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Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES

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Romain Teyssier (CEA Saclay, France)

Astrophysics · Submitted 19 Nov 2001 · 61 references

Pith's verdict: A genuinely important methods paper — the AMR code and the coarse–fine shock study are the real contribution; the abstract's halo-model sentence oversells the gas side, which the body itself admits.

T0 · AI review

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CitationFrance), Romain Teyssier (CEA Saclay. "Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES." arXiv:astro-ph/0111367 (2001). https://pith.science/paper/XOS5WLUE
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The paper

The paper claims

The paper presents RAMSES, a tree-based adaptive-mesh code that couples an ART-like N-body solver to a second-order Godunov hydro solver and argues that density-driven refinement alone is sufficient for cosmological structure formation.

The reading

The paper aims to show that one code can follow both collisionless dark matter and shock-heated gas through hierarchical collapse without paying for a uniform high-resolution grid, which would let cosmological simulations put resolution where matter actually clusters. RAMSES does this with a fully threaded tree: cells are refined or derefined one at a time, gravity mirrors the ART mesh scheme, and gas is evolved with a second-order Godunov method. The author tests the pieces separately—point-mass forces, shock tubes, Sedov blasts, a Zel'dovich pancake, and spherical secondary infall—then runs a $100h^{-1}$ Mpc $Lambda$CDM simulation with $256^3$ particles and $4.1times10^7$ AMR cells, a formal $8192^3$ resolution. The central methodological claim is that cosmological strong shocks mostly run from dense, high-resolution regions into low-resolution voids, so shock fronts need not be refined; the paper reports no significant spurious effects from that choice in the cosmological runs. The convergence runs show the dark matter power spectrum matching halo-model predictions down to the formal Nyquist frequency, while gas pressure and halo profiles converge more slowly and agree with the halo model only at the factor-of-two level on large scales.

What carries the argument

The machinery is a fully threaded tree of octs—groups of $2^{rm dim}$ sibling cells—with linked lists that let the code split and destroy child cells cheaply at every time step. Gravity uses a particle linked list, CIC mass assignment, an FFT coarse-grid Poisson solve, and Gauss-Seidel relaxation with coarse-to-fine boundary buffers on refined levels. Hydrodynamics uses a second-order Godunov (piecewise linear) scheme with an almost-exact Riemann solver and Min-Mod slopes, plus conservative interpolation at level boundaries. The cosmological refinement rule is the part that carries the argument: cells refine when their dark matter or baryon density exceeds a level-dependent threshold chosen to keep a roughly constant number of particles per cell, not when a shock passes through.

Extended reading notes

Core claim

RAMSES establishes that tree-based AMR can carry a coupled N-body and hydrodynamical cosmological simulation to a dynamic range of $8192^3$ while keeping the mesh only about 2.5 times the coarse cell count. The load-bearing result is not just that the code passes standard tests; it is that a quasi-Lagrangian refinement rule based on dark matter and gas density thresholds, with no refinement of shock fronts, is adequate in cosmology. The author argues this because strong accretion shocks propagate outward from high-density haloes into low-density voids, the favorable direction for coarse-fine transitions, while weak shocks that enter refined regions are reported to leave no detectable oscillations. On the largest simulation, the dark matter density power spectrum converges to the formal resolution limit and follows the halo-model prediction, while the gas pressure spectrum and individual halo profiles show convergence at scales above roughly $50h^{-1}$ kpc and only approximate agreement with an isothermal halo model.

Load-bearing premise

The weakest load-bearing premise is that the halo-model comparison is an independent check on the gas physics, even though the paper states that the halo-model parameters were tuned to recover simulation results and the gas model assumes isothermal hydrostatic equilibrium, which the paper's own temperature profiles contradict.

Editorial extensions

If this is right

  • Cell-by-cell tree refinement can follow hierarchical clustering with a final mesh only about 2.5 times the coarse cell count, making an $8192^3$-equivalent dynamic range practical on a vector supercomputer.
  • Cosmological production runs can omit shock-front refinement, saving the large memory cost of covering two-dimensional shock surfaces in three dimensions, because strong accretion shocks run from high- to low-resolution regions.
  • The dark matter density power spectrum is reliable down to the formal Nyquist frequency of each run, so the N-body side can be used for precision clustering tests at the stated resolution.
  • Gas pressure and halo profiles are converged only above roughly $50h^{-1}$ kpc in the largest run, which sets the scale at which the adiabatic simulation can be compared with X-ray or Sunyaev-Zeldovich observations.
  • The mismatch with the isothermal halo model at small radii and high $k$ points to a needed extension using a $eta$-model gas profile and a hydrostatic temperature profile.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If density-only refinement is safe for outward-running cosmological shocks, the same logic should fail for implosions or merger shocks that converge into dense regions; a targeted convergence-inflow test would map the boundary of the method.
  • The pressure-spectrum excess at intermediate scales is naturally read as missing warm filaments; adding a third, filamentary component to the halo model would be a direct way to test that interpretation.
  • Because the halo-model parameters are calibrated against simulations, the agreement is a consistency check rather than a prediction; a blind comparison with parameters fixed from independent data would turn it into a real test.
  • The 2.5-fold cell overhead from refinement-map smoothing suggests that adaptive smoothing could trade a little mesh regularity for memory, which matters for extending the same box to higher resolution.
Original 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.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,077 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.66 · mentions code or data availability 0.04.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A new N-body and hydrodynamical code, called RAMSES, is presented. contribution 0.99 0.85 0.08 asserted 1.00
s1 It has been designed to study structure formation in the universe with high spatial resolution. contribution 0.83 0.44 0.05 asserted 0.99
s2 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. method 0.99 0.53 0.03 asserted 1.00
s3 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. method 0.94 0.25 0.02 asserted 1.00
s4 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. method 0.99 0.36 0.04 asserted 1.00
s5 The accuracy of the code is carefully estimated using various test cases, from pure gas dynamical tests to cosmological ones. method 0.90 0.93 0.04 asserted 1.00
s6 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. method 0.81 0.95 0.09 asserted 1.00
s7 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. result 0.81 0.97 0.21 asserted 1.00
s8 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. result 0.94 0.95 0.52 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Acceleration of massless test particles dropped randomly around single massive particles, whose positions are also chosen randomly in the box. The coarse grid has 323 cells. The number of refinement levels is progressively increased from 0 to 6, with increased spatial resolution around the massive particles. The radial AMR acceleration divided by the true acceleration is shown as light grey dots (versus radius in units of coarse cell size). The same ratio for the tangential AMR acceleration is shown as dark grey dots. The force corresponding to an homogeneous sphere with radius…
Figure 2. Particle positions obtained in a ΛCDM simulation are considered in this test. Each panel shows the force error for particles sitting at different levels of refinement. The error is defined as the difference between the AMR force and the force computed by a PM code of equivalent spatial resolution. In each panel, the average and the variance of the error are also shown
Figure 4. Planar Sedov Blast Wave Test: Density, velocity, pressure and refinement level as a function of position for times t =0.05, 0.1, 0.15, 0.2, 0.25 and 0.3. Numerical results are shown as squares, and compared to the analytical solutions (solid lines). See text for details. contact surfaces, since as soon as the code spreads them over, say, 6 cells, no matter how much one refines them af￾terwards, they will preserve their original thickness. Shock waves, however, have a self-steepening mechanism that al￾lows them to adapt to the local resolution and restore their sharp profile over 2…
Figure 6. Spherical Sedov Blast Wave Test: Rescaled density, velocity, pressure and volume-averaged refinement level as a function of radius for times t = 10−4 , 5.7 × 10−4 and 3.2 × 10−3 . Numerical results (solid lines with error bars) are compared to the analytical solutions (solid lines). See text for details. nature of the mesh. In
Figure 7. Zel’dovich Pancake Test: Density, velocity, pressure and refinement level as a function of position from the pancake mid-plane at z = 0. The solid line shows AMR results if refinements are activated using both density thresholds and pressure gradients. This explains why the 2 accretion shocks are refined. The squares show AMR results if refinements are activated using only density thresholds. See text for details
Figure 9. Top: Energy conservation as a function of expan￾sion factor for run P256L5 (solid line), P128L4 (dotted line) and P064L3 (dashed line). Bottom: Total number of cells in the AMR grid hierarchy (including split cells) di￾vided by the initial number of coarse cells as a function of expansion factor for the same 3 runs. be satisfied in cosmological simulations, as discussed in the next section. The 3 different initial particle grids considered here (643 , 1283 and 2563 ) defines also the coarse level (ℓ = 0) of the AMR hierarchy in each run. The maximum level of refinement was set to 3,…
Figure 10. Gray scale images of the gas temperature (T > 105 K), the gas density (ρ > Ωbρc) and the dark matter density (ρ > Ωmρc) in a planar cut through the computational volume for run P256L5. The mesh structure within the plane is plotted in the upper right panel (only octs boundaries are shown for visibility). For sake of comparison, the density and temperature maps obtained for run P256L0 (same initial conditions without refinements) are shown in the 2 lower panels. spatial resolution to improve the accuracy of the solution in the refined regions
Figure 11. Dark matter density (left panels) and gas pressure (right panels) power spectra for RAMSES runs with refinements (upper panels) and without refinements (lower panels). In each plot, the solid line corresponds to the halo model prediction, while the dotted line (dashed and dot-dashed) corresponds to numerical results with 2563 (1283 and 643 ) particles. Label “AMR” stands for AMR runs (P256L5, P128L4 and P64L3), while label “PM” stands for runs without refinement (P256L0, P128L0 and P64L0). For each power spectrum, the curve ends at the Nyquist frequency corresponding to the formal…
Figure 12. Color maps showing various projected quantities for the 5 most massive halos extracted from run P256L5. The projected volume is in each case a cube of 6.25 h−1Mpc aside. The color coding is based on a logarithmic scale for each plot. From top to bottom: 1- Projected dark matter particle distribution (the color coding corresponds to the local particle density). 2- X-ray emissivity map. 3- X-ray (emission weighted) temperature map. 4- Sunyaev￾Zeldovich decrement parameter (equivalent to the integrated pressure along the line of sight). 5- Projected adaptive mesh structure (only oct…
Figure 13. Radial profiles for the 5 most massive halos showing various quantities averaged along radial bins. In each plot, the dotted line (dashed and dot-dashed) comes from run P256L5 (P128L4 and P64L3). From top to bottom: 1- Dark matter overdensity profile (the best-fit NFW analytical profile is shown as a solid line). 2- Gas overdensity profile (the corresponding “hydrostatic isothermal model” analytical profile is also shown as a solid line). 3- Mass averaged temperature profile (the corresponding “hydrostatic beta model” analytical profile is also shown as a solid line). 4- Pressure…

Showing 10 of the paper's 13 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:astro-ph/0111367 by the authors.

References
How later papers used it

700 later papers cite it

Evidence: substantial. 651 of the citing papers share no author with it, and 478 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 832 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 24 of 513 papers with this label · 4 by the same authors

By the same authors

How the literature uses it

143 arXiv papers cite this in 176 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 61 sentences without a confident label

Uses its method or tool 85 papers
Uses its data or values 1 paper
  • Finally Ref. [ref] found that present-day N-body codes (Ramses [ref] , Pkdgrav3 [ref] , Gadget3 [ref] ) agree to within 1% at $k=1$ h/Mpc and 3% at $k=10$ h/Mpc.

    Cosmology in the era of Euclid and the Square Kilometre Array · Power spectrum error modelling (galaxy clustering + intensity mapping) · 0.86

Compares with it 3 papers
Cites it as background 11 papers
  • The standard approach to investigate the non-linear process of structure formation is N-body simulations [ref] , which however ignore any relativistic effect.

    $\texttt{fRevolution}$ $-$ Relativistic Cosmological Simulations in $f(R)$ Gravity I: Methodology · Introduction · 0.83

  • Even though this model seems to be quite simple from a conceptual point of view, no general solution is known and one usually has to resort to N-body simulations which tackle the problem of solving the dynamical equations numerically, see [ref] .

    Schr\"odinger method as N-body double and UV completion of dust · Introduction · 0.83

  • The variety of available options is noteworthy, even when restricting oneself to the particular case of scientific software chiefly intended for galaxy evolution and non-linear structure formation studies; MHD solvers developed for such applications include the high-order Godunov scheme of [ref] that was incorporated into the adaptive mesh refinement (AMR) code [ref] , the mesh-less smoothed particle magnetohydrodynamics (SPMHD) method of [ref] that was conceived as a constituent of [ref] , the second-order finite-volume scheme of [ref] implemented into the moving-mesh code [ref] , the `mesh-less finite mass'/`mesh-less finite volume' (MFM/MFV) approaches of [ref] that are a part of [ref] , and `geometric density average' formulation of SPMHD conceived by [ref] that was recently included in [ref] and [ref] .

    Smoothed particle magnetohydrodynamics for simulations of galaxy and cosmic structure formation · Introduction · 0.80

Discussion

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