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flowcode - evolve an N-body system based on a given flow (2D only)
flowcode is an equal-timestep N-body integrator
which evolves the particles based on the computed flow (currently only
in 2D) at their current position. The flow is obtained from a standard potential
descriptor, given by the three keywords potname=,potpars=,potfile= (See
also potential(3,5NEMO)), except that flow velocity must be returned instead
of forces. The potential returns the density, if this is meaningful for
In addition to integrating the equations of motion,
the particles are allowed to loose some (eta) of their random energy (smoothed
over a certain ‘‘box’’ size (cell)), and turn it into mean orbital motion. (NOT
IMPLEMENTED - see potcode(1NEMO)
Orbits can also be diffused: at regular
intervals the velocity vector can be rotated over a randomly gaussian
distributed angle (sigma).
The following parameters are recognized;
they may be given in any order.
RK, PC and PC1 don’t work in rotating potentials
- use EULER or RK4.
- Initial conditions will be read
from in-file in snapshot format [default: none - but is required].
- If given, results are written to out-file in snapshot format [default: empty,
no snapshot output file produced].
- name of file of potential(5NEMO)
descriptor [no default].
- List of parameters to the potential
descriptor. The first parameter must be the pattern speed in the x-y plane
(rotating frames of reference are not supported for all integration modes).
The remaining parameters are used by the inipotential() routine in the
potential descriptor. [default: none - let them be defined by routine itself].
- name of an optional datafile to the potential descriptor.
This might be an N-body snapshot or list of spline fit coefficients etc.
- Inverse time-step, to be used with the time
integrator. [Default: 64.0 (64 steps per unit time)].
mode number: 0=Euler, 1=PC (Predictor Corrector), 2=modified PC, 3=Runge-Kutta
(JEB modified), 4=4th order Runge-Kutta, 5=LeapFrog. [default: 4].
- Time to stop integration in N-body model units. Default is 2.0.
- Frequency of major N-body data outputs. Default is 4.0 (4 frames per unit
- Frequency of minor diagnostic outputs. Default
is 32.0 (32 diagnostic measurements per unit time).
- Miscellaneous control options, specified as a comma-separated list of keywords.
Currently recognized keywords are: reset_time: when reading initial data,
set tnow to zero; new_tout: when restarting, set new output times; mass,
phi, acc, aux: output mass, potential (density really) acceleration data
and auxilliary (the deflection angle from diffusion is stored here) with
major data outputs.
- *** Fraction of random energy that
is dissipated [Default: 0.0].
- *** Cell size in which dissipation
is performed after every timestep. Dissipation is current performed on a
cartesian grid, in which cells are square (2D)
or a cube (3D)
- *** Maximum size of the "box" (actually cube) within
which dissipation is performed. If a negative number is given, the box is
allow to grow as large as is needed, though this may consume a lot of memory.
Default: -1, i.e. box can grow indefinite.
- *** The ratio of diffusion
angle to rms velocity dispersion in a cell. If fheat>0, each time dissipation
is applied, the rms velocity dispersion in a cell is computed, and a diffusion
angle computed. The velocity vector of each particle is then rotated with
a gaussian distributed value with rms fheat*velsig. This in effect gives
a dissipation dependant heating source. See also sigma=, which is position
independant. [Default: 0].
- Diffusion angle, gaussian distributed
with this sigma, about which each velocity vector is rotated after each
timestep. Diffusion is used only when sigma > 0. [Default: 0].
- Frequency of diffusion. Currently the same diffusion angle is used between
changes, instead of during a single integration step Default is the same
as the integration frequency (freq=).
- Random number seed,
only used when diffusion (sigma=) is used. 0 must be used to get the random
seed from the time of the day. [Default: 0].
- Identifying text for
this run. Default: not used.
Since cell is a fixed number throughout the execution,
is doesn’t deal well with systems who’s lenght-scale changes, in particular,
expanding systems will allocate more and more space to hold the dissipation
Normally a distinction is made between a streamline and streakline.
A streamline is what we compute here: with a "frozen" field we compute
how a tracer particle would have flown through space. A streamline also
takes into account that the flow could be a function of time, and now
it computes how a tracer particle would have streamed through space in
the fluid that changed its flow.
Various schemes of dissipation
can be invoked. Here’s one, see also Lin & Pringle (1974):
For each cell the
relative position and velocity for each particle within that cell is computed:
R = r - <r >
i i i
V = v - <v >
i i i
after which the dimensionless viscosity parameter ’alpha’ controls the new
velocity for each particle after a timestep:
< R x V >
u = <v> - alpha R x ------------ + (1-alpha) V
i i i i
< R . R >
10-apr-96 V0.1 cloned of potcode PJT
7-feb-04 V0.6 implemented diffusion for modes 0,1,4 PJT
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