolongs the red emission at t ≳ 5 days. Conclusions. Coupling hydrodynamics to an in situ NN is crucial for reliable nucleosynthesis and kilonova predictions. Resolving the first several hundred milliseconds of the hydrodynamics is essential for robust nucleosynthesis calculations. Composition-dependent thermalization and frequency-dependent, atomic-physics-based opacities are needed to accurately capture the temperature evolution of the ejecta and the brightness and color evolution of the kilonova. Calibrated analytic nuclear-power fits with simplified thermalization and opacity prescriptions can still reproduce the density and temperature evolution of the ejecta.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1984

Numerical simulations of fission

Hydrodynamic simulation techniques to the fission problem of the lunar origin were applied. It is indicated that, for fluids with the compressibility of stars, dynamic fission instabilities lead to spiral arm ejection of mass and angular momentum in the form of a ring or disk of debris, not as a single body. Some quantitative aspects of these results seem favorable to lunar origin by fission. Fission instabilities in fluid objects with a smaller degree of compressibility, more closely approximating terrestrial material are considered. Although the qualitative features are similar, there are significant quantitative differences for the stiffer equation of state. The implications of the results for the fission hypothesis of lunar origin are discussed. Evolutions illustrating possible approaches to instability are presented.

Durisen, R. H.↗
DOE OSTI2026

Molecular dynamics simulation of hydrodynamic transport coefficients in plasmas

Molecular dynamics simulations are used to calculate transport coefficients in a two-component plasma interacting through a repulsive Coulomb potential. The thermal conductivity, electrical conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity are computed using the Green–Kubo formalism over a broad range of Coulomb coupling strength, 0.01 ≤ Γ ≤ 140. Emphasis is placed on testing standard results of the Chapman–Enskog solution in the weakly coupled regime (Γ ≪ 1) using these first-principles simulations. As expected, the results show good agreement for Γ ≲ 0.1. However, this agreement is only possible if careful attention is paid to the definitions of linear constitutive relations in each of the theoretical models, a point that is often overlooked. For example, the standard Green–Kubo expression for thermal conductivity is a linear combination of thermal conductivity, electrothermal, and thermoelectric coefficients computed in the Chapman–Enskog formalism. Meaningful results for electrical conductivity are obtained over the full range of coupling strengths explored, but it is shown that potential and virial components of the other transport coefficients diverge in the strongly coupled regime (Γ ≫ 1). In this regime, only the kinetic components of the transport coefficients are meaningful for a classical plasma.

Electrical conductivity↗
DOE OSTI2024

Hyperparameter Studies for Vision Transformers Trained on High-Fidelity Simulations

This library is a collection of python modules that define, train, and analyze vision-transformer (ViT) machine learning models. The code implements, with mild modifications, ViT models that have been made publicly available through publication and GitHub code. The training data for these models is hydrodynamic simulation output in the form of numpy arrays. This library contains code to train these ViT models on the hydrodynamic simulation output with a variety of hyperparameters, and to compare the results of such models. Furthermore, the library contains definitions of simple convolutional neural network (CNN) machine learning architectures which can be trained on the same hydrodynamic simulation output. These are included as a reference point to compare the ViT models to. Additionally, the library includes trained ViT and CNN models and example input data for demonstration purposes. The code is based on the PyTorch python library.

Callis, Skylar↗
DOE OSTI2024

Do not forget the electrons: Extending moderately-sized nuclear networks for multidimensional hydrodynamic codes

Context.Nuclear networks are widely used coupled with hydrodynamical simulations of explosive scenarios to account for the change of nuclear species and energy generation rate due to nuclear reactions. In this way, there is a feedback mechanism between the hydrodynamical state and the nuclear processes. Unfortunately, the timescale of nuclear reactions is orders of magnitude smaller than the dynamical timescale that drives hydrodynamical simulations. Therefore, these nuclear networks are usually very small, reduced in most cases to a dozen elements, especially when simulations are carried out in more than one dimension. Aims.We present here an extended nuclear network, with 90 species, designed for being coupled with hydrodynamic simulations, which includes neutrons, protons, electrons, positrons, and the corresponding neutrino and anti-neutrino emission. This network is also coupled with temperature, making it extremely robust and, together with its size, unique of its kind. The inclusion of electron captures on free protons makes the network very appropriate for multidimensional studies of Type Ia supernova explosions, especially when the exploding object is a massive white dwarf. Methods.We perform several tests that are relevant to simulate explosive scenarios, such as Type Ia supernovae and core-collapse supernovae. We compare the results of the 90 nuclei network with a standardα-chain network with 14 elements to evaluate the differences in the energy generation rate. We also evaluate the relevance of including the electrons in the network in terms of generated yields and how it affects the pressure of a degenerate fluid such as that of white dwarfs. The results obtained with the 90-nuclei network have been verified with a much larger 2000-nuclei network built from REACLIB (WinNet), in terms of nuclear energy generation rate, pressure, and produced yields. Results.The results obtained with the proposed medium-sized network compare fairly well, to a few percent, with those computed withWinNetin scenarios reproducing the gross physical conditions of current Type Ia supernova explosion models. In those cases where the carbon and oxygen fuel ignites at high density, the high-temperature plateau typical of the nuclear statistical equilibrium regime is well defined and stable, allowing large integration time steps. We show that the inclusion of electron captures on free protons substantially improves the estimation of the electron fraction of the mixture. Therefore, the pressure is better determined than in networks where electron captures are excluded, which will ultimately lead to more reliable hydrodynamic models. Explosive combustion of helium at low density, occurring near the surface layer of a white dwarf, is also better described with the proposed network, which gives nuclear energy generation rates much closer toWinNetthan typical reduced alpha networks. Conclusions.A nuclear network withN= 90 species, including electrons, aimed at multidimensional calculations of supernova explosions is described and verified. The proposed network is suitable for the study of Type Ia supernova explosions because it provides better values of pressure and electron abundance than other existing networks with smaller or even a similar size but without including electron capture processes.

Astronomy & Astrophysics↗
DOE OSTI2025

Evidence for large baryonic feedback at low and intermediate redshifts from kinematic Sunyaev-Zel’dovich observations with ACT and DESI photometric galaxies

Recent advances in cosmological observations have provided an unprecedented opportunity to investigate the distribution of baryons relative to the underlying matter. In this work, we show that the gas is more extended than the dark matter, and the amount of baryonic feedback at $z \lesssim 1$ disfavors low-feedback models such as that of state-of-the-art hydrodynamical simulation IllustrisTNG compared with high-feedback models such as that of the original Illustris simulation. This has important implications for bridging the gap between theory and observations and understanding galaxy formation and evolution. Furthermore, a better grasp of the baryon-dark matter link is critical to future cosmological analyses, which are currently impeded by our limited knowledge of baryonic feedback. Here, we measure the kinematic Sunyaev-Zel'dovich (kSZ) effect from the Atacama Cosmology Telescope (ACT), stacked on the luminous red galaxy (LRG) sample of the Dark Energy Spectroscopic Instrument (DESI) imaging survey. This is the first analysis to use photometric redshifts for reconstructing galaxy velocities. Due to the large number of galaxies comprising the DESI imaging survey, this is the highest signal-to-noise stacked kSZ measurement to date: we detect the signal at 13$σ$, finding strong evidence that the gas is more spread out than the dark matter, as well as a preference for larger feedback compared to some commonly used state-of-the-art hydrodynamical simulations. Here, our work opens up the possibility of recalibrating large hydrodynamical simulations using the kSZ effect. In addition, our findings highlight the importance of properly accounting for baryonic feedback with future surveys such as LSST through direct probes such as the kSZ, and shed light on long-standing enigmas in astrophysics, such as the “missing baryon” problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Observation of ponderomotively driven bow shock using Thomson scattering

High-energy speckled lasers are known to exert ponderomotive forces on a plasma. This can reduce flow transverse to the propagation of the beams. When coupled with a supersonic flow, this has been shown to lead to the formation of a shock that travels against the flow. Experiments conducted on the OMEGA laser facility have used Thomson scattering to observe density and velocity changes consistent with this ponderomotively driven shock. Comparisons of the data with hydrodynamic simulations with the ponderomotive force, particle-in-cell simulations with a full Maxwell field solver, and hydrodynamic simulations without the ponderomotive force show that this shock feature is only reproduced when accounting for the ponderomotive force.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1994

X-ray clusters from a high-resolution hydrodynamic PPM simulation of the cold dark matter universe

A new three-dimensional hydrodynamic code based on the piecewise parabolic method (PPM) is utilized to compute the distribution of hot gas in the standard Cosmic Background Explorer (COBE)-normalized cold dark matter (CDM) universe. Utilizing periodic boundary conditions, a box with size 85 h(exp-1) Mpc, having cell size 0.31 h(exp-1) Mpc, is followed in a simulation with 270(exp 3)=10(exp 7.3) cells. Adopting standard parameters determined from COBE and light-element nucleosynthesis, Sigma(sub 8)=1.05, Omega(sub b)=0.06, we find the X-ray-emitting clusters, compute the luminosity function at several wavelengths, the temperature distribution, and estimated sizes, as well as the evolution of these quantities with redshift. The results, which are compared with those obtained in the preceding paper (Kang et al. 1994a), may be used in conjuction with ROSAT and other observational data sets. Overall, the results of the two computations are qualitatively very similar with regard to the trends of cluster properties, i.e., how the number density, radius, and temeprature depend on luminosity and redshift. The total luminosity from clusters is approximately a factor of 2 higher using the PPM code (as compared to the 'total variation diminishing' (TVD) code used in the previous paper) with the number of bright clusters higher by a similar factor. The primary conclusions of the prior paper, with regard to the power spectrum of the primeval density perturbations, are strengthened: the standard CDM model, normalized to the COBE microwave detection, predicts too many bright X-ray emitting clusters, by a factor probably in excess of 5. The comparison between observations and theoretical predictions for the evolution of cluster properties, luminosity functions, and size and temperature distributions should provide an important discriminator among competing scenarios for the development of structure in the universe.

Bryan, Greg L.↗
NASA NTRS2014

Water Flow Simulation using Smoothed Particle Hydrodynamics (SPH)

Simulation of water flow from the rainbird nozzles has been accomplished using the Smoothed Particle Hydrodynamics (SPH). The advantage of using SPH is that no meshing is required, thus the grid quality is no longer an issue and accuracy can be improved.

Hydrodynamics↗
DOE OSTI2026

Constraining hydrodynamic models of inertial confinement fusion implosions using capsule surrogate experiments

We conduct capsule surrogate experiments at the National Ignition Facility to calibrate radiation hydrodynamic simulations to infer hydrodynamic conditions that are not observable in indirect drive ignition implosions. We tune the simulations by applying laser power and cross beam energy transfer (CBET) saturation multipliers to match the observables from capsule surrogate experiments. Shock timing, velocity, and symmetry are measured in liquid D 2 filled Keyhole capsule surrogate experiments and implosion trajectory, stagnation time, and shape time history are measured in in-flight 2D backlit x-ray radiography experiments (“2DConA”) of D 2 gas filled capsule implosions. Calibrated simulations suggest that the N210808 ignition implosion (fusion target gain = 0.7) had a shell mass remaining at stagnation of less than the nominal %5 (3.8%) and resulted in less confinement. For N221204, the shell was made 5.75 μm thicker to trade implosion velocity for increased confinement and resulted in a target gain = 1.5 with a shell mass remaining of 5.7%. Furthermore, a single adjusted model can reproduce all shock timing data as changes are made to shell thickness (79–85 μm) and laser wavelength separation (1.8–4.0 Å). However, for the 2DConA implosions, a 5% variation in the peak power laser multipliers and a 30% variation in late-time CBET between experiments are needed to match the observed stagnation times, in-flight $P_2$ shape, and hot-spot $P_2$ shape. While progress is being made to improve the models in simulations using focused experiments, capsule surrogate experiments will continue to be needed to optimize future ignition designs.

Lasers↗
DOE OSTI2024

Impact of mid- Z gas fill on dynamics and performance of shock-driven implosions at the OMEGA laser

Shock-driven implosions with 100% deuterium (D 2 ) gas fill compared to implosions with 50:50 nitrogen-deuterium (N 2 ⁢D 2 ) gas fill have been performed at the OMEGA laser facility to test the impact of the added mid-Ζ fill gas on implosion performance. Ion temperature (Τ ion ) as inferred from the width of measured DD-neutron spectra is seen to be 34%±6% higher for the N 2⁢ D 2 implosions than for the D 2 -only case, while the DD-neutron yield from the D 2 -only implosion is 7.2±0.5 times higher than from the N 2⁢ D 2 gas fill. The T ion enhancement for N 2 ⁢D 2 is observed in spite of the higher Z, which might be expected to lead to higher radiative loss, and higher shock strength for the D 2 -only versus N 2 ⁢D 2 implosions due to lower mass, and is understood in terms of increased shock heating of N compared to D, heat transfer from N to D prior to burn, and limited amount of ion-electron-equilibration-mediated additional radiative loss due to the added higher-Z material. Further, this picture is supported by interspecies equilibration timescales for these implosions, constrained by experimental observables. The one-dimensional (1D) kinetic Vlasov-Fokker-Planck code ifp and the radiation hydrodynamic simulation codes hyades (1D) and xrage [1D, two-dimensional (2D)] are brought to bear to understand the observed yield ratio. Comparing measurements and simulations, the yield loss in the N 2 ⁢D 2 implosions relative to the pure D 2 -fill implosion is determined to result from the reduced amount of D 2 in the fill (fourfold effect on yield) combined with a lower fraction of the D 2 fuel being hot enough to burn in the N 2 ⁢D 2 case. The experimental yield and T ion ratio observations are relatively well matched by the kinetic simulations, which suggest interspecies diffusion is responsible for the lower fraction of hot D 2 in the N 2 ⁢D 2 relative to the D 2 -only case. The simulated absolute yields are higher than measured; a comparison of 1D versus 2D XRAGE simulations suggest that this can be explained by dimensional effects. The hydrodynamic simulations suggest that radiative losses primarily impact the implosion edges, with ion-electron equilibration times being too long in the implosion cores. The observations of increased T ion and limited additional yield loss (on top of the fourfold expected from the difference in D content) for the N 2 ⁢D 2 versus D 2 -only fill suggest it is feasible to develop the platform for studying CNO-cycle-relevant nuclear reactions in a plasma environment.

47 OTHER INSTRUMENTATION↗
NASA NTRS1995

The ocean response to operational westerly wind bursts during the 1991 - 1992 El Nino

Numerical simulations of the remotely forced ocean response to westerly wind bursts prior to and during the 1991 - 1992 El Nino are examined; the models are forced by wind stress from the U.S. Navy's atmospheric global operational analysis/forecast system. The study focuses on (1) the relative response of the first and second internal modes to a single episode of westerly bursts; (2) the role of westerly bursts in producing the eastern Pacific sea level variations from October 1990 to February 1992; and (3) the relative importance of the remotely forced sea level responses generated by central and western Pacific wind anomalies. The simulation use the Naval Research Laboratory global multilayer formulation; the suite of experiments includes hydrodynamic simulations that use both one- and three- active-layer reduced gravity models as well as an experiment that also includes thermodynamic effects. The models are executed from January 1, 1990, to March 1, 1992, a period that includes 10 significant westerly wind bursts or burst clusters and the 1991 - 1992 El Nino event. The numerical experiments reveal an ability to accurately simulate the eastern Pacific sea level variations during this period. In response to a single burst, the three-layer hydrodynamic simulation reveals that the second internal mode Kelvin wave yields a sea level change at the eastern boundary that is approximately one third that of the first mode and a surface velocity signature that is equivalent to the first mode. During the onset of the El Nino event the inclusion of higher modes also produces a more realistic representation of the observed eastern boundary sea level signal. Furthermore, by comparing the model response to particular wind bursts with the observed sea level at Baltra, Galapagos, a value of 2.5 - 2.6 m/s is suggested as the most appropriate mean speed for the first internal mode Kelvin wave during the onset phase. A scenario for the onset of the 1991 - 1992 El Nino is given.

Kindle, John C.↗
DOE OSTI2026

Reduced instability growth and improved radiation trapping with optimized shock timing in double-shell inertial confinement fusion capsules

The double shell is a volume-burn inertial confinement fusion concept consisting of two concentric shells: a low-Z outer shell that collides with and transfers momentum to a high-Z inner shell which compresses and heats the thermonuclear fuel. The increased number of capsule interfaces and severe hydrodynamic instability of the high-density pusher during its acceleration phase provide challenges to the success of the double shell. Two-dimensional radiation-hydrodynamics simulations predict the hydrodynamic instability growth on the outer surface of the pusher can be greatly reduced through appropriate timing of two shocks that cross this interface. One of these shocks, unique to multi-shell designs, arises from radiation-driven ablation of the inner shell ahead of the main shock, the second shock of concern. The shock timing is optimized by increasing the thickness of a low-Z tamper layer exterior to the pusher, resulting in only minimal changes to the implosion timing. Reducing the instability growth on the outer surface of the high-Z pusher can dramatically decrease the modulations that feedthrough to the pusher inner surface, improving the efficacy of radiation trapping in the thermonuclear fuel and increasing the predicted thermonuclear yield by ≳20×.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Towards Robust Calibration of the AWSD Reactive Burn Model

Calibration of a reactive burn model for detonation of high explosive is an important step towards predictive hy drodynamic simulations of detonation. A typical calibration consists of varying model parameters (e.g., rate constants, activation energies) until results of hydrodynamic simulations match the experimental data for a certain set of ex periments. Hydrodynamic simulations of the dependence of steady detonation velocity on the radius of a cylindrical high-explosive charge - often used in such calibrations - can be computationally expensive. In this work, we propose a method where such expensive simulations are performed infrequently, and only to parameterize and refine a surrogate model for the dependence of the detonation velocity on calibrated parameters. The method is developed, implemented and applied to an example problem - calibration of the AWSD reactive burn model for important high explosive PBX 9502. Two different flavors of the surrogate model are investigated, and the calibration is performed successfully.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

X-ray phase-contrast imaging of strong shocks on OMEGA EP

The ongoing improvement in laser technology and target fabrication is opening new possibilities for diagnostic development. An example is x-ray phase-contrast imaging (XPCI), which serves as an advanced x-ray imaging diagnostic in laser-driven experiments. In this work, we present the results of the XPCI platform that was developed at the OMEGA EP Laser-Facility to study multi-Mbar single and double shocks produced using a kilojoule laser driver. Two-dimensional radiation-hydrodynamic simulations agree well with the shock progression and the spherical curvature of the shock fronts. It is demonstrated that XPCI is an excellent method to determine with high accuracy the front position of a trailing shock wave propagating through an expanding CH plasma that was heated by a precursor Mbar shock wave. Furthermore, the interaction between the rarefaction wave and the shock wave results in a clear signature in the radiograph that is well reproduced by radiation-hydrodynamic simulations.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Three-dimensional reconstruction of inertial confinement fusion hot-spot plasma from x-ray and nuclear diagnostics on OMEGA

Multidimensional effects degrade the neutron yield and the compressed areal density of laser-direct-drive inertial confinement fusion implosions of layered deuterium–tritium cryogenic targets on the OMEGA Laser System with respect to 1D radiation-hydrodynamic simulation predictions. A comprehensive physics-informed 3D reconstruction effort is under way to infer hot-spot and shell conditions at stagnation from four x-ray and seven neutron detectors distributed around the OMEGA target chamber. Neutron diagnostics, providing measurements of the neutron yield, hot-spot flow velocity, and apparent ion-temperature distribution, are used to infer the mode-1 perturbation at stagnation. The x-ray imagers record the shape of the hot-spot plasma to diagnose mode-1 and mode-2 perturbations. A deep-learning convolutional neural network trained on an extensive set of 3D radiation-hydrodynamic simulations is used to interpret the x-ray and nuclear measurements to infer the 3D profiles of the hot-spot plasma conditions and the amount of laser energy coupled to the hot-spot plasma. A 3D simulation database shows that larger mode-1 asymmetries are correlated with higher hot-spot flow velocities and reduced laser-energy coupling and neutron yield. Three-dimensional hot-spot reconstructions from x-ray measurements indicate that higher amounts of residual kinetic energy are correlated with higher measured hot-spot flow velocities, consistent with 3D simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗