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From: Volker Springel <volker_at_MPA-Garching.MPG.DE>

Date: Fri, 30 Mar 2007 12:13:44 +0200

Hi Yves,

You need to solve the cooling part in the energy equation with an

implicit time-integration scheme to cure this problem.

For example, the new energy (or entropy) at the end of the timestep can

be computed as

u' = u + (du/dt)_visc * dt + (du/dt)'_cool * dt

Here (du/dt)'_cool is the cooling rate evaluated for the *new*

temperature u'. It's a bit cumbersome to solve this equation (will

require some iterative scheme), but then your oscillations should be gone.

Volker

Yves Revaz wrote:

*> Dear Gadget list,
*

*>
*

*> Using Gadget-2 with radiative cooling,
*

*> I encounter problems in reproducing the Temperature-Density distribution
*

*> of gas particles in a LCDM model (see for example Fig. 3 of Katz et al
*

*> 96 or Fig.11 of
*

*> Springel & Hernquist 2002).
*

*>
*

*> The overall distribution is correct, however, I fail to reproduce the
*

*> thinness
*

*> of the horizontal branch, corresponding to high density regions
*

*> ((rho/rhom)>1e4, T<1e5K).
*

*> In my simulations, the temperature dispersion of the horizontal branch
*

*> is high,
*

*> with some particles having temperature up to 1e6 K !
*

*>
*

*> This problem comes from the competition between cooling (dA/dt)_rad and
*

*> viscosity heating (dA/dt)_visc, where A is the entropy.
*

*> For a particle with a density (rho/rhom)>1e4 and temperature > 1e4K,
*

*> we have:
*

*> |(dA/dt)_rad| >> |(dA/dt)_visc| => dA/dt)_tot << 0,
*

*>
*

*> the cooling dominates and the temperature quickly decreases. When the
*

*> temperature of
*

*> the particle goes below 1e4K, (dA/dt)_rad drops nearly to zero (cutoff
*

*> in the cooling function),
*

*> and the entropy variation is only due to the (dA/dt)_visc therm, which,
*

*> in some cases is so high
*

*> that the particle temperature instantaneously rises up to 1e6K !!!
*

*> In summary, in the horizontal branch, instead of being more or less
*

*> constant at 1e4K (equilibrium between
*

*> viscosity heating and radiative cooling), the temperature of the
*

*> particles oscillate between 1e4 and 1e5-1e6K.
*

*>
*

*> This behavior is the result of the cooling and heating time scale, much
*

*> shorter than
*

*> the time-step imposed by the currant condition. The cooling is limited
*

*> by the condition
*

*> that :
*

*> dA/dt > -0.5 A.
*

*>
*

*> Imposing also
*

*>
*

*> dA/dt < A,
*

*>
*

*> in not sufficient to damp the temperature oscillation.
*

*> There is probably a well known solution to this problem,
*

*> but I haven't found it in the literature.
*

*>
*

*> Does anyone has a solution ?
*

*>
*

*> Thanks in advance.
*

*>
*

*>
*

*> Yves
*

*>
*

*>
*

*> MY PARAMETERS
*

*> ---------------
*

*>
*

*> The simulation test contains 2*64^3 particles in 20 Mpc^3 h^-3
*

*>
*

*> I use the following parameters :
*

*>
*

*> ErrTolIntAccuracy 0.025
*

*> CourantFac 0.15
*

*> MaxSizeTimestep 0.03
*

*> MinSizeTimestep 0
*

*>
*

*> ErrTolTheta 0.8
*

*> TypeOfOpeningCriterion 0
*

*> ErrTolForceAcc 0.005
*

*>
*

*> DesNumNgb 32
*

*> MaxNumNgbDeviation 2
*

*> ArtBulkViscConst 0.8
*

*>
*

*> MinGasHsmlFractional 0.25
*

*> SofteningGas 8.
*

*> SofteningHalo 8.
*

*>
*

Received on 2007-03-30 12:13:44

Date: Fri, 30 Mar 2007 12:13:44 +0200

Hi Yves,

You need to solve the cooling part in the energy equation with an

implicit time-integration scheme to cure this problem.

For example, the new energy (or entropy) at the end of the timestep can

be computed as

u' = u + (du/dt)_visc * dt + (du/dt)'_cool * dt

Here (du/dt)'_cool is the cooling rate evaluated for the *new*

temperature u'. It's a bit cumbersome to solve this equation (will

require some iterative scheme), but then your oscillations should be gone.

Volker

Yves Revaz wrote:

Received on 2007-03-30 12:13:44

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