Integration of particle-gas systems with stiff mutual drag interaction
(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.
(Less)
- author
- Yang, Chao Chin LU and Johansen, Anders LU
- organization
- publishing date
- 2016-06-01
- 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
- article number
- 39
- publisher
- American Astronomical Society
- 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
- 2025-04-05 16:52:30
@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>}},
author = {{Yang, Chao Chin and Johansen, Anders}},
issn = {{0067-0049}},
keywords = {{hydrodynamics; instabilities; methods: numerical; planets and satellites: formation; protoplanetary disks; turbulence}},
language = {{eng}},
month = {{06}},
number = {{2}},
publisher = {{American Astronomical Society}},
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}},
doi = {{10.3847/0067-0049/224/2/39}},
volume = {{224}},
year = {{2016}},
}