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A wind, not an accretion disk, shapes the early light of a 10,000-solar-mass black hole tidal disruption event.

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2026-08-03 17:05 UTC pith:QNX3MPT3

load-bearing objection First 3D radiation-hydro IMBH TDE simulation with honest caveats; the central wind/Eddington picture is plausible, but the under-resolved nozzle shock keeps the peak luminosity and extrapolations shakier than the paper fully admits. the 2 major comments →

arxiv 2512.10564 v2 pith:QNX3MPT3 submitted 2025-12-11 astro-ph.HE

Wind-mediated Eddington-limited emission in a 10⁴M_odot Black Hole Tidal Disruption Event

Paola Martire , Elena Maria Rossi , Nicholas Chamberlain Stone , Elad Steinberg , Konstantinos Kilmetis , Itai Linial This is my paper
classification astro-ph.HE
keywords tidal disruption eventsintermediate-mass black holeradiation hydrodynamicsradiation-driven windEddington limitnozzle shockphotospherelight curve
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper presents the first end-to-end 3D radiation-hydrodynamics simulation of a star torn apart by a 10^4 solar-mass intermediate-mass black hole, following the debris for more than two fallback times. It claims that early optical and ultraviolet emission from such events is not powered by an accretion disk but by shock dissipation at the returning stream's pericenter passage, which launches a radiation-driven wind. The wind advects photons outward and releases them at an expanding photosphere, producing a bolometric light curve that peaks near twice the Eddington luminosity and then settles at the Eddington value. Because the debris fails to circularize, the classical expectation of a luminous disk fed by fallback is replaced by a nearly Eddington-limited, quasi-spherical outflow. This matters because upcoming surveys like LSST and ULTRASAT could detect dozens of such events per year, and the shape of the early light curve could reveal the presence of intermediate-mass black holes.

Core claim

For an intermediate-mass black hole tidal disruption event with M_BH = 10^4 solar masses, the returning stellar debris does not circularize into a disk on fallback timescales. Instead, the pericentric nozzle shock dissipates a small fraction of the orbital energy, and that dissipation drives a low-density, radiation-dominated wind. The wind expands quasi-spherically, advecting radiation from small radii; the photosphere embedded in this wind grows to about 10^13 cm with temperatures of a few times 10^4 K. The emergent bolometric luminosity briefly exceeds the Eddington limit, peaking around twice L_Edd, then settles at L_Edd ≈ 3 x 10^41 erg/s. The dissipation rate and emitted luminosity are

What carries the argument

The central mechanism is the radiation-driven wind launched from the pericenter region. Flux-limited diffusion couples radiation to the gas, and the return stream's vertical compression at pericenter (the nozzle shock) is the main site of irreversible dissipation. The paper shows this wind behaves as an adiabatic, optically thick outflow: with constant mass-loss rate, density falls as r^-2, radiation energy density as r^(-8/3), and the advected luminosity decays as r^(-2/3). This connects the dissipation luminosity at the base to the Eddington-limited luminosity at the trapping radius via L(r_tr) = L_Edd [(r_g/r_diss)(Mdot_w/Mdot_Edd)]^(1/3), an analytical scaling that explains how shock pow

Load-bearing premise

The global results assume that the numerical dissipation rate of the pericenter nozzle shock, though under-resolved, is close enough to the true rate that the wind mass-loss and luminosity it drives are not substantially different — an assumption the resolution tests support only to within a factor of about two.

What would settle it

A single well-observed IMBH TDE with a fast rise and early optical light curve that does not saturate near Eddington (for instance, peak luminosity much above L_Edd with photospheric radius much smaller than about 10^13 cm) would contradict the wind-advection picture, as would a detection of early X-ray emission exceeding the Eddington limit for a 10^4 solar-mass black hole, or spectropolarimetry showing no quasi-spherical expanding photosphere.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Early-time optical and UV light of IMBH TDEs becomes a probe of shock physics and wind launch, not of the accretion disk; black hole masses inferred from early light curves via disk models could be biased.
  • The quasi-spherical expanding photosphere and near-Eddington luminosity imply LSST and ULTRASAT can detect such events out to redshifts of about 0.1 and 0.06, respectively, with rates of roughly 100 and 15 per year.
  • The lack of circularization suggests mass-injection simulations that treat the debris stream as a given may be more robust for IMBH TDEs than for supermassive black hole TDEs.
  • The Eddington cap is not universal: the analytical scaling predicts it holds for main-sequence disruptions across black hole masses but breaks for white dwarfs, very massive stars, and partial disruptions where the dissipation rate is sub-Eddington.
  • The under-resolved nozzle shock could change quantitative estimates of stream width and wind mass-loss, but the global results (photospheric radius, light curve, dissipation rate) are converged to within a factor of about two across resolutions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same wind mechanism may explain the photospheric radii and temperatures of optically selected TDEs around more massive black holes, offering an alternative to reprocessing models that does not require a pre-existing disk.
  • A population of 'fast risers' in Rubin/LSST light curves, with rise times of a few days and an Eddington plateau, could provide a demographic handle on intermediate-mass black holes across cosmic time.
  • The wind's launching efficiency appears tied to the nozzle shock dissipation rate, which is exactly the part of the simulation that is under-resolved; observed early-time luminosities could therefore serve as empirical calibration for the unresolved shock physics.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. Martire et al. present an end-to-end 3D radiation-hydrodynamic simulation of a solar-type star (0.5 Msun, n=1.5 polytrope) disrupted by a 10^4 Msun black hole, run with RICH from before disruption to ~2.2 fallback times, with two additional lower-resolution runs for convergence. The debris stream fails to circularize on the simulated timescale; a radiation-driven, quasi-spherical wind launched near pericenter develops, advecting radiation to a photosphere that expands to ~100 r_t (~10^13-10^14 cm). The bolometric FLD light curve rises to ~2 L_Edd and then plateaus near L_Edd, with photospheric temperatures of a few x 10^4 K. The authors propose an analytic optically thick wind model (Sec. 3.3.2) that connects the trapping radius to the Eddington luminosity, and they estimate that LSST and ULTRASAT could detect such events to z~0.1 and z~0.06.

Significance. If correct, the paper provides the first end-to-end RHD simulation of an IMBH TDE and a concrete physical mechanism—advection in a radiation-driven wind—for the Eddington-limited optical/UV emission seen in many TDEs, without relying on an accretion disk. The systematic three-resolution study is commendable: orbital energies agree to <1%, thermal/radiation energies to 10-15%, and photospheric radius/light curve to within a factor ~2 (Figs. 8 and A1). The model makes testable predictions for upcoming surveys. The main weakness is that the dominant dissipation site (the pericentric nozzle shock) is explicitly admitted to be under-resolved, and the convergence tests do not by themselves establish that the numerical dissipation rate at the nozzle is close to the physical value.

major comments (2)
  1. [Sec. 4, Fig. 8; Sec. 6] The convergence tests are well designed but do not address the load-bearing concern. The authors state (Sec. 6) that fully resolving the pericentric nozzle requires cell sizes ~10^-3-10^-4 R_sun, whereas the High-res run's minimum cell size is 0.041 R_sun; all three resolutions therefore lie far from the resolved regime. Sec. 4 further reports that increasing resolution decreases the nozzle dissipation rate at fixed time—the hallmark of numerical dissipation—while near-convergence of the total dissipation rate across three under-resolved runs (Fig. 8, R<=2) does not exclude a systematically incorrect value. Since Sec. 3.1 and Fig. 12 identify the nozzle shock as the dominant dissipation site, and since the wind mass-loss rate (Fig. 10) and emergent luminosity scale with that dissipation, the central wind-mediated Eddington-limited emission scenario remains quantitatively conditional on t
  2. [Sec. 3.3.2, Eq. (16); Sec. 5.2] The extrapolation in Eq. (16) from the simulated point to other MBH masses and stellar parameters assumes zeta=0.04, kappa=kappa_T, and r_diss=r_p, where zeta is a simulation output that is itself resolution-sensitive (Fig. 10) and tied to the under-resolved nozzle. The statement in Sec. 5.2 that 'most main sequence TDEs should saturate at near-Eddington peak luminosities' is therefore a stronger claim than the simulation alone supports. Please either derive a physical scaling for zeta from the simulation or explicitly restrict the prediction to the simulated mass/parameter neighborhood.
minor comments (4)
  1. [Throughout] Many exponents render as '10 4 M' instead of '10^4 M_sun'. Equation (5) appears to contain a corrupted '√' or bracket; please check the typesetting.
  2. [Fig. 2] The caption states that the right panels report volume-integrated dissipation rates but does not define the integration volume. Please state whether this is the entire simulation domain or a selected region.
  3. [Sec. 3.3.2, Fig. 7] The text states t_dyn(r_tr) << t_fb but does not define t_dyn explicitly. A one-line definition would help readers verify the quasi-static wind assumption.
  4. [Appendix A2] Eq. (A3) is invalid at shocks; the authors acknowledge this in the footnote, but the main text would benefit from a clearer statement that Eq. (A7) is the discretized weak-form approximation used by RICH.

Circularity Check

0 steps flagged

No significant circularity: the simulation results are independent outputs, and the analytic wind model is a consistency check rather than a fitted prediction.

full rationale

The paper's central claims—slow circularization, an Eddington-level light curve, and an expanding photosphere embedded in a radiation-driven wind—are produced by the 3D radiation-hydrodynamics simulation RICH and are not derived by fitting the analytic model to the claimed outputs. The analytic model in Sec. 3.3.2 is constructed from physical scalings (advection, trapping radius, adiabatic radiation-energy scaling) and then evaluated using measured simulation quantities: the wind mass-loss rate Mdot_w, the opacity kappa_p, and r_diss ≈ r_p. The resulting estimate L(r_tr) ≈ 5 L_Edd is compared with the simulated FLD light curve (~2 L_Edd at peak) as a consistency check, not used to calibrate the light curve. Equation (16) is an extrapolation using zeta = 0.04, kappa = kappa_T, and the standard fallback-rate scaling, so it is not a hidden re-statement of the simulated luminosity. The definition of L_Edd uses the simulation-derived kappa_p, but this is a normalization convention and does not force the peak or plateau behavior seen in Fig. 4. The self-citations (Rossi & Begelman 2009; Linial & Quataert 2024; Steinberg & Stone 2024) provide context and a modeling approach, but the relevant scalings are re-derived in the text, and the simulation does not depend on those citations for its results. The acknowledged nozzle-shock under-resolution is a numerical-convergence caveat explicitly flagged by the authors; it is a correctness risk, not a circularity, because the global results are not defined or constructed from the assumption under test.

Axiom & Free-Parameter Ledger

8 free parameters · 6 axioms · 0 invented entities

The central claims are tied to one chosen simulation scenario and to several numerical/physical approximations. The main hand-chosen inputs are the black-hole and stellar parameters, the penetration factor, the gravitational softening radius, and the AMR thresholds. The analytic extrapolation uses simulation-calibrated wind efficiency and opacity, so it is not a fully independent derivation. No new physical entities are introduced.

free parameters (8)
  • Black hole mass M_BH = 10^4 M_sun
    Defines the IMBH regime; L_Edd, t_fb, and all radii scale with M_BH; Eq. 16 extrapolates to other masses.
  • Stellar mass and radius (M_star, R_star) = 0.5 M_sun, 0.47 R_sun
    Chosen main-sequence-like star; debris energy spread, fallback rate and wind properties depend on stellar structure; authors note different stars would change L(r_tr).
  • Penetration factor beta = beta = 1
    Sets pericenter equal to tidal radius; controls nozzle-shock compression and hence dissipation and wind.
  • Polytropic index n = n = 1.5
    Chosen stellar density profile; affects debris specific-energy distribution.
  • Gravitational softening radius r0 = r0 = 0.6 r_p
    Ad hoc softening of gravity near the BH (Eq. 1); assumes negligible mass and accretion luminosity inside r0; checked via enclosed mass, but accretion power could matter at late times.
  • AMR resolution parameters = N = 4e6 initial cells; Mmax = 3.75e-8 M_star; Mmin = 8.75e-9 M_star; volume thresholds
    Numerical resolution scheme; the three-resolution convergence study is the main evidence that these choices do not drive the qualitative results.
  • Wind efficiency zeta = zeta ~ 0.04 at t_p, ~0.5 at end
    Measured from the simulation and used in Eq. 16 for the Eddington-cap scaling; it is a simulation-calibrated quantity, not a fit to the light-curve peak.
  • Photospheric opacity kappa_p = kappa_p ~ 1.44 (simulation-computed)
    Harmonic-mean opacity at peak; sets the Eddington luminosity used to normalize the light curve and appears in the analytic extrapolation.
axioms (6)
  • domain assumption Paczyński–Wiita pseudo-Newtonian potential is adequate for r_p >> r_g (r_p ≈ 600 r_g).
    Used in Methods Sec. 2; authors argue relativistic precession is negligible, but this is an approximation that could affect stream orbits.
  • domain assumption Grey flux-limited diffusion captures the radiation transport that sets the photosphere and bolometric light curve.
    Methods Sec. 2 and Sec. 5.1; authors state spectral predictions are approximate; the light curve extraction relies on this scheme and on the Krumholz flux limiter.
  • domain assumption Opacities from solar-abundance LTE tables (Krief et al. 2016) apply to the debris; the peak opacity kappa_p is computed from them.
    Methods Sec. 2 and Appendix B; L_Edd and Eq. 16 depend on kappa_p; different abundances/non-LTE effects would shift results.
  • domain assumption Viscosity and magnetic fields are negligible during the simulated 2.2 t_fb.
    Sec. 5.1 estimates viscous time ~3.4 t_fb and argues MHD stresses are minor; if false, circularization and dissipation could be stronger.
  • domain assumption The photosphere can be represented by radial tau=2/3 surfaces averaged over 192 sight lines; the bolometric luminosity is the average FLD flux through them.
    Sec. 3.2, Eqs. (9)-(11); the outflow is anisotropic, so line-of-sight averaging is an approximation.
  • domain assumption The analytic wind model (steady, radiation-dominated, Mdot_w roughly constant in radius, rho ~ r^-2) describes the outflow for extrapolation to other masses.
    Sec. 3.3.2 and Eq. (16); the predicted near-Eddington behavior for other BH masses depends on this model.

pith-pipeline@v1.3.0-alltime-deepseek · 27738 in / 17984 out tokens · 165707 ms · 2026-08-03T17:05:48.246648+00:00 · methodology

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read the original abstract

Observations of tidal disruption events (TDEs) have already produced tens of strong candidate flares, and their number will greatly increase with upcoming wide field surveys. Nevertheless, the origin of the measured luminosity peak at early times is still unknown, and the ultimate sources of energy dissipation in TDEs are not fully understood. Here we present the first three-dimensional end-to-end simulation of a TDE by a $10^{4}M_\odot$ intermediate mass black hole (IMBH) with realistic parameters, run with the radiation-hydrodynamics code RICH. We find that the stellar debris fails to circularize efficiently, while a low-density, radiation-driven wind forms near pericenter and expands quasi-spherically. Radiation is advected by this outflow and released at the photosphere, which expands to radii of $\approx10^{13}$ cm and reaches temperatures of ~few $10^{4}$K at the peak of the light curve. The resulting luminosity briefly exceeds the Eddington limit before settling near that value. We systematically test the numerical convergence of our simulation by running it at three resolutions. While the nozzle shock at pericenter may be under-resolved, we find that global results are qualitatively converged and, largely, quantitatively robust. The upcoming Vera Rubin Observatory's LSST (g and r band) and ULTRASAT (near UV) will be able to observe events like our simulated IMBH TDE up to redshifts of z$\approx$0.1 and z$\approx$0.06, respectively.

Figures

Figures reproduced from arXiv: 2512.10564 by Elad Steinberg, Elena Maria Rossi, Itai Linial, Konstantinos Kilmetis, Nicholas Chamberlain Stone, Paola Martire.

Figure 1
Figure 1. Figure 1: Cumulative distribution function (CDF) at the last common time available among resolutions (𝑡 = 1.6𝑡fb). Orange, green and violet solid lines are respectively for Low, Middle and High resolution. Upper panel: CDF of cell mass. Vertical lines show the resolution of previous 3D simulations by Bonnerot & Lu (2020); Norman et al. (2021); Fancher et al. (2023); Price et al. (2024); Kubli et al. (2025) and Fitz … view at source ↗
Figure 2
Figure 2. Figure 2: Mass column density (left panel) and dissipation rate column density (right panel) in the High res at the onset of mass return (top panel, with a zoom-in insert), after one fallback time 𝑡fb (middle panel) and at the last time available 𝑡 = 2.2𝑡fb (bottom panel). The volume integrated dissipation rates 𝐸¤ irr are reported in the right panels. In the left panels, the dashed white lines represent the initial… view at source ↗
Figure 3
Figure 3. Figure 3: Luminosities from orbital energy of unbound (solid light pink line) and bound gas (dotted light pink line), thermal energy (magenta line), radi￾ation energy (purple line), and dissipation energy (dashed gray line), plotted against time 𝑡 normalized to the fallback time 𝑡fb. After 0.5𝑡fb dissipation rate tracks the evolution of radiation energy. lower resolution, hereafter called Low res and Middle res. The… view at source ↗
Figure 4
Figure 4. Figure 4: Left panel: time evolution of the photospheric radius, 𝑟ph, computed as a median value over different lines of sight. Dashed gray lines define 1𝜎 scatter around the median among the total number of evenly spaced sight lines, 𝑁obs = 192. Points are coloured by the fraction 𝑓 of unbound photospheric cells. The photosphere expands beyond the apocenter of the most bound debris (𝑟a, the dash-dotted black line) … view at source ↗
Figure 5
Figure 5. Figure 5: Time evolution of the wind mass rate (𝑀¤ w, scatter plot) at 𝑟 = 0.5𝑎mb, colour-coded by the ratio of volume-integrated (over the whole wind material) radiation energy 𝐸rad and gas thermal energy 𝐸th. A super￾Eddington fallback rate (𝑀¤ fb, dashed black line) drives a super-Eddington outflow that becomes radiation-dominated after ≈ 1.5 𝑡fb, where a naive Ed￾dington rate is defined as 𝑀¤ Edd = 𝐿Edd/𝑐 2 . Th… view at source ↗
Figure 7
Figure 7. Figure 7: Radial profiles at 𝑡 = 1𝑡fb (light pink line), 𝑡p = 1.5𝑡fb (magenta line) and the last time available, 𝑡 = 2.2𝑡fb (purple line). Solid coloured lines are obtained as mass-weighted (except for the wind mass rate) means on spherical shells and span from the tidal radius up to the median photospheric radius. Diamonds on the lines mark the median trapping radius among the lines of sight that contain an advecti… view at source ↗
Figure 8
Figure 8. Figure 8: Resolution tests for radiation. Orange, green and purple lines are, respectively, for Low, Middle and High res. Upper left panel: Time evolution of the median value of the photospheric radii 𝑟ph. As 𝑟ph varies depending on line-of-sight, the shaded regions show 1𝜎 contours across an isotropically distributed set of viewing directions. Upper right panel: light curves (solid lines) according to the FLD schem… view at source ↗
Figure 9
Figure 9. Figure 9: Space-time evolution of the ratio between gas eccentricity computed in different resolutions. Left panel: 𝑒Middle/𝑒Low. Right panel: 𝑒High/𝑒Middle. The ratio is always ≤ 10% outside the tidal radius (vertical dashed line) and up to 10 − 20% at smaller radii, indicating good convergence of bulk orbital properties. origin for a subset of the dissipation rate. However, the late times convergence to a uniform … view at source ↗
Figure 10
Figure 10. Figure 10: Resolution test for the wind analysis. Upper panel: Time evolution of the wind mass loss rate 𝑀¤ w, measured at 𝑟 = 0.5𝑎mb in three different resolutions. Diamonds on the lines show the time 𝑡p of the light curve peak for each resolution. Lower panel: R for 𝑀¤ w among two pairs of resolutions. Colours follow the scheme of [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Material enclosed inside 𝑟0 (pink line), 𝑟t (purple line) and 𝑎mb (black line), plotted as a function of time. Left panel: Time evolution of the total enclosed mass. Right panel: Time evolution of the dissipation energy rate by the enclosed material. For the entire evolution of the simulation, the dissipation energy rate for the material inside 𝑟0 (pink line) is about one order of magnitude lower than the… view at source ↗
Figure 12
Figure 12. Figure 12: Radii of observable interest for the High resolution. The solid vio￾let line is the photospheric radius, computed as a median value over different lines of sight. The dissipation radius (magenta line) indicates the physical site where shock dissipation is maximized; conversely, the “shock radius” (dashed black line) shows the dissipation site that would be inferred under the assumption that luminosity is … view at source ↗

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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    AT 2019ijn is an off-axis jetted transient (E~2e52 erg) with a fast-rising, slowly-declining optical flare from a z=0.273 dwarf galaxy, most consistent with a low-mass BH TDE.

  2. Low-hard to high-soft spectral state transitions in the faintest early-X-ray-detected optical tidal disruption event TDE 2025aarm

    astro-ph.HE 2026-07 conditional novelty 7.0

    TDE 2025aarm is the faintest early-X-ray-detected optical TDE and the first thermal TDE reported to show a low-hard to high-soft X-ray state transition resembling black-hole X-ray binaries.

  3. Implications of the UV/optical Plateau of AT2018cow

    astro-ph.HE 2026-07 conditional novelty 6.0

    A wind-and-irradiation disk model fits the AT2018cow UV plateau with accretor masses from 1.4 to ~100 solar masses, removing the need for a >200 solar-mass black hole.

  4. Low-hard to high-soft spectral state transitions in the faintest early-X-ray-detected optical tidal disruption event TDE 2025aarm

    astro-ph.HE 2026-07 unverdicted novelty 6.0

    TDE 2025aarm exhibits the first reported low-hard to high-soft X-ray state transition in a thermal tidal disruption event, at the faintest early X-ray luminosity yet measured.

  5. On the origin of anomalous dissipation in simulations of tidal disruption events

    astro-ph.HE 2026-05 unverdicted novelty 6.0

    Anomalous pre-intersection dissipation in TDE simulations is numerical in origin, arising from pericenter kinematics combined with algorithm sensitivities to converging versus diverging flows.

  6. TDE 2025abcr: A Tidal Disruption Event in the Outskirts of a Massive Galaxy

    astro-ph.HE 2026-02 conditional novelty 6.0

    TDE 2025abcr is the first optical tidal disruption event found more than 30,000 light-years from its host galaxy's center, implying a wandering black hole.

Reference graph

Works this paper leans on

4 extracted references · cited by 5 Pith papers

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    Colours follow the scheme of Fig.8

    for different energies.From left to right: orbital energy for bound gas, orbital energy for unbound gas, gas thermal energy, radiation energy. Colours follow the scheme of Fig.8. Resolutions are highly converged in the evolution of orbital energy, and converged at the∼10−15%level in the evolution of gas thermal energy and radiation energy. Convergence is ...

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    (ii) Compton scattering is used as a lower limit at low densities (𝜌<10 −10g/cm3) or at high temperatures (𝑇 >6·107K)

    For the Rosseland mean absorption coefficient𝛼 Ross, we performed a bilinear extrapolation in log-space for density and temperature outside the tabulated range usingtheboundarypointandtheseventhpointinward.Thisapproach includes the following exceptions: (i) For temperatures exceeding the tabulated maximum,𝛼Ross is assumed to be independent of temperature....

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    There- fore, the rate of change of the dissipation energy is ¤𝐸irr = ¤𝐸tot− ¤𝐸rev=− ∑︁ interfaces 𝐴(𝑃∗𝒗∗−𝑃 𝑐𝒗∗−𝒗 𝑐𝑃∗)·𝒏 A,(A7) as given in Eq.(7)

    gives ¤𝐸rev≡ d dt ∫ 𝑢dV=− ∫ ∇·(P𝒗)dV=− ∫ (P∇·𝒗+𝒗·∇P)dV =−𝑃 𝑐 ∮ 𝒗·d𝑨−𝒗 c·𝒏 A ∮ PdA ≈− ∑︁ interfaces 𝐴 𝑃𝑐𝒗∗+𝒗 𝑐𝑃∗ ·𝒏 A, (A6) where𝑃 c,𝒗 c are gas pressure and velocity at the cell centre. There- fore, the rate of change of the dissipation energy is ¤𝐸irr = ¤𝐸tot− ¤𝐸rev=− ∑︁ interfaces 𝐴(𝑃∗𝒗∗−𝑃 𝑐𝒗∗−𝒗 𝑐𝑃∗)·𝒏 A,(A7) as given in Eq.(7). 19 Radiation is not cons...

    2009