Define the viscosity beta as a constant instead of a hardcoded value

Set #define const_viscosity_beta in const.h instead of the hardcoded value of 3 in hydro_iact.h.

Note: default cosmology alpha = 0.8, beta = 3; and planetary alpha = 1.5, beta = 4.

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• 1212c95e - Add the defined viscosity beta to gizmo schemes too

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• 426b874d - Rename viscosity beta

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I do not understand the factor 2 that appears everywhere. Where does it come from?

I just depends what we want the user input "BETA" to be. I was keeping it BETA = beta/alpha from the original Monaghan/Balsara form of
visc = -alpha * c * mu + beta * mu^2 (1)
We're instead using
visc = -1/2 * alpha * mu * v_sig (2)
where the 1/2 is because of the two sound speeds in
v_sig = 2 * c - BETA * mu (3)
So (3) into (2) gives
visc = -alpha * c * mu + 1/2 * alpha * BETA * mu (4)
Compare with (1) and BETA would = 2 * beta / alpha which is not what we want (unless it is). So to keep the BETA = beta/alpha I added the factor of 2 in (3).

It comes down to whether you want the user to input
#define const_viscosity_beta 1.5f or 3.f

From my end, it's nicer to say "beta = 1.5 * alpha". But like you said, anything's fine as long as it's made clear

The reference I have been using thus far is my own derivation based on Price+10.

derivation.pdf

That would be equation (46), (48) and (49) and (52). Sorry about the scale-factors, let's just assume a==1 and H==0.

Do these make sense to you?

Sure that's fine, so beta=3 for the cosmology default and I'll take out the factors of 2.

and

\Pi_{ij}

expands into

\alpha (c_i + c_j - \beta \mu_{ij}) \mu_{ij}

which means

\alpha (c_i + c_j)\mu_{ij} - \alpha\beta \mu_{ij}^2

Yep, so just to be extra sure: with the half, your

\beta = 2 \beta / \alpha

in their Monaghan definitions, right?

So we're using Price (2010) eqn 103 instead of 98.

http://users.monash.edu.au/~dprice/SPH/price-spmhd.pdf

Wait how do I write maths?

https://gitlab.cosma.dur.ac.uk/help/user/markdown#math

Yes, (103).

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• 49f8f377 - Set Balsara as the default for Planetary hydro
• 2152b19a - Tweak the viscosity beta definition

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• c677952f - Tweak the viscosity beta definition

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The (1/2) is because equation (98) of Price has an average of c.

Yes, but the

(c+c)/2

compared with

\bar{c}

issue is only for

\alpha

, whereas

\beta

simply doesn't have the 1/2 in (98) but does have it in (103). So the two

\alpha

are the same but the two

\beta

are not, right? Sorry if I'm still missing something but I just want to make sure.

Agreed. The beta are different.

Note that the term that beta multiplies in the Monaghan expression is also different as it contains an extra

h/\hat{r}_{ij}

Right, good.

So as a final focus on the end point: If someone says they use Monaghan/Balsara viscosity with

\alpha=1.5

and

\beta=2 \alpha = 3

, then in SWIFT they need to set const_viscosity_beta 4.0f for the

\sim

same behaviour.

Agreed.

• alpha_Monaghan == SWIFT_alpha
• beta_Monaghan == (1/2) * SWIFT_alpha * SWIFT_beta

Great, that took a while but I'm happy with the end formulation if you are

Aside from making any of them run-time parameters of course

Yes, all good. :)

We'll make alpha a runtime parameter in due course. beta is too deep into the core of the code to do so and barely anyone ever changes it.

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• c677952f...bfe5e47c - 30 commits from branch master
• 9f747b8b - Add email to author list
• 4edc5565 - Define the viscosity beta as a constant instead of hard-coded
• e5aa7a68 - Add variable viscosity beta to all 'normal' hydro schemes
• d8c492ec - Set the default cosmology viscosity parameters before merging
• 0266c335 - Add the defined viscosity beta to gizmo schemes too
• cfa8ac1b - Rename viscosity beta
• c89b6aab - Set Balsara as the default for Planetary hydro
• cc7b2b00 - Tweak the viscosity beta definition

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@jwillis can you cross-check that this is fine with the vectorized version?

It looks okay to me.

merged

mentioned in commit 954074a7