Particle-Gas Dynamics with Athena: Method and Convergence

Abstract

The Athena MHD code has been extended to integrates the motion of particles coupled with the gas via aerodynamic drag, in order to study the dynamics of gas and solids in protoplanetary disks and the formation of planetesimals. Our particle-gas hybrid scheme is based on a second order predictor-corrector method. Careful treatment of the momentum feedback on the gas guarantees exact conservation. The hybrid scheme is stable and convergent in most regimes relevant to protoplanetary disks. We describe a semi-implicit integrator generalized from the leap-frog approach. In the absence of drag force, it preserves the geometric properties of a particle orbit. We also present a fully-implicit integrator that is unconditionally stable for all regimes of particle-gas coupling. Using our hybrid code, we study the numerical convergence of the non-linear saturated state of the streaming instability. We find that gas flow properties are well converged with modest grid resolution (128 cells per pressure length ηr for dimensionless stopping time tau_s=0.1), and equal number of particles and grid cells. On the other hand, particle clumping properties converge only at higher resolutions, and finer resolution leads to stronger clumping before convergence is reached. Finally, we find that measurement of particle transport properties resulted from the streaming instability may be subject to error of about 20%.

33 pages, accepted to ApJS

References in corpus (9)

• Athena: A New Code for Astrophysical MHD
• Forming Planetesimals in Solar and Extrasolar Nebulae
• Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation
• The Effect of the Radial Pressure Gradient in Protoplanetary Disks on Planetesimal Formation
• Implementation of the Shearing Box Approximation in Athena
• Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows
• A Hybrid Scheme for Gas-Dust Systems Stiffly Coupled via Viscous Drag
• A Symplectic Integrator for Hill's Equations
• The Validity of the Super-Particle Approximation during Planetesimal Formation

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