[Paper Review] Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES

Romain Teyssier|arXiv (Cornell University)|Nov 19, 2001

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy50 references1,070 citations

TL;DR

This paper presents RAMSES, a new cosmological hydrodynamics code using Adaptive Mesh Refinement (AMR) with a tree-based data structure for dynamic grid refinement. It combines a second-order Godunov hydrodynamics scheme with a TREE-based N-body solver, achieving high-resolution simulations of structure formation in a low-density ΛCDM universe with a formal resolution of 8192³, demonstrating convergence down to the resolution limit and good agreement with halo model predictions for dark matter and gas power spectra.

ABSTRACT

A new N-body and hydrodynamical code, called RAMSES, is presented. It has been designed to study structure formation in the universe with high spatial resolution. The code is based on Adaptive Mesh Refinement (AMR) technique, with a tree based data structure allowing recursive grid refinements on a cell-by-cell basis. The N-body solver is very similar to the one developed for the ART code (Kravtsov et al. 97), with minor differences in the exact implementation. The hydrodynamical solver is based on a second-order Godunov method, a modern shock-capturing scheme known to compute accurately the thermal history of the fluid component. The accuracy of the code is carefully estimated using various test cases, from pure gas dynamical tests to cosmological ones. The specific refinement strategy used in cosmological simulations is described, and potential spurious effects associated to shock waves propagation in the resulting AMR grid are discussed and found to be negligible. Results obtained in a large N-body and hydrodynamical simulation of structure formation in a low density LCDM universe are finally reported, with 256^3 particles and 4.1 10^7 cells in the AMR grid, reaching a formal resolution of 8192^3. A convergence analysis of different quantities, such as dark matter density power spectrum, gas pressure power spectrum and individual haloes temperature profiles, shows that numerical results are converging down to the actual resolution limit of the code, and are well reproduced by recent analytical predictions in the framework of the halo model.

Motivation & Objective

• To develop a high-resolution cosmological simulation code capable of resolving both large-scale structure and small-scale baryonic physics in a ΛCDM universe.
• To overcome limitations of traditional N-body and Eulerian hydrodynamics methods in achieving high dynamical range and accurate shock capturing.
• To implement an adaptive mesh refinement strategy that maintains a constant number of particles per cell, minimizing two-body relaxation and Poisson noise.
• To validate the code’s accuracy and convergence using standard hydrodynamical and cosmological test cases.
• To demonstrate the code’s ability to reproduce analytical predictions from the halo model for dark matter and gas power spectra.

Proposed method

• The code uses a tree-based data structure to enable recursive, cell-by-cell refinement of the AMR grid, allowing high spatial resolution in dense regions.
• The N-body solver is based on a TREE algorithm with multipole expansion for long-range forces and direct particle-particle interactions at the finest level, ensuring high dynamical range.
• The hydrodynamics solver employs a second-order Godunov method with a Riemann solver, ensuring accurate shock capturing and exact total energy conservation (excluding gravity).
• A quasi-Lagrangian refinement strategy maintains roughly constant particles per cell across refinement levels, reducing numerical noise and two-body relaxation.
• The code uses a hierarchical grid structure with nested grids, enabling efficient force and hydrodynamics calculations on adaptive grids.
• Simulations are initialized with fixed box size (100 h⁻¹ Mpc) and varying initial grid resolutions (64³ to 256³), achieving a formal resolution of 8192³ in the highest run.

Experimental results

Research questions

• RQ1 Can a high-resolution AMR code with a tree-based data structure achieve accurate and convergent simulations of cosmological structure formation?
• RQ2 How does the quasi-Lagrangian refinement strategy affect numerical noise and two-body relaxation in N-body simulations?
• RQ3 To what extent do the numerical results for dark matter and gas power spectra converge at high resolution and match analytical halo model predictions?
• RQ4 What are the spurious effects associated with shock wave propagation across AMR grid interfaces, and are they negligible?
• RQ5 Can the halo model be extended to accurately describe the gas density and temperature profiles in simulated haloes?

Key findings

• The RAMSES code achieves a formal spatial resolution of 8192³ in a 100 h⁻¹ Mpc box, corresponding to 12 h⁻¹ kpc comoving resolution.
• Numerical results for the dark matter density power spectrum converge down to the formal resolution limit and agree well with analytical halo model predictions.
• For the gas pressure power spectrum, convergence is observed at scales greater than 50 h⁻¹ kpc in the highest-resolution run.
• The halo model reproduces the dark matter power spectrum within a few percent at all scales down to the resolution limit.
• The halo model approximates the gas power spectrum within a factor of 2 at scales above 50 h⁻¹ kpc, with a proposed extension using a β-model for gas density profiles improving agreement.
• Analytical temperature profiles derived from hydrostatic equilibrium and a β-model gas density profile accurately match the simulated temperature profiles of individual haloes.