Two-dimensional adaptive mesh refinement simulations of colliding flows

M Niklaus,W Schmidt,J C Niemeyer

doi:10.1051/0004-6361/200912483

M Niklaus, W Schmidt + Show 1 more

Open Access

https://doi.org/10.1051/0004-6361/200912483

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Abstract

Colliding flows are a commonly used scenario for the formation of molecular clouds in numerical simulations. Due to the thermal instability of the warm neutral medium, turbulence is produced by cooling. We carry out a two-dimensional numerical study of such colliding flows in order to test whether statistical properties inferred from adaptive mesh refinement (AMR) simulations are robust with respect to the applied refinement criteria. We compare probability density functions of various quantities as well as the clump statistics and fractal dimension of the density fields in AMR simulations to a static-grid simulation. The static grid with 2048^2 cells matches the resolution of the most refined subgrids in the AMR simulations. The density statistics is reproduced fairly well by AMR. Refinement criteria based on the cooling time or the turbulence intensity appear to be superior to the standard technique of refinement by overdensity. Nevertheless, substantial differences in the flow structure become apparent. In general, it is difficult to separate numerical effects from genuine physical processes in AMR simulations.

Highlights

Computational fluid dynamics in astrophysics rely on numerical methods that are capable of covering a huge range of scales
There are comparative studies of adaptive mesh refinement (AMR) vs. SPH, the degree of reliance of AMR in comparison to non-adaptive methods has met only little attention so far. For turbulent flows, it is a non-trivial question whether the solutions obtained from AMR simulations agree with the correct solutions of the fluid dynamical equations at a given resolution level
While the main fraction of the gas is situated in the warm phase with temperatures between 5000 and 10 000 K and low densities ∼1 cm−3, the cold gas with temperatures between 30 K and 100 K and densities in the range 30−350 cm−3 can be found close to the equilibrium curve

Summary

Introduction

Computational fluid dynamics in astrophysics rely on numerical methods that are capable of covering a huge range of scales. Apart from smoothed particle hydrodynamics (Monaghan 1992), adaptive mesh refinement (AMR) has been applied to variety of problems. This method was developed by Berger & Oliger (1984) and Berger & Colella (1989). For turbulent flows, it is a non-trivial question whether the solutions obtained from AMR simulations agree with the correct solutions of the fluid dynamical equations at a given resolution level. For this reason, we systematically compare AMR and static-grid simulations for a particular test problem in this article. Hennebelle et al (2008) and Banerjee et al (2008) applied refinement by fixed density thresholds and refinement by Jeans mass, respectively, in their three-dimensional high-resolution AMR simulations

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