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Integration of particle-gas systems with stiff mutual drag interaction

Yang, Chao Chin LU and Johansen, Anders LU (2016) In The Astrophysical Journal Supplement Series 224(2).
Abstract

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff - particularly because of small particles and/or strong local solid concentration - that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively... (More)

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff - particularly because of small particles and/or strong local solid concentration - that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
hydrodynamics, instabilities, methods: numerical, planets and satellites: formation, protoplanetary disks, turbulence
in
The Astrophysical Journal Supplement Series
volume
224
issue
2
publisher
University of Chicago Press
external identifiers
  • scopus:84977527938
  • wos:000381013200026
ISSN
0067-0049
DOI
10.3847/0067-0049/224/2/39
language
English
LU publication?
yes
id
8060883f-d47c-402d-bdae-61eadb922260
date added to LUP
2016-07-25 13:46:44
date last changed
2017-07-02 04:53:03
@article{8060883f-d47c-402d-bdae-61eadb922260,
  abstract     = {<p>Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff - particularly because of small particles and/or strong local solid concentration - that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.</p>},
  articleno    = {39},
  author       = {Yang, Chao Chin and Johansen, Anders},
  issn         = {0067-0049},
  keyword      = {hydrodynamics,instabilities,methods: numerical,planets and satellites: formation,protoplanetary disks,turbulence},
  language     = {eng},
  month        = {06},
  number       = {2},
  publisher    = {University of Chicago Press},
  series       = {The Astrophysical Journal Supplement Series},
  title        = {Integration of particle-gas systems with stiff mutual drag interaction},
  url          = {http://dx.doi.org/10.3847/0067-0049/224/2/39},
  volume       = {224},
  year         = {2016},
}