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MOGLI: Model for Multiphase Gas using Multifluid hydrodynamics

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read MOGLI is a two-fluid subgrid model that reproduces resolved multiphase gas behavior with only two free parameters.

desk verdict A genuine new subgrid framework with honest testing, but the verification is partly in-sample; worth a serious referee. read the letter →

arxiv 2412.03751 v1 pith:YJBCBTVK submitted 2024-12-04 astro-ph.GA astro-ph.IMphysics.flu-dyn

Hitesh Kishore Das , Max Gronke , Rainer Weinberger This is my paper · ORCID
classification astro-ph.GAastro-ph.IMphysics.flu-dyn
keywords multiphasegassubgridmodelmultifluidhydrodynamicsturbulentmixingcoldgrowthcloudsurvivalcircumgalacticmediumnumericalmethods
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces MOGLI, a subgrid model that lets simulations track unresolved cold and hot gas as two fluids occupying the same grid cell, instead of requiring the cold clouds to be resolved. The model's source terms split phase interactions into hydrodynamic drag, turbulent mixing of cold gas into hot gas, and growth of cold gas by cooling of mixed gas, with local turbulent velocity estimated either by Kolmogorov scaling or from the velocity gradient. The central claim is that with only two free parameters this prescription quantitatively matches resolved single-fluid turbulent-box simulations across resolution, Mach number, turbulence realizations, and resolved or unresolved initial clouds, including destruction timescales, growth rates, and the cloud survival criterion. If this holds, the model gives large-scale simulations of galaxy halos and clusters a computationally cheap route to include the parsec-scale cold gas that observations show is ubiquitous.

What carries the argument

The load-bearing machinery is the cell-level source-term closure. Cold gas in a cell is assigned an effective spherical size $l_{\rm cold}=(\alpha V_{\rm cell}/(4\pi/3))^{1/3}$, and all exchanges between the cold and hot fluids are written as rates proportional to the cold-gas surface area, using the Monte-Carlo fit $2h(\alpha)$ for overlapping spheres at volume fraction $\alpha$, times a flux with timescale $t_{\rm destroy}=\chi^{1/2} l_{\rm cold}/v_{\rm turb}$ for destruction and $t_{\rm grow}=\chi(t_{\rm destroy}t_{\rm cool,cold})^{1/2}\alpha^{1/9}$ for growth. Mixing is switched off in cells where the cold mass fraction exceeds $\alpha_{\rm mass}=0.15$, encoding shielding of cloud interiors, and the gradient-based turbulence estimator uses $\xi=2$ as the normalization in Eq. (29). These two values are the only free parameters; everything else, including the cross-sectional drag area $A_{\rm cross}(\alpha)$, follows from geometry and earlier resolved-simulation results. The machinery's job is to convert a cell's unresolved cold-gas volume fraction into the rates at which that gas mixes, drags, and grows.

What would settle it

Run a high-resolution resolved single-fluid turbulent-box simulation initialized with a cold phase that is filamentary or produced by shattering rather than a single spherical cloud, measure the cold-gas surface area per cell as a function of $\alpha$, and compare the MOGLI-predicted destruction and growth timescales (Eqs. 15 and 18) with the resolved evolution. A substantial deviation from the overlapping-sphere area fit (Eq. 30) would show the closure is not universal.

Watch

Extended reading notes

Core claim

The paper claims that unresolved multiphase gas can be represented faithfully by two co-located fluids whose interactions are governed by physically motivated rates rather than by tuned destructive behavior. The mass exchange between phases is written as an interface area times a flux, with the area set by a Monte-Carlo fit for overlapping cold spheres at volume fraction $\alpha$, and the flux timescales set by the cloud-crushing destruction time $\chi^{1/2} l_{\rm cold}/v_{\rm turb}$ and the cooling-regulated growth time $\chi (t_{\rm destroy}t_{\rm cool,cold})^{1/2}\alpha^{1/9}$. A cold-mass-fraction threshold suppresses mixing in shielded cold-dominated cells, and a gradient-normalization constant calibrates the local turbulence estimate. The paper verifies the full model against resolved single-fluid simulations, finding that cold gas destruction and growth rates, the emergence of the survival criterion from prior resolved-simulation work, and cold gas dispersion all match within the stochastic scatter of the benchmarks. It also demonstrates a 64$^3$-cell run tracking 100 unresolved clouds that would need roughly 3000$^3$ cells in a single-fluid code.

Load-bearing premise

The model's rates depend on the assumption that unresolved cold gas inside a cell occupies the surface area of an effective sphere (or overlapping spheres) at the cell's volume fraction; if the real subgrid cold gas is filamentary, sheet-like, or otherwise has a different area-to-volume relation, the mixing and growth rates would be wrong.

Editorial extensions

If this is right

  • Cold gas mass in large-scale simulations becomes resolution independent: a 64$^3$ multifluid run tracks what would require roughly a 3000$^3$ single-fluid run to resolve, so cosmological and halo simulations can include subgrid cold gas without resolving parsec-scale clouds.
  • The survival criterion for cold clouds (the boundary in $t_{\rm cool}/t_{\rm cc}$ and Mach number where clouds grow instead of being destroyed) emerges from the local source terms, so it is not an input to the model.
  • The gradient-based turbulence estimator makes the model applicable where turbulence varies in space and time, not only in boxes with a globally known turbulent velocity.
  • Growth rates match the analytic prediction $t_{\rm grow}\sim 1.5\,t_{\rm grow,theory}$ with scatter comparable to resolved simulations, so the model can quantitatively predict cold gas mass evolution in growth-dominated regimes.

Reading between the lines

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

  • If the overlapping-sphere area fit is universal, MOGLI should also capture statistically filamentary subgrid gas, because only the cell-level area-to-volume relation matters; testing with resolved simulations that start from filamentary or shattering-produced geometries would settle this.
  • The gradient-based velocity estimator could be reused as a general subgrid turbulence proxy in other multi-fluid codes, since it only needs the local velocity Jacobian; the paper notes slope-limiting distorts high-velocity tails, so accuracy in strongly shocked flows is an open question.
  • The model's shielding threshold ($\alpha_{\rm mass}=0.15$) acts like a per-cell switch between destruction and growth; a similar switch might be needed in three-phase extensions (molecular-cold-hot), but the paper leaves that to future work.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. Das, Gronke, and Weinberger present MOGLI, a subgrid model for unresolved cold gas implemented in the multifluid extension of AREPO. The model evolves hot and cold fluids with source terms for three physical processes: drag, turbulent mixing of cold into hot gas, and cold-gas growth by cooling of mixed gas. Local turbulent velocities are estimated either by Kolmogorov scaling from the box scale or locally from velocity gradients. The cold-gas surface area and cross-sectional area are represented through Monte-Carlo fits for ensembles of overlapping spheres. The paper verifies both a reduced non-radiative version and the full radiative version of the model against resolved Athena++ turbulent-box simulations, varying Mach number, spatial resolution, initial cloud resolvedness, and turbulence seeds. The reported diagnostics include cold-gas destruction timescales, growth rates, the Gronke et al. (2022) survival criterion, and cold-gas dispersion. The paper closes with a demonstration of a 64^3-cell simulation containing 100 unresolved clouds, which the authors argue would require roughly 3000^3 cells in a resolved single-fluid calculation.

Significance. The model addresses a real and widely recognized need: cosmological and galaxy-scale simulations cannot resolve the small cold clouds observed in galactic halos, and current simulations are non-converged in cold-gas content. The manuscript's main strength is its extensive verification suite: it tests a reduced model and the full model, compares two independent local-turbulence estimators, uses quantitative diagnostics (t_half, t_grow, survival, dispersion) across Mach number, resolution, resolvedness, and random seeds, and contains an honest discussion of limitations. The implementation in a widely used code and the small number of free parameters are additional assets. The main caveats are that the two free parameters are selected using the same benchmark class used for validation, and that the survival criterion is in large part a consistency check with the growth/destruction theory built into the model. If the calibration/validation distinction is addressed, the model would be a valuable tool for future large-scale multiphase simulations.

major comments (4)
  1. [Secs. 3.4 and 5; Eqs. (15) and (29)] The two model parameters are calibrated against the same benchmark suite used for validation: alpha_mass=0.15 is introduced because it 'works well across all tests' (Sec. 3.4), and xi=2 is selected during the non-radiative mixing tests by comparing with benchmark Athena++ runs (Sec. 5). Consequently, the agreement in Figs. 7, 11, and 12 is partly in-sample fitting rather than independent prediction. To support the abstract's claim of predictive verification, the paper should provide a sensitivity scan over alpha_mass and xi and/or perform a holdout exercise in which one portion of the parameter space is used for calibration and the remainder for validation. The discussion should also clearly separate calibrated quantities from genuinely out-of-sample predictions.
  2. [Sec. 4.2.2; Eqs. (17) and (34)] The per-cell growth timescale in Eq. (17) is built from the same theoretical framework that produces the analytical global growth rate in Eq. (34), and the Monte-Carlo area factor is explicitly introduced to reproduce the 0.5 fudge factor from Gronke et al. (2022). Therefore Fig. 11 and the survival criterion in Fig. 12 verify the internal consistency of the implemented rates rather than an emergent, independent prediction. The paper should either identify a genuinely independent prediction not used in calibration or reframe the survival criterion as a consistency check rather than an emergent result.
  3. [Sec. 4.2.3; Figs. 13 and 18] Cold-gas dispersion is a diagnostic directly relevant to the intended applications, and the MOGLI runs overpredict it substantially: in the unresolved initial-cloud case, the normalized dispersion reaches roughly 10^4 at t = 2.5 t_eddy while the Athena++ benchmarks reach roughly 10^2, and the resolved case also shows a systematic offset. The text attributes this difference to numerical diffusion, but the abstract's statement of 'very good quantitative agreement across the different simulation parameters and diagnostics' and the conclusion bullet that dispersion is 'similar' are too strong. Please either reduce the discrepancy or quantify and qualify the claim, reporting absolute as well as normalized dispersion.
  4. [Sec. 3.7; Eqs. (30) and (33)] The interface-area and cross-sectional-area relations are derived from ensembles of overlapping spheres, and the validation benchmarks are initialized with spherical clouds. If the unresolved cold gas is filamentary or has a different area-volume relation, the mixing and growth rates in Eqs. (15) and (18) would change. Since the intended applications include small, potentially elongated cold structures in the CGM, the paper should either provide a sensitivity test with non-spherical initial morphologies or explicitly state this geometric assumption as a central limitation rather than implying general validity.
minor comments (6)
  1. [Fig. 8 and Sec. 4.2.1] The text describing the right two columns of Fig. 8 labels the resolved-cloud case as L_box/R_cloud = 32, but Sec. 4.1 and the surrounding discussion use L_box/R_cloud = 8 for resolved clouds; this is inconsistent and should be corrected.
  2. [Sec. 3.7, Eq. (30)] For a single non-overlapping sphere the geometric limit is A R/(2V) = 1.5 alpha, whereas Eq. (30) gives h=1 in the dilute limit, which corresponds to A R/(2V) = alpha; a sentence clarifying how the Monte-Carlo fit treats overlapping spheres and how the normalization was chosen would help.
  3. [Sec. 3.5, Eq. (17)] The origin of the alpha^(1/9) factor in Eq. (17) is not derived in the text; a one-sentence justification or a reference for this scaling would improve readability.
  4. [Sec. 2.3] The quasi-isothermal EOS for the cold fluid, which resets the internal energy after each timestep, is a significant approximation; its effect on the energy-exchanging source terms in Eqs. (11) and (16) should be discussed or tested.
  5. [Sec. 3.6.2, Eqs. (24)-(27)] The derivation of the velocity-gradient estimator assumes a uniform distribution of neighbours and roughly equal neighbour distances; the manuscript would benefit from a quantitative error estimate beyond the factor-of-two statement in the caption of Fig. 3.
  6. [Sec. 6.4] The possible sensitivity of the area and cross-section fits (Sec. 3.7) to non-spherical subgrid morphology is not listed among the limitations; given the intended CGM applications, this deserves explicit mention in the limitations section.

Circularity Check

3 steps flagged · score 6.0 of 10

Two calibrated parameters and the imported same-form growth rate make part of the benchmark agreement in-sample; independent diagnostics remain.

  1. fitted input called prediction [Sec. 3.6.3, Eq. (29), and Sec. 5 / Fig. 14]
    "During our non-radiative turbulent mixing tests, explained later in Sec. 5, we find a ξ = 2 works better in matching with the benchmark Athena++ simulations. Hence, we use ξ = ξMOGLI≡ 2 in MOGLI runs"

    ξ is a free normalization of the velocity-gradient turbulence estimator. It is chosen by matching the same non-radiative benchmark Athena++ simulations that Sec. 5 then presents as verification of the grad method. In particular, the t_half/t_cc scatter in Fig. 14 is in-sample for this parameter, so the stated agreement of the destruction timescale is partly a calibration result rather than an independent prediction.

  2. fitted input called prediction [Sec. 3.4, Eq. (15), and Sec. 4.1 / Figs. 6–7]
    "The effect is that the mass exchange from cold to hot occurs only in cells that possess a mass fraction αmass less than a threshold. We find that a αmass threshold of 0.15 works well across all tests (§ 4.1), i.e., ṁcold→hot = {2h(α) mcold/tdestroy αmass < 0.15; 0 otherwise. (15)"

    The αmass = 0.15 cutoff is a free parameter introduced to suppress mixing in cold-dominated cells. Its only stated calibration is that it 'works well across all tests (§ 4.1)', and those tests are the very resolved Athena++ non-radiative runs used as the destruction-timescale benchmark. Consequently, the t_half/t_cc agreement reported for the reduced model includes a parameter tuned to that comparison; it is not a clean out-of-sample verification of the mixing rate.

1 more flagged steps
  1. self definitional [Sec. 3.5 Eq. (17); Sec. 4.2.2 Eq. (34); Figs. 10–11]
    "We can rewrite the expression for tgrow in terms of the local cell properties as, tgrow = χ(tdestroy tcool,cold)^{1/2} α^{1/9} (17) ... The analytical growth timescale, tgrow,theory, is given by (Gronke et al. 2022) tgrow,theory/tcc = 0.5χ(tcool,cold/tcc)^{1/2}(Lbox/Rcloud)^{1/6} (34). Note that while this equation is of the same form as the implemented Eq. (17), on a per-cell basis, it is important to point out that whether our simulations recover the correct global growth rate is far from obvious."

    Equation (17) is presented as the cell-level form of the same Gronke et al. (2022) growth law that later defines the 'analytical' growth timescale in Eq. (34). MOGLI evolves exactly this per-cell growth source, so the near-unity tgrow/tgrow,theory ratios in Figs. 10–11 and 15–16 largely verify that the implementation returns the formula that was put into it. The benchmark also includes the resolved simulations of Gronke et al. (2022) and Das & Gronke (2024), the same body of work from which the growth rate was imported. The growth-rate agreement is therefore a consistency check, not an independent first-principles confirmation.

full rationale

The strongest circularity is concentrated in the two free parameters and the imported growth law. ξ = 2 and αmass = 0.15 are both calibrated against the resolved Athena++ turbulent-box simulations, and the same simulations are then used as the benchmark for the destruction-timescale and growth-rate verification. The growth timescale comparison is additionally weakened by the paper's own admission that Eq. (34) is 'of the same form' as the implemented Eq. (17); the subgrid growth term is effectively the analytical growth law repackaged per cell, so recovering that law in Figs. 10–11 is partly built in. The survival criterion is not explicitly coded, so its reproduction has some emergent content, but because the growth and destruction rates that determine survival were imported from the same Gronke et al. (2022) theory and benchmark set, it functions more as an internal consistency check than as an independent prediction. I do not rate the paper as wholly circular: the multifluid AREPO implementation, the geometric Monte-Carlo area factors, and the drag formulation are independently constructed, and the cold-gas dispersion diagnostic (Fig. 13) is a comparatively independent test that shows only qualitative agreement, with MOGLI over-predicting dispersion. The central quantitative claims of reproduction are nonetheless partially in-sample, giving a circularity score of 6 rather than a lower score.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The model rests on two tuned free parameters, on imported scaling laws from previous resolved simulations, on assumptions about subgrid cold gas geometry and a Kolmogorov cascade, and on an unpublished source-term integrator. No new physical entities are introduced; the cold fluid is a numerical representation.

free parameters (2)
  • alpha_mass mixing threshold = 0.15
    Threshold on cold fluid mass fraction below which cold-to-hot mass exchange operates (Eq. 15). Admitted as a fudge parameter and tuned so results match benchmark Athena++ across tests.
  • xi_MOGLI gradient normalization = 2
    Normalization constant in the velocity-gradient-based turbulent velocity estimate (Eq. 29). Theoretical value is 3 (Eq. A2), but xi=2 was chosen because it matched the non-radiative mixing benchmarks better.
assumptions (7)
  • domain assumption Multifluid hydrodynamics in AREPO (Weinberger & Hernquist 2023) accurately describes two compressible fluids sharing a grid.
    The entire MOGLI model is built on this framework; no independent check is provided within this paper.
  • domain assumption The Bader-Deuflhard semi-implicit integrator (Weinberger et al., in prep) stably integrates the MOGLI source terms over a timestep.
    Invoked in Sec. 3 without a published reference or convergence details.
  • domain assumption Cold gas destruction timescale t_destroy = chi^(1/2) l_cold / v_turb (Eq. 12) from cloud-crushing theory and resolved simulations (Klein et al. 1994; Gronke et al. 2022) holds at the subgrid cell level.
    Basis for the mixing source term; imported from resolved-scale studies.
  • domain assumption Cold gas growth timescale t_grow = chi (t_destroy t_cool,cold)^(1/2) alpha^(1/9) (Eq. 17) from combustion-theory-derived resolved simulations (Tan et al. 2021; Gronke et al. 2022) holds per cell.
    Basis for the growth source term; the paper notes that recovering the global growth rate is far from obvious, but the per-cell validity is assumed.
  • domain assumption A fully developed Kolmogorov cascade extends from the box scale down to subgrid cold-gas scales (Eq. 21 and Sec. 3.6).
    Used for both kol and grad turbulent velocity estimates.
  • ad hoc to paper Cold gas within a cell can be treated as an effective sphere with size l_cold=(alpha V_cell/(4 pi/3))^(1/3) and with surface area given by the overlapping-sphere Monte Carlo relation 2 h(alpha) (Sec. 3.7, Eq. 30).
    A subgrid morphology assumption unique to this model; not validated against resolved simulations of non-spherical structures.
  • domain assumption Quasi-isothermal EOS for the cold fluid emulates the temperature floor and fast cooling of resolved single-fluid runs (Sec. 2.3).
    Assumed to reproduce the single-fluid cooling floor in the multifluid setup.

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Pith. "Pith review of MOGLI: Model for Multiphase Gas using Multifluid hydrodynamics." pith.science (2026). https://pith.science/paper/YJBCBTVK

@misc{pith2026241203751,
  author       = {Pith},
  title        = {Pith review of: MOGLI: Model for Multiphase Gas using Multifluid hydrodynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YJBCBTVK}},
  note         = {Machine review of arXiv:2412.03751}
}
abstract

Multiphase gas, with hot ($\sim10^6$K) and cold ($\sim10^4$K) gas, is ubiquitous in astrophysical media across a wide range of scales. However, simulating multiphase gas has been a long-standing challenge, due to the large separation between the size of cold gas structures and the scales at which such gas impacts the evolution of associated systems. In this study, we introduce a new subgrid framework for such multiphase gas, MOGLI: Model for Multiphase Gas using Multifluid hydrodynamics, in multifluid AREPO. We develop this approach based on first principles and theoretical results from previous studies with resolved small-scale simulations, leading to a minimal number of free parameters in the formulation. We divide the interactions in the model into three sources: drag, turbulent mixing and cold gas growth. As part of the model, we also include two methods for estimating the local turbulent velocities, one using the Kolmogorov scaling, and the other using the local velocity gradients. We verify the different components of the framework through extensive comparison with benchmark single-fluid simulations across different simulation parameters, such as how resolved the cold gas is initially, the turbulent Mach number, spatial resolution, and random initialisation of turbulence. We test the complete scheme and a reduced version, with and without cold gas growth. We find a very good qualitative and quantitative agreement across the different simulation parameters and diagnostics for both local turbulent velocity estimation methods. We also reproduce behaviour like the cold gas survival criteria as an emergent property. We discuss the applications and possible extensions of MOGLI and demonstrate its capability by running a simulation which would be computationally prohibitive to run as a resolved single-fluid simulation.

Figures

Figures reproduced from arXiv: 2412.03751 by the authors.

Figure 1
Figure 1. Initial cold fluid volume fraction slices for MOGLI simulations with resolved and unresolved cold gas clouds. The left panel shows an example of a resolved cold gas cloud with 643 cells and 𝐿box/𝑅cloud = 8, where the cloud is bigger than the grid cells and grid cells inside the volume of the cloud have an 𝛼 = 1 − 𝛼floor. On the other hand, the right panel shows the initial cold fluid volume fraction for MOGLI simula… view at source ↗
Figure 2
Figure 2. Top panel shows a slice of 𝑣turb,grad from a simulation with a turbulent Mach number, Mturb,box = 0.5 at the box scale. It shows how the velocity gradient-based estimation (grad) can capture the spatial variation in the local velocity dispersion, in other words, the local turbulent velocity. Bottom panel shows, in solid lines, the distribution of the local turbulent velocity, at the scales of average cell size inste… view at source ↗
Figure 3
Figure 3. The comparison between the directly calculated velocity disper￾sion (𝑣turb,direct) and the approximated local velocity dispersions using both estimation methods. The top panel shows the comparison with the velocity gradient-based method (grad) and the bottom panel show the comparison with the Kolmogorov spectrum-based method (kol). regime, the cold gas mass follows an exponential growth, with a char￾acteristic times… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Variation of 𝐴𝑅/(2𝑉box ) with volume fraction (𝛼) in a 3D box. The colour of the points shows the size of the individual spheres, relative to the box size and the orange lines correspond to the approximate fit for the points (Eq. (30)). subtracted 𝐸¤ cooling = 𝑚¤ hot→c…
Figure 6
Figure 6. Figure 6: Cold gas evolution in non-radiative MOGLI runs with time, nor￾malised to the initial cloud-crushing time (𝑡cc), with Mturb = 0.5. The solid lines show the cold gas evolution, as the total mass of the cold fluid, with the colour of the line denoting the initial 𝑅cloud/𝑑…
Figure 7
Figure 7. Figure 7: Scatter plot of the half mass time (𝑡half) normalised to the initial cloud-crushing timescale (𝑡cc = 𝜒𝑅cloud/𝑣turb), for different turbulent Mach numbers. Athena++ simulations with different resolutions (1923 , 3843 , and 7683 , represented by the colour of the point) …
Figure 8
Figure 8. Figure 8: Projected 𝛼𝜌cold/𝜌hot,ini, i.e. ∫ los 𝛼(𝜌cold/𝜌hot,ini)𝑑𝑧/𝐿box, plots at different times for MOGLI runs with M = 0.5 different 𝑡cool,cold/𝑡cc values. Two columns on the left show the evolution of an unresolved (𝐿box/𝑅cloud = 32) initial cloud and two columns on the rig…
Figure 9
Figure 9. Figure 9: Early-time hot fluid mass flux (𝑚¤ hot) slices, normalised with ratio of total hot fluid mass and eddy-turnover time (𝑚hot,box/𝑡eddy), for MOGLI simulations with resolved and unresolved cold gas clouds, at M = 0.5. The left panel shows an example of a resolved cold gas…
Figure 11
Figure 11. Figure 11: Scatter plot of the ratio of the 𝑡grow from the simulations and the analytical 𝑡grow,theory (Eq. (34)), across different turbulent Mach number (M). Crosses show the values from the MOGLI runs, with the colours denoting their "Resolvedness" (𝑅/𝑑 𝑥), while the black cir…
Figure 10
Figure 10. Figure 10: Cold gas evolution in MOGLI runs with time, normalised to the initial cloud-crushing time (𝑡cc), with Mturb = 0.5. The two groups of curves correspond to 𝑡cool,cold/𝑡cc = {10−4 , 10}. The solid lines show the cold gas evolution, as the total mass of the cold fluid, wi…
Figure 12
Figure 12. Figure 12: Scatter plot of survival or destruction of cold gas in the MOGLI runs, in a parameter space of 𝑡cool,mix/𝑡cc and turbulent Mach number, M, where 𝑡cool,mix (c.f. Eq. (35)). The circles show the points from resolved (𝑅/𝑑 𝑥 > 1) MOGLI simulations, while crosses denote th…
Figure 13
Figure 13. Figure 13: Evolution of the cold gas dispersion, normalised to its initial value, in the benchmark Athena++, as dashed lines, and MOGLI runs, as solid lines, with time normalised with turbulent eddy turnover time. The colour of dashed lines shows the resolution of the Athena++ s…
Figure 14
Figure 14. Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]
Figure 15
Figure 15. Figure 15: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]
Figure 16
Figure 16. Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_16.png]
Figure 18
Figure 18. Figure 18: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_18.png]
Figure 19
Figure 19. Figure 19: Evolution of projected 𝛼𝜌cold/𝜌hot,ini for a turbulent box with MOGLI, grad method, 643 cells, 100 unresolved clouds with a radius 𝐿box/256, where 𝐿box is the box size, and 𝑡cool/𝑡cc = 5 × 10−4 . The unresolved clouds grow and subsequently fill the box due to its fini…

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    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.