A Fast Parallel Simulation Code for Interaction between ProtoPlanetary Disk and Embedded ProtoPlanets: Implementation for 3D Code
Abstract
We develop a 3D simulation code for interaction between the protoplanetary disk and embedded protoplanets. The protoplanetary disk is treated as a threedimensional (3D), selfgravitating gas whose motion is described by the locally isothermal NavierStokes equations in a spherical coordinate centered on the star. The differential equations for the disk are similar to those given in Kley et al. (2009) with a different gravitational potential that is defined in Nelson et al. (2000). The equations are solved by directional split Godunov method for the inviscid Euler equations plus operatorsplit method for the viscous source terms. We use a subcycling technique for the azimuthal sweep to alleviate the time step restriction. We also extend the FARGO scheme of Masset (2000) and modified in Li et al. (2001) to our 3D code to accelerate the transport in the azimuthal direction. Furthermore, we have implemented a reduced 2D (r, {theta}) and a fully 3D selfgravity solver on our uniform disk grid, which extends our 2D method (Li, Buoni, & Li 2008) to 3D. This solver uses a mode cutoff strategy and combines FFT in the azimuthal direction and direct summation in the radial and meridional direction. An initial axissymmetric equilibrium disk is generatedmore »
 Authors:

 Los Alamos National Laboratory
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1044080
 Report Number(s):
 LAUR1222213
TRN: US201214%%294
 DOE Contract Number:
 AC5206NA25396
 Resource Type:
 Conference
 Resource Relation:
 Conference: ASTRONUM2012 ; 20120624  20120624 ; Kona,, Hawaii, United States
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 97 MATHEMATICAL METHODS AND COMPUTING; ACCRETION DISKS; ASPECT RATIO; DIFFERENTIAL EQUATIONS; EFFICIENCY; HYDRODYNAMICS; IMPLEMENTATION; NAVIERSTOKES EQUATIONS; PLANETS; SIMULATION; SOURCE TERMS; TORQUE; TRANSPORT; PROTOPLANETS
Citation Formats
Li, Shengtai, and Li, Hui. A Fast Parallel Simulation Code for Interaction between ProtoPlanetary Disk and Embedded ProtoPlanets: Implementation for 3D Code. United States: N. p., 2012.
Web.
Li, Shengtai, & Li, Hui. A Fast Parallel Simulation Code for Interaction between ProtoPlanetary Disk and Embedded ProtoPlanets: Implementation for 3D Code. United States.
Li, Shengtai, and Li, Hui. Thu .
"A Fast Parallel Simulation Code for Interaction between ProtoPlanetary Disk and Embedded ProtoPlanets: Implementation for 3D Code". United States. https://www.osti.gov/servlets/purl/1044080.
@article{osti_1044080,
title = {A Fast Parallel Simulation Code for Interaction between ProtoPlanetary Disk and Embedded ProtoPlanets: Implementation for 3D Code},
author = {Li, Shengtai and Li, Hui},
abstractNote = {We develop a 3D simulation code for interaction between the protoplanetary disk and embedded protoplanets. The protoplanetary disk is treated as a threedimensional (3D), selfgravitating gas whose motion is described by the locally isothermal NavierStokes equations in a spherical coordinate centered on the star. The differential equations for the disk are similar to those given in Kley et al. (2009) with a different gravitational potential that is defined in Nelson et al. (2000). The equations are solved by directional split Godunov method for the inviscid Euler equations plus operatorsplit method for the viscous source terms. We use a subcycling technique for the azimuthal sweep to alleviate the time step restriction. We also extend the FARGO scheme of Masset (2000) and modified in Li et al. (2001) to our 3D code to accelerate the transport in the azimuthal direction. Furthermore, we have implemented a reduced 2D (r, {theta}) and a fully 3D selfgravity solver on our uniform disk grid, which extends our 2D method (Li, Buoni, & Li 2008) to 3D. This solver uses a mode cutoff strategy and combines FFT in the azimuthal direction and direct summation in the radial and meridional direction. An initial axissymmetric equilibrium disk is generated via iteration between the disk density profile and the 2D diskselfgravity. We do not need any softening in the disk selfgravity calculation as we have used a shifted grid method (Li et al. 2008) to calculate the potential. The motion of the planet is limited on the midplane and the equations are the same as given in D'Angelo et al. (2005), which we adapted to the polar coordinates with a fourthorder RungeKutta solver. The disk gravitational force on the planet is assumed to evolve linearly with time between two hydrodynamics time steps. The Planetary potential acting on the disk is calculated accurately with a small softening given by a cubicspline form (Kley et al. 2009). Since the torque is extremely sensitive to the position of the planet, we adopt the corotating frame that allows the planet moving only in radial direction if only one planet is present. This code has been extensively tested on a number of problems. For the earthmass planet with constant aspect ratio h = 0.05, the torque calculated using our code matches quite well with the the 3D linear theory results by Tanaka et al. (2002). The code is fully parallelized via messagepassing interface (MPI) and has very high parallel efficiency. Several numerical examples for both fixed planet and moving planet are provided to demonstrate the efficacy of the numerical method and code.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2012},
month = {6}
}