TY - JOUR

T1 - Two-fluid dusty gas in smoothed particle hydrodynamics

T2 - Fast and implicit algorithm for stiff linear drag

AU - Stoyanovskaya, O. P.

AU - Glushko, T. A.

AU - Snytnikov, N. V.

AU - Snytnikov, V. N.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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 tstop during which the velocity of a solid particle is equalized with respect to the gas velocity) to obtain solution, while some implicit methods require 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 hststop guarantees 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 hststop is not required anymore for accurate results.

AB - 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 tstop during which the velocity of a solid particle is equalized with respect to the gas velocity) to obtain solution, while some implicit methods require 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 hststop guarantees 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 hststop is not required anymore for accurate results.

KW - Epstein drag simulation

KW - Hydrodynamics

KW - Protoplanetary discs

KW - MIXTURES

KW - PLANETS

KW - CODE

KW - DYNAMICS

KW - SIMULATIONS

KW - FLOWS

UR - http://www.scopus.com/inward/record.url?scp=85053066025&partnerID=8YFLogxK

U2 - 10.1016/j.ascom.2018.08.004

DO - 10.1016/j.ascom.2018.08.004

M3 - Article

AN - SCOPUS:85053066025

VL - 25

SP - 25

EP - 37

JO - Astronomy and Computing

JF - Astronomy and Computing

SN - 2213-1337

ER -