A new gravitational N-body simulation algorithm for investigation of Lagrangian turbulence in astrophysical and cosmological systems

Turbulent-like behaviour is an important and recent ingredient in the investigation of largescale structure formation in the observable universe [1]. Recently, an established statistical method was used to demonstrate the importance of considering chaotic advection (or Lagrange turbulence) in combination with gravitational instabilities in the Λ CDM simulations performed from the Virgo Consortium (VC) [2]. However, the Hubble volumes simulated from GADGET-VC algorithm have some limitations for direct lagrangian data analysis due to the large amount of data and no real time computation for particle kinetic velocity along the dark matter structure evolution. Hence, the Lab for Computing and Applied Mathematics at INPE, Brazil, has been working for the past two years in computational environments to achieve the so-called COsmic LAgrangian TUrbulence Simulator (COLATUS) allowing N-body simulation from a Lagrangian perspective. The COLATUS prototype, as usual packages, computes gravitational forces with a hierarchical tree algorithm in combination with a local particle kinetic velocity vector in a particle-mesh scheme for long-range gravitational forces. In the present work we show preliminary simulations for 106 particles showing Lagrangian power spectra for individual particles. The code may be run on an arbitrary number of processors, with a restriction to powers of two. COLATUS has a potential to evaluate complex kinematics of a single particle in a simulated N-body gravitational system. However, to introduce this method as a GNU software further improvements and investigations are necessary. Then, the mapping techniques for the N-body problem incorparating radiation pressure and fluid characteristics by means of smoothed particle hydrodynamics (SPH) are discussed. Finally, we focus on the all-pairs computational kernel and its future GPU implementation using the NVIDIA CUDA programming model. Key-words: Cosmology, dark matter,turbulence