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Anders Johansen. Profile picture.

Anders Johansen


Anders Johansen. Profile picture.

Integration of particle-gas systems with stiff mutual drag interaction


  • Chao Chin Yang
  • Anders Johansen

Summary, in English

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.


  • Lund Observatory
  • eSSENCE: The e-Science Collaboration

Publishing year





The Astrophysical Journal Supplement Series





Document type

Journal article


IOP Publishing


  • Astronomy, Astrophysics and Cosmology


  • hydrodynamics
  • instabilities
  • methods: numerical
  • planets and satellites: formation
  • protoplanetary disks
  • turbulence




  • ISSN: 0067-0049