[Paper Review] EvoL: The new Padova T-SPH parallel code for cosmological simulations - I. Basic code: gravity and hydrodynamics

E. Merlin, U. Buonomo+3 more|arXiv (Cornell University)|Dec 9, 2009

Fluid Dynamics Simulations and Interactions63 references20 citations

TL;DR

EvoL is a new parallel, adaptive, and fully Lagrangian N-body code in Fortran95 designed for cosmological simulations of galaxy formation and evolution. It combines the Barnes-Hut tree algorithm for gravity and smoothed particle hydrodynamics (SPH) with advanced features like adaptive softening lengths, variable artificial viscosity, and artificial thermal conduction, achieving excellent energy and angular momentum conservation in standard hydrodynamic tests with errors below 1% and 6% respectively.

ABSTRACT

We present EvoL, the new release of the Padova N-body code for cosmological simulations of galaxy formation and evolution. In this paper, the basic Tree + SPH code is presented and analysed, together with an overview on the software architectures. EvoL is a flexible parallel Fortran95 code, specifically designed for simulations of cosmological structure formation on cluster, galactic and sub-galactic scales. EvoL is a fully Lagrangian self-adaptive code, based on the classical Oct-tree and on the Smoothed Particle Hydrodynamics algorithm. It includes special features such as adaptive softening lengths with correcting extra-terms, and modern formulations of SPH and artificial viscosity. It is designed to be run in parallel on multiple CPUs to optimize the performance and save computational time. We describe the code in detail, and present the results of a number of standard hydrodynamical tests.

Motivation & Objective

• To develop a flexible, parallel, and self-adaptive N-body code for cosmological simulations across cluster, galactic, and sub-galactic scales.
• To improve upon the previous Pd-Tsph code by enhancing numerical accuracy, performance, and algorithmic robustness.
• To implement modern formulations of SPH and artificial viscosity to address known SPH shortcomings such as spurious shear viscosity and poor treatment of contact discontinuities.
• To ensure high conservation of energy and angular momentum in hydrodynamic tests, critical for reliable cosmological simulations.
• To lay the foundation for future inclusion of non-standard physics like radiative cooling, star formation, and feedback mechanisms in a companion paper.

Proposed method

• The code uses the Barnes-Hut oct-tree algorithm for efficient gravitational force computation with O(N log N) scaling.
• It implements smoothed particle hydrodynamics (SPH) with modern formulations, including ∇h terms and variable α artificial viscosity to reduce numerical diffusion.
• Adaptive softening lengths are used with self-consistent correction terms to prevent energy errors in close encounters.
• Artificial thermal conduction is added to stabilize contact discontinuities and improve modeling of instabilities like Kelvin-Helmholtz.
• The code is parallelized using MPI for multi-CPU execution, with load-balancing and efficient data structures to optimize performance.
• Time integration uses variable time steps with periodic boundary conditions, and the code is designed for full Lagrangian, grid-free particle tracking.

Experimental results

Research questions

• RQ1 How well does EvoL conserve energy and angular momentum in standard hydrodynamic tests involving gravity and fluid dynamics?
• RQ2 Can adaptive softening lengths with correction terms significantly reduce energy errors compared to fixed softening in SPH simulations?
• RQ3 To what extent do artificial thermal conduction and variable viscosity improve the resolution of contact discontinuities and instabilities like Kelvin-Helmholtz?
• RQ4 How does the performance of the Barnes-Hut tree algorithm scale in parallel execution across multiple CPUs for cosmological simulations?
• RQ5 What is the impact of modern SPH formulations on the accuracy of simulations involving rotating and collapsing gas and dark matter components?

Key findings

• Energy conservation is excellent across all tests, with maximum errors below 1%, and the adaptive softening scheme outperforms the fixed softening approach.
• Angular momentum conservation is highly accurate, with a maximum relative error of only ~6% in the most challenging counter-rotating test.
• The inclusion of artificial thermal conduction significantly improves the treatment of contact discontinuities and the Kelvin-Helmholtz instability, reducing numerical noise.
• The gas and dark matter components in rotating tests (TC3 and TC4) show realistic disk formation and velocity patterns, with the gas co-rotating with dark matter in counter-rotating cases.
• The code successfully reproduces theoretical expectations in all standard hydrodynamic tests, including Sedov-Taylor explosions and shock tube problems.
• The parallel implementation scales efficiently, enabling large-scale cosmological simulations with reduced computational time on multi-CPU systems.