[FLASH-USERS] 2D disk models

[Peter Woitke]

Dear Tomasz,

> The simplest recipe is to advect the gas specific angular momentum. This
> is quite similar to advecting mass scalars (individual species) and you
> can use one of the mass scalars for that purpose. (I hope mass scalars
> are supported in the official 2.5 version.) Once you know actual
> distribution of specific angular momentum, centrifugal force can be
> easily calculated.

thank you very much for this comment! In fact, in (r,z,phi) cylinder
coordinates with axisymmetry (d./dphi=0), the phi-component of the
equation of motion is equivalent to

   D/Dt(rho L3) = 0                           (1)

where D/Dt means the Lagrangian derivative, r=sqrt(x^2+y^2), and

   L3 = r vphi,                               (2)

i.e. the angular momentum density rho*L3 in an invariant of the flow. So I
just have to define and initialize the mass scalar L3 and FLASH will solve
Eq.(1) automatically for me. The z-comonent of the equation of motion is
already correct, even with phi-rotation. Only the r-component needs a
modification, namely the additional source term +rho vphi^2/r (the
centrigugal force) on the r.h.s.

I will implement this by a modified gravity module which uses L3 as:

   gr = -GM/(r^2+z^2)^(3/2)*r + L3/r^3        (3)
   gz = -GM/(r^2+z^2)^(3/2)*z                 (4)

>From my experience with radiation pressure as additional force,
I can confirm that mass scalars work properly with Flash 2.4.
A modified gravity module might be more accurate, since it is
called several times during the hydro-integration, than an additional
force term which would be treated by operator splitting, wouldn't it?

Thank you,

   Peter Woitke


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Dr. Peter Woitke
--------------------------------------------
School of Physics & Astronomy
University of St Andrews
North Haugh
St Andrews KY16 9SS
Scotland
UK
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Room 329a
Tel.:  (+44) 1334 463068
Fax.:  (+44) 1334 463104
URL.:  http://www.strw.leidenuniv.nl/~woitke
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