Multidimensional, compressible viscous flow on a moving Voronoi mesh

D. J. Muñoz*, V. Springel, R. Marcus, M. Vogelsberger, L. Hernquist

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Numerous formulations of finite-volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi-)Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in two and three dimensions. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite-volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disc models.

Original languageEnglish (US)
Pages (from-to)254-279
Number of pages26
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
StatePublished - Jan 2013


  • Hydrodynamics-methods
  • Numerical

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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