Two-dimensional Hydrodynamic Simulations Research Articles

Two-Dimensional Hydrodynamic Simulation of the Effect of Stormwater Inlet Blockage on Urban Waterlogging

The drainage capacity of stormwater inlets, which serve as the connection between the surface and the underground drainage system, directly affects surface runoff and the drainage capacity of underground drainage systems. However, in reality, stormwater inlets are often blocked due to the accumulation of leaves, human waste disposal and other factors, resulting in a greatly reduced drainage capacity of the drainage network and, in turn, urban waterlogging disasters. In view of the problem of stormwater inlet blockage, employing a typical waterlogging point in the Lianjiang Middle Road area of Fuzhou city as the research object, the stormwater inlet equivalent drainage method was adopted in this paper to characterize the drainage capacity of the pipe network and enable the control of the stormwater inlet blockage state. Coupled with the stormwater inlet drainage equation, an improved ITF-FLOOD two-dimensional hydrodynamic model was constructed, and the influence of stormwater inlet blockage on urban waterlogging under different rainfall return periods was simulated and analyzed. With increasing rainfall return period, the influences of stormwater inlet blockage on both the maximum area and the depth of accumulated water in the study area gradually decreased compared with those of a nonblocked stormwater inlet, and the growth proportions decreased from 43.35% and 34.58% under the 1-year rainfall scenario to 3.34% and 9.76% under the 50-year rainfall scenario, respectively. However, in terms of the change in the accumulated water level, stormwater inlet blockage will cause an increase, and the influence will always be significant. Overall, stormwater inlet blockage aggravated the waterlogging risk and the extent of waterlogging. Therefore, the results provided a reference for the construction of an urban waterlogging model and have certain guiding significance for waterlogging prevention and control in the study area prone to stormwater inlet blockage.

A semi-analytical model for the propagation of a relativistic jet in a magnetized medium

ABSTRACT The merger of two magnetized compact objects, such as neutron stars, forms a compact object which may launch a relativistic and collimated jet. Numerical simulations of the process show that a dense and highly magnetized medium surrounds the system. This study presents a semi-analytical model that models the effects that a static magnetized medium with a tangled field produces in relativistic, collimated, and non-magnetized jets. The model is a first approximation that addresses the magnetic field present in the medium and is based on pressure equilibrium principles between the jet, cocoon, and external medium. A fraction of the ambient medium field is allowed to be entrained in the cocoon. We find that the jet and cocoon properties may be affected by high magnetic fields (≳ 1015 G) and mixing. The evolution of the system may vary up to $\sim 10{{\ \rm per\ cent}}$ (compared to the non-magnetized case). Low-mixing may produce a slower broader jet with a broader and more energetic cocoon would be produced. On the other hand, high-mixing could produce a faster narrower jet with a narrow and less-energetic cocoon. Two-dimensional hydrodynamical simulations are used to validate the model and to constrain the mixing parameter. Although the magnetic field and mixing have a limited effect, our semi-analytic model captures the general trend consistent with numerical results. For high magnetization, the results were found to be more consistent with the low mixing case in our semi-analytic model.

Two-dimensional hydrodynamic simulation for synchronized oscillatory flows in two collapsible channels connected in parallel.

We investigated self-sustained oscillation in a collapsible channel, in which a part of one rigid wall is replaced by a thin elastic wall, and synchronization phenomena in the two channels connected in parallel. We performed a two-dimensional hydrodynamic simulation in a pair of collapsible channels which merged into a single channel downstream. The stable synchronization modes depended on the distance between the deformable region and the merging point; only an in-phase mode was stable for the large distance, in-phase and antiphase modes were bistable for the middle distance, and again only an in-phase mode was stable for the small distance. An antiphase mode became stable through the subcritical pitchfork bifurcation by decreasing the distance. Further decreasing the distance, the antiphase mode became unstable through the subcritical Neimark-Sacker bifurcation. We also clarified the distance dependences of the amplitude and frequency for each stable synchronization mode.

Space-time dependent non-local thermal transport effects on laser ablation dynamics in inertial confinement fusion

In inertial confinement fusion (ICF), electron thermal transport plays a key role in laser ablation and the subsequent implosion processes, which always exhibits intractable non-local effects. Simple modifications of the local Spitzer–Härm model with either an artificially-assumed constant flux limiter or a purely time-dependent one are applied to explain some experimental data, but fail to simultaneously reproduce the space-time evolution of the whole laser ablation process. Here, by carrying out a series of one-dimensional and two-dimensional radiation hydrodynamic simulations where the space-time-dependent non-local thermal transport model proposed by Schurt, Nicolaï and Busquet (the SNB model) are self-consistently included, we systematically study the non-local effects on the whole laser ablation dynamics including those occurring at the critical surface, the conduction zone and the ablation front. Different from those obtained previously, our results show that due to the non-local heat flow redistribution and redirection, at the critical surface the thermal flux is more inhibited, in the conduction zone the lateral thermal transport is suppressed, and ahead of the ablation front the plasma is preheated. When combined together they eventually result in significant improvement of the laser absorption efficiency, extension of the conduction zone, increase of both the mass ablation rate and shock velocity. Furthermore, the dependence of these laser ablation dynamics on different drive laser intensities is investigated, which provides beneficial enlightenments on potential laser pulse shaping and/or ignition scheme optimization in ICF.

Nonplanar effects in simulations of laser-driven ejecta microjet experiments

Recent experiments of laser-driven ejecta microjets performed at OMEGA 60 reveal tortuous jets whereby the jets appear to deviate from their initial trajectory as they travel in vacuum. To understand these data, we perform two dimensional numerical simulations, considering different target thicknesses, pressures, and models of the drive conditions. In particular, modeling the finite laser spot size appears essential in reproducing qualitatively the non-planar shock observed in the experiment. Simulations capture jet deflection by accounting for a slight misalignment of the laser pointing with respect to the groove axis along with spatial variation of the laser pulse intensity. The principal physical mechanism appears to be that lateral momentum is imparted by release waves arising from the non-planar drive. The induced off-axis velocity is small in comparison to the jet axial velocity but integrates into a pronounced deflection over the course of the experiment. The analysis of jet axial and lateral mass distributions is found to be reproduced reasonably by the simulations. Simulated radiographs are in qualitative agreement with the experiments, though their differences point to potential shortcomings in modeling strictly three-dimensional experiments using two-dimensional hydrodynamic simulations. The simple analysis is able to explain part of the observed discrepancy in simulated vs experimental jet masses.

Effects of Kelvin–Helmholtz instability on the material mixing in the double-cone ignition

The Kelvin–Helmholtz instability (KHI) occurs on the interface of gold cones and embedded fuels for fusion schemes with gold cones. The development of KHI on the inner surface of gold cones in the double-cone ignition scheme is investigated with two-dimensional radiation hydrodynamic simulations. It has been found that the colliding high-density fuel plasma between the tips of the two cones is spatiotemporally separated from the mixed gold ions from the inner surface of the gold cones due to the KHI. Furthermore, it is found that fuel layers coated on the inner surface of the cones can effectively mitigate the energy loss in the compression process. These results could provide a reference for fast ignition schemes with gold cones.

Orbital evolution of close binary systems: comparing viscous and wind-driven circumbinary disc models

ABSTRACT Previous work has shown that interactions between a central binary system and a circumbinary disc (CBD) can lead to the binary orbit either shrinking or expanding, depending on the properties of the disc. In this work, we perform two-dimensional hydrodynamical simulations of CBDs surrounding equal mass binary systems that are on fixed circular orbits, using the athena++ code in Cartesian coordinates. Previous studies have focused on discs where viscosity drives angular momentum transport. The aim of this work is to examine how the evolution of a binary system changes when angular momentum is extracted from the disc by a magnetized wind. In this proof-of-concept study, we mimic the effects of a magnetic field by applying an external torque that results in a prescribed radial mass flux through the disc. For three different values of the radial mass flux, we compare how the binary system evolves when the disc is either viscous or wind driven. In all cases considered, our simulations predict that the binary orbit should shrink faster by a factor of a few when surrounded by a wind-driven CBD compared to a corresponding viscous CBD. In-spiral time-scales of ∼106–107 yr are obtained for circular binaries surrounded by CBDs with masses typical of protoplanetary discs, indicating that significant orbital shrinkage can occur through binary–disc interactions during Class I/II pre-main-sequence phases.

Efficient photo-dissociation-induced production of hydrogen radicals using vacuum ultraviolet light from a laser-produced plasma

One of the critical issues in lithography using extreme ultraviolet (EUV) light is tin contamination of the EUV collector mirrors in the tin-based LPP-EUV light source. The contamination can be removed by the reaction of tin atoms with hydrogen radicals producing stannane (SnH4), which is gaseous at the normal temperature. Hydrogen radicals can be produced from hydrogen molecules through photo-dissociation and photo-ionization induced by broadband radiation emitted from the EUV light source. In this work, an efficient production of hydrogen radical using vacuum ultraviolet (VUV) light emitted from laser-produced high-Z plasma is experimentally demonstrated. A two-dimensional radiation hydrodynamic simulation, coupled with photoionization and photo-dissociation cross sections, also shows the efficient hydrogen radical production by increased VUV light emission, as observed in the experiment.

Formation of a wide-orbit giant planet in a gravitationally unstable subsolar-metallicity protoplanetary disc

ABSTRACT Direct imaging observations of planets revealed that wide-orbit (>10 au) giant planets exist even around subsolar-metallicity host stars and do not require metal-rich environments for their formation. A possible formation mechanism of wide-orbit giant planets in subsolar-metallicity environments is the gravitational fragmentation of massive protoplanetary discs. Here, we follow the long-term evolution of the disc for 1 Myr after its formation, which is comparable to disc lifetime, by way of a two-dimensional thin-disc hydrodynamic simulation with the metallicity of 0.1 $\rm {Z}_{\odot }$. We find a giant protoplanet that survives until the end of the simulation. The protoplanet is formed by the merger of two gaseous clumps at ∼0.5 Myr after disc formation, and then it orbits ∼200 au from the host star for ∼0.5 Myr. The protoplanet’s mass is ∼10 MJ at birth and gradually decreases to 1 MJ due to the tidal effect from the host star. The result provides the minimum mass of 1 MJ for the protoplanet in our simulation. We anticipate that the mass of a protoplanet experiencing reduced mass loss thanks to the protoplanetary contraction in higher resolution simulations can increase to ∼10 MJ. We argue that the disc gravitational fragmentation would be a promising pathway to form wide-orbit giant planets with masses of ≥1 MJ in subsolar-metallicity environments.

Hydrodynamical simulations of circumbinary accretion: balance between heating and cooling

ABSTRACT Hydrodynamical interaction in circumbinary discs (CBDs) plays a crucial role in various astrophysical systems, ranging from young stellar binaries to supermassive black hole binaries in galactic centres. Most previous simulations of binary-disc systems have adopted locally isothermal equation of state. In this study, we use the grid-based code Athena++ to conduct a suite of two-dimensional viscous hydrodynamical simulations of circumbinary accretion on a Cartesian grid, resolving the central cavity of the binary. The gas thermodynamics is treated by thermal relaxation towards an equilibrium temperature (based on the constant − β cooling ansatz, where β is the cooling time in units of the local Keplerian time). Focusing on equal mass, circular binaries in CBDs with (equilibrium) disc aspect ratio H/R = 0.1, we find that the cooling of the disc gas significantly influences the binary orbital evolution, accretion variability, and CBD morphology, and the effect depends sensitively on the disc viscosity prescriptions. When adopting a constant kinematic viscosity, a finite cooling time (β ≳ 0.1) leads to a binary inspiral as opposed to an outspiral and the CBD cavity becomes more symmetric. When adopting a dynamically varying α-viscosity, binary inspiral only occurs within a narrow range of cooling time (corresponding to β around 0.5).

Optimization of target compression for high-gain fast ignition via machine learning

The hydrodynamic scaling relations are of great importance for the design and optimization of target compression in laser-driven fusion. In this paper, we propose an artificially intelligent method to construct the scaling relations of the implosion velocity and areal density for direct-drive fast ignition by combining one-dimensional hydrodynamic simulations and machine learning methods. It is found that a large fuel mass and a high areal density required for high-gain fusion can be obtained simultaneously by optimizing the implosion velocity with less compression laser energy, taking full advantage of the separation of the compression and ignition processes in the fast ignition scheme. The obtained scaling relations are applied to the implosion design for the double-cone ignition scheme [Zhang et al., “Double-cone ignition scheme for inertial confinement fusion,” Philos. Trans. R. Soc., A 378(2184), 20200015 (2020)]. An optimized implosion is proposed with an areal density of 1.30 g/cm2 and a fuel mass of 215.7 μg with a compression laser energy of 168 kJ. Two-dimensional hydrodynamic simulations are further employed to validate the results. Our methods and results may be useful for the optimization of fusion experiments toward high-gain fusion.

Performance Assessment of DEM Vertical Sensitivity on Two-Dimensional Hydrodynamic Simulation in an Alluvial Tributary Floodplain of the Brahmaputra Lower Basin in India

Performance Assessment of DEM Vertical Sensitivity on Two-Dimensional Hydrodynamic Simulation in an Alluvial Tributary Floodplain of the Brahmaputra Lower Basin in India

Migration of pairs of giant planets in low-viscosity discs

Context. When considering the migration of Jupiter and Saturn, a classical result is to find the planets migrating outwards and locked in the 3:2 mean motion resonance (MMR). These results were obtained in the framework of viscously accreting discs, in which the observed stellar accretion rates constrained the viscosity values. However, it has recently been shown observationally and theoretically that discs are probably less viscous than previously thought. Aims. Therefore, in this paper, we explore the dynamics of pairs of giant planets in low-viscosity discs. Methods. We performed two-dimensional hydrodynamical simulations using the grid-based code FARGOCA. Results. In contrast to classical viscous discs, we find that the outer planet never crosses the 2:1 resonance and the pair does not migrate outwards. After a wide parameter exploration, including the mass of the outer planet, we find that the planets are primarily locked in the 2:1 MMR and in some cases in the 5:2 MMR. We explain semi-analytically why it is not possible for the outer planet to cross the 2:1 MMR in a low-viscosity disc. Conclusions. We find that pairs of giant planets migrate inwards in low-viscosity discs. Although, in some cases, having a pair of giant planets can slow down the migration speed with respect to a single planet. Such pairs of slowly migrating planets may be located, at the end of the disc phase, in the population of exoplanets of ’warm Jupiters’. However, the planets never migrate outwards. These results could have strong implications on the Solar System’s formation scenarios if the Sun’s protoplanetary disc had a low viscosity.

Calculation and evaluation of suitable ecological flows for eco-environmental recovery of cascade-developed rivers

River cascade development affects the hydrological and habitat characteristics of the region and disrupts the dynamic balance of stable river ecosystems. The most profound impact of river cascade development is on the resident fish species. River ecosystem restoration for maximum river habitat improvement is generally based on water security and environment improvement and effectively embodies the nature-based solutions (NbS) concept of naturalized restoration. Yuanjiang (Y.J.) River is an international river in southwest China seriously affected by cascade development. By determining the response of the river ecosystem and using the key performance indicator method, Yuanjiang carp (Cyprinus carpio rubrofuscus) and red giant catfish (Bagarius rutilus) were identified as the key species in the main stream of the Y.J. River., and the ecological effects of river cascade development on them were studied by applying two-dimensional hydrodynamic physical habitat simulation and multi-objective ecological scheduling models. Based on the calculation results for ecological operation optimization of cascade reservoirs, an improved progressive optimality algorithm was used to calculate the ecological flows required to maintain the stability of the river ecosystem. With the increasing extent of cascade development in the river, important indicators, such as the intra-annual, extreme, high, and low flows have changed significantly, and the hydrological characteristics of the main stream have changed rapidly and comprehensively. Habitat suitability curves were used to determine the appropriate water depth and delineate the weighted usable area required for the spawning, nursing, and growing periods of the key fish species. The suitable ecological flows required for the three life-cycle stages of the C. carpio rubrofuscus accounted for 34, 45, and 62 %, respectively, of the multi-year mean natural water inflow at the Qiaotou (Q.T.) cascade, whereas those required for the three respective periods of B. rutilus accounted for 47, 98, and 27 %, respectively, of the multi-year mean natural water inflow at the Madushan (M.D·S.) cascade. Considering the physiological lifecycle demands of the indicator/key fish species and the upper limit of water resources development and utilization in the key river section, the ecological flow precipitation frequency in the Q.T.-Luodie (Q.T.-L.D.) and M.D·S.-Xinjie (M.D·S.-X.J.) sections (currently at 25, 50, and 75 %, respectively) can be increased to 100 % under optimal operating conditions (cascade hydropower station optimal operation). After implementing the multi-objective ecological operation at the Y.J. River main-stream cascade reservoirs, the suitable habitat area for C. carpio rubrofuscus and B. rutilus increased significantly (>10 % and 15 %, respectively). In general, the NbS-based ecological flow calculation method for cascade-developed rivers has a wide range of applications, which can be useful for the eco-environment restoration of rivers and improving the living habitats of waterway organisms.

Two-dimensional hydrodynamic simulation for synchronization in coupled density oscillators.

A density oscillator is a fluid system in which oscillatory flow occurs between different density fluids through the pore connecting them. We investigate the synchronization in coupled density oscillators using two-dimensional hydrodynamic simulation and analyze the stability of the synchronous state based on the phase reduction theory. Our results show that the antiphase, three-phase, and 2-2 partial-in-phase synchronization modes spontaneously appear as stable states in two, three, and four coupled oscillators, respectively. The phase dynamics of coupled density oscillators is interpreted with their sufficiently large first Fourier components of the phase coupling function.

Accretion-induced Collapse of Dark Matter-admixed Rotating White Dwarfs: Dynamics and Gravitational-wave Signals

We present two-dimensional hydrodynamic simulations of the accretion-induced collapse (AIC) of rotating white dwarfs admixed with an extended component of dark matter (DM) comprising sub-gigaelectronvolt degenerate fermionic DM particles. We find that the DM component follows the collapse of the normal matter (NM) component to become a bound DM core. Thus, we demonstrate how a DM-admixed neutron star could form through DM-admixed AIC (DMAIC) for the first time, with the dynamics of DM taken into account. The gravitational-wave (GW) signature from the DMAIC shows distinctive features. In the diffusive DM limit, the DM admixture indirectly suppresses the post-bounce spectral peak of the NM GWs. In the compact DM limit, the collapse dynamics of the DM in a Milky Way event generate GWs that are strong enough to be detectable by Advanced LIGO as continuous low-frequency (<1000 Hz) signals after the NM core bounce. Our study not only is the first-ever computation of GW from a collapsing DM object but also provides the key features to identify DM in AIC events through future GW detections.

Intricate structure of the plasma Rayleigh–Taylor instability in shock tubes

Spikes and bubbles grow on unstable interfaces that are accelerated in high-energy-density conditions. If a shock propagates ahead of the interface, the plasma can be heated to extreme conditions where conduction and radiation fluxes influence the hydrodynamics. For example, a National Ignition Facility experiment found reduced single-mode nonlinear mixed-width growth in conditions scaled from a supernova explosion [Kuranz et al., Nat. Commun. 9, 1564 (2018)]. We present high-resolution two-dimensional radiation hydrodynamic simulations with the Flash code that quantitatively reproduce the experiment. Radiative fluxes are primarily responsible for ablating the spike and removing the mushroom caps. The ablated plasma increases the mixed mass and forms a low-density halo with spikes forming in both directions. This is considerably more complex than classical instability. The halo is sensitive to ablative physics, so radiographing it may aid in the verification of energy transport modeling. Although ablation changes the spike shape, it has little effect on the overall mixed width for these parameters. This is because ablation enhances the bubble velocity but it has the opposite effect on the spike. The radiation transport instead suppresses the growth via increasing the shocked foam density, thus decreasing the Atwood number. A terminal velocity model including the rarefaction expansion agrees with the experimental mixed-width growth.

Two saturated states of the vertical shear instability in protoplanetary disks with vertically varying cooling times

Abstract Turbulence in protoplanetary disks plays an important role in dust evolution and planetesimal formation. The vertical shear instability (VSI) is one of the candidate hydrodynamic mechanisms that can generate turbulence in the outer disk regions. The VSI requires rapid gas cooling in addition to vertical shear. A linear stability analysis suggests that the VSI may not operate around the midplane where gas cooling is inefficient. In this study, we investigate the nonlinear outcome of the VSI in disks with a linearly VSI-stable midplane region. We perform two-dimensional global hydrodynamical simulations of an axisymmetric disk with vertically varying cooling times. The vertical cooling time profile determines the thicknesses of the linearly VSI-stable midplane layer and unstable layers above and below the midplane. We find that the thickness of the midplane stable layer determines the vertical structure of VSI-driven turbulence in the nonlinear saturated state. We identify two types of final saturated state: (i) T states, characterized by vertical turbulent motion penetrating into the VSI-stable midplane layer, and (ii) pT states, characterized by turbulent motion confined in the unstable layers. The pT states are realized when the midplane VSI-stable layer is thicker than two gas scale heights. We also find that the VSI-driven turbulence is largely suppressed at all heights when the VSI-unstable region lying above and below the midplane is thinner than two gas scale heights. We present empirical formulas that predict the strength of VSI-driven turbulence as a function of the thicknesses of the unstable and stable layers. These formulas will be useful for studying how VSI-driven turbulence and dust grains controlling the disk cooling efficiency evolve simultaneously.

A study of convective core overshooting as a function of stellar mass based on two-dimensional hydrodynamical simulations

ABSTRACT We perform two-dimensional (2D) numerical simulations of core convection for zero-age main-sequence stars covering a mass range from 3 to 20 M⊙. The simulations are performed with the fully compressible time-implicit code music. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. We also study the impact of artificially increasing the stellar luminosity for 3 M⊙ models. The simulations cover hundreds to thousands of convective turnover time-scales. Applying the framework of extreme plume events previously developed for convective envelopes, we derive overshooting lengths as a function of stellar masses. We find that the overshooting distance (dov) scales with the stellar luminosity (L) and the convective core radius (rconv). We derive a scaling law $d_{\rm ov} \propto L^{1/3} r_{\rm conv}^{1/2}$, which is implemented in a one-dimensional stellar evolution code and the resulting stellar models are compared to observations. The scaling predicts values for the overshooting distance that significantly increase with stellar mass, in qualitative agreement with observations. Quantitatively, however, the predicted values are underestimated for masses ≳10 M⊙. Our 2D simulations show the formation of a nearly adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent three-dimensional simulations of convection. The most luminous models show a growth in size with time of the nearly adiabatic layer. This growth seems to slow down as the upper edge of the nearly adiabatic layer gets closer to the maximum overshooting length and as the simulation time exceeds the typical thermal diffusive time-scale in the overshooting layer.

Revisit of recombination processes of low-charge-state ion generation during picosecond intense laser–gas interaction

The origin of He+ ions in picosecond intense laser–gas interaction was experimentally and numerically investigated. A nanosecond laser pulse was used to modulate the plasma condition, which helps to distinguish the origin of the helium ions with different charge states. By comparing the energy spectra of He2+ and He+ ions in the experiments with/without plasma shaping, we found neither ion–atom nor electron–ion recombination is responsible for the He+ generation, which is supported by two-dimensional hydrodynamic simulations and theoretical calculations.