Two-fluid Smoothed Particle Hydrodynamics Research Articles

Investigation of Submerged Soil Excavation by High-Velocity Water Jet Using Two-Fluid Smoothed Particle Hydrodynamics Method

AbstractIn this paper, submerged soil excavation by high-velocity water jet was investigated by means of a two-fluid smoothed-particle hydrodynamics (SPH) method. A critical state theory was couple...

Two-fluid dusty gas in smoothed particle hydrodynamics: Fast and implicit algorithm for stiff linear drag

Simulation of the dynamics of dust-gas circumstellar discs is crucial in understanding the mechanisms of planet formation. The dynamics of small grains in the disc is stiffly coupled to the gas, while the dynamics of grown solids is decoupled. Moreover, in some parts of the disc the concentration of the dust is low (dust to gas mass ratio is about 0.01), while in other parts it can be much higher. These factors place high requirements on the numerical methods for disc simulations. In particular, when gas and dust are simulated with two different fluids, explicit methods require very small timestep (must be less than dust stopping time $t_{\rm stop}$ during which the velocity of a solid particle is equalized with respect to the gas velocity) to obtain solution, while some implicit methods requires high temporal resolution to obtain acceptable accuracy. Moreover, recent studies underlined that for Smoothed particle hydrodynamics (SPH) when the gas and the dust are simulated with different sets of particles only high spatial resolution $h<c_{\rm s} t_{\rm stop}$ guaranties suppression of numerical overdissipation due to gas and dust interaction. To address these problems, we developed a fast algorithm based on the ideas of (1) implicit integration of linear (Epstein) drag and (2) exact conservation of local linear momentum. We derived formulas for monodisperse dust-gas in two-fluid SPH and tested the new method on problems with known analytical solutions. We found that our method is a promising alternative for the previously developed two-fluid SPH scheme in case of stiff linear drag thanks to the fact that spatial resolution condition $h<c_{\rm s} t_{\rm stop}$ is not required anymore for accurate results.

Dilatancy and compaction effects on the submerged granular column collapse

The effects of dilatancy on the collapse dynamics of granular materials in air or in a liquid are studied experimentally and numerically. Experiments show that dilatancy has a critical effect on the collapse of granular columns in the presence of an ambient fluid. Two regimes of the collapse, one being quick and the other being slow, are observed from the experiments and the underlying reasons are analyzed. A two-fluid smoothed particle hydrodynamics model, based on the granular-fluid mixture theory and the critical state theory, is employed to investigate the complex interactions between the solid particles and the ambient water. It is found that dilatancy, resulting in large effective stress and large frictional coefficient between solid particles, helps form the slow regime. Small permeability, representing large inter-phase drag force, also retards the collapse significantly. The proposed numerical model is capable of reproducing these effects qualitatively.

Two-fluid smoothed particle hydrodynamics simulation of submerged granular column collapse

In this paper, a two-fluid smoothed particle hydrodynamics (SPH) model, based on the mixture theory, is employed to investigate the complex interactions between the solid particles and the ambient water during the process of submerged granular column collapse. From the simulation, two regimes of the collapse, one being quick and the other being slow, are identified and the reasons of formation are analyzed. It is found that, a large internal friction angle of the granular phase, representing large drag force between solid particles, helps form the slow regime. Small hydraulic conductivity, representing large inter-phase drag force, also retards the collapse dramatically. Good agreements between our numerical results and other researchers’ numerical and experimental results are observed, which demonstrates the capability of the proposed two-fluid SPH approach in dealing with saturated water–soil mixture flows.

Two-fluid dust and gas mixtures in smoothed particle hydrodynamics: a semi-implicit approach

A method to avoid the explicit time integration of small dust grains in the two fluid gas/dust smoothed particle hydrodynamics (SPH) approach is proposed. By assuming a very simple exponential decay model for the relative velocity between the gas and dust components, all the effective characteristics of the drag force can be reproduced. A series of tests has been performed to compare the accuracy of the method with analytical and explicit integration results. We find that the method performs well on a wide range of tests, and can provide large speed ups over explicit integration when the dust stopping time is small. We have also found that the method is much less dissipative than conventional explicit or implicit two-fluid SPH approaches when modelling dusty shocks.

A two-fluid smoothed particle hydrodynamics (TF-SPH) method for gas–solid fluidization

A two-fluid smoothed particle hydrodynamics (TF-SPH) method was proposed in this work for the simulation of gas–solid fluidization, which combines an Eulerian solution of the gas phase and a Lagrangian SPH solution of the solid phase. The basic governing equations of TF-SPH are the same with those of the two-fluid model (TFM). The SPH solution of the solid phase allows significant reduction of the amount of particles that is actually simulated as compared to that encountered in industrial reactors. Thus, it can be expected to speed up the simulation. The sensitivity of SPH parameters to smoothing length and its ratio to particle space was tested. Quantitative comparison was also provided against the experimental data in literature. The TF-SPH method can be expected to be a promising approach for simulation of gas–solid fluidization.

Planet gaps in the dust layer of 3D protoplanetary disks

[Abridged] Aims: We provide predictions for ALMA observations of planet gaps that account for the specific spatial distribution of dust that results from consistent gas+dust dynamics. Methods: In a previous work, we ran full 3D, two-fluid Smoothed Particle Hydrodynamics (SPH) simulations of a planet embedded in a gas+dust T Tauri disk for different planet masses and grain sizes. In this work, the resulting dust distributions are passed to the Monte Carlo radiative transfer code MCFOST to construct synthetic images in the ALMA wavebands. We then use the ALMA simulator to produce images that include thermal and phase noise for a range of angular resolutions, wavelengths, and integration times, as well as for different inclinations, declinations and distances. We also produce images which assume that gas and dust are well mixed with a gas-to-dust ratio of 100 to compare with previous ALMA predictions, all made under this hypothesis. Results: Our findings clearly demonstrate the importance of correctly incorporating the dust dynamics. We show that the gap carved by a 1 M_J planet orbiting at 40 AU is visible with a much higher contrast than the well-mixed assumption would predict. In the case of a 5 M_J planet, we clearly see a deficit in dust emission in the inner disk, and point out the risk of interpreting the resulting image as that of a transition disk with an inner hole if observed in unfavorable conditions. Planet signatures are fainter in more distant disks but declination or inclination to the line-of-sight have little effect on ALMA's ability to resolve the gaps. Conclusions: ALMA has the potential to see signposts of planets in disks of nearby star-forming regions. We present optimized observing parameters to detect them in the case of 1 and 5 M_J planets on 40 AU orbits.

Evolution of density perturbations in a cylindrical molecular cloud using smoothed particle hydrodynamics

Molecular clouds have a hierarchical structure from few tens of parsecs for giants to few tenth of a parsec for proto-stellar cores. Nowadays, our observational techniques are so advanced that it has become possible to detect the small-scale substructures inside the molecular cores. The question that arises is how these small condensations are formed. In the present research, we study the effect of ambipolar diffusion heating on the ubiquitous perturbations in a molecular cloud and investigate the possibility of converting them to dense substructures. For this purpose, a small azimuthal perturbation is implemented on the density of an axisymmetric two-dimensional cylindrical cloud, and its evolution is simulated by the technique of two-fluid smoothed particle hydrodynamics. The self-gravity is not included and the initial state has uniform density, temperature and magnetic field, parallel to the axis of cylinder. In addition, all perturbed quantities are assumed to depend only on azimuth angle and time. Computer experiments show that if the ambipolar diffusion heating is ignored, the perturbation will be dispersed over the time. Including the heating due to ambipolar diffusion heats the matter in regions adjacent to the perturbation, thus, leading to the transfer of matter into the perturbed area. In this case, the density of perturbations can be increased. Also, the results of simulations show that an increase of the initial magnetic pressure leads to the intensification of difference between density of perturbations and their surroundings (i.e. increasing of density contrast). This effect is due to the direct relationship of the drift velocity to the intensity of the magnetic field and its gradient. Simulations with different initial uniform densities show that the growth of relative density contrast is more clear with a special density. This result can be explained by the intensification of thermal instability in this special density.

Investigating thermal evolution of the self-gravitating one dimensional molecular cloud by smoothed particle hydrodynamics

The heating of the ion-neutral (or ambipolar) diffusion may affect the thermal phases of the molecular clouds. We present an investigation on the effect of this heating mechanism in the thermal instability of the molecular clouds. A weakly ionized one-dimensional slab geometry, which is allowed for self-gravity and ambipolar diffusion, is chosen to study its thermal phases. We use the thermodynamic evolution of the slab to obtain the regions where slab cloud becomes thermally unstable. We investigate this evolution using the model of ambipolar diffusion with two-fluid smoothed particle hydrodynamics, as outlined by Hosking and Whitworth. Firstly, some parts of the technique are improved to test the pioneer works on behavior of the ambipolar diffusion in an isothermal self-gravitating slab. Afterwards, the improved two-fluid technique is used for thermal evolution of the slab. The results show that the thermal instability may persist inhomogeneities with a large density contrast at the intermediate parts of the cloud. We suggest that this feature may be responsible for the planet formation in the intermediate regions of a collapsing molecular cloud and/or may also be relevant to the formation of star forming dense cores in the clumps.

On the fragmentation of magnetized cloud cores

Recent calculations with a two-fluid smoothed particle hydrodynamics (SPH) code of the collapse of a magnetized dense core have found little evidence for fragmentation. These calculations have been interpreted as implying that magnetic braking by magnetic tension forces is sufficient to inhibit fragmentation, contrary to a suggestion by Boss that magnetic fields might encourage fragmentation. However, the type of fragmentation considered by Boss did not require the presence of significant rotation, contrary to the case with the SPH calculations, so the relevance of magnetic braking to Boss' suggestion is unclear. The SPH calculations used a barotropic equation of state which tended to produce a single central clump that resisted fragmentation in clouds where the Eddington approximation radiative transfer used by Boss led to fragmentation. While a definitive calculation has yet to be accomplished, fragmentation seems to remain as a possible outcome of the collapse of magnetic clouds.

Modelling ambipolar diffusion with two-fluid smoothed particle hydrodynamics

We describe a fully three-dimensional, Lagrangian magnetohydrodynamics code that is able to treat self-gravitating gas dynamics and to take account of ambipolar diffusion. The ion density is given as a function of the local neutral density, using an expression derived from models of ionization balance in molecular clouds. In turn, the ion density determines the strength of the coupling between the ionized and neutral fluids. The code is tested by modelling the evolution of a dense core, which is initially thermally supercritical but magnetically subcritical. The core steadily loses its magnetic support through ambipolar diffusion, and eventually becomes unstable against collapse. Our results agree well with those obtained by Fiedler and Mouschovias, who modelled the same system using a two-dimensional finite-difference code. In a second paper, we apply this code to the collapse and fragmentation of a rotating prestellar core.