Transcript Out-of-Core Hydrodynamical Simulations Hy Trac, Department

Simulations of Compressible MHD Turbulence
in Molecular Clouds
Lucy Liuxuan Zhang, CITA / University of Toronto, [email protected]
Chris Matzner, University of Toronto, [email protected]
Ue-Li Pen, CITA / University of Toronto, [email protected]
Abstract
Here, we describe simulations of compressible MHD
turbulence in molecular clouds. The code we use is an
isothermal, MPI version of the efficient TVD MHD code
made available by Pen et al. (2003) [1]. We employ initial
conditions and turbulence driving schemes similar to that
described by Stone, Ostriker, Gammie (1998), with the
introduction of a coherence time scale and a modified
energy normalization procedure. We present results from
turbulence simulations up to the resolution of 512^3 grid
cells. Results from 1024^3 simulations will be available in
the near future. The large runs are performed on CITA's
540-CPU Beowulf cluster.
MHD Equations
The set of MHD equations expresses conservation of mass,
momentum and energy, as well as magnetic flux freezing.
The equations governing the flow of magnetized fluid with
an adiabatic equation of state are
Numerical Model (cont’d)
Simulation Results (cont’d)
Initial Conditions The fluid is initially set up to have zero
A View of the Fluid Figure 2 is a cross section of the fluid
velocity, uniform density and uniform magnetic field in the xdirection as in Stone, Ostriker, Gammie (1998) [2].
perpendicular to the initial uniform B-field with beta=1 after
0.04 sound crossing time at the resolution of 5123. The
background color changes from red to white as the fluid
density increases, and the arrows indicate the magnetic field
lines.
Turbulence Driving Scheme The turbulence is driven by
the addition of velocity perturbations at regular time intervals.
Every one thousandth of a sound crossing time, a velocity
perturbation is generated and added to the fluid. In our
simulations, two different turbulence driving methods are used.
Method A is intended to be identical to that described in Stone,
Ostriker, Gammie (1998) [2] for the purpose of comparison;
whereas, a coherence time scale and a constant energy
normalization is introduced to method B.
Velocity Perturbation Each velocity perturbation field
is
a Gaussian random field with a prescribed power spectrum
Each velocity perturbation
is divergence-free with zero net
momentum. In method A, the input energy of each velocity
perturbation is normalized to the desired value, and each
velocity perturbation is independent of the previous velocity
perturbation.
Coherence Time & Energy Normalization (B) In
method B, the velocity perturbation is prescribed by
3D Power Spectrum Figure 3 is a plot of the 1D kinetic
where
is the velocity perturbation added to the fluid in
the previous driving, and
is the newly generated
Gaussian random field.
is a constant coefficient used to
achieve the desired average input power.
energy power spectrum for simulations of resolution 512^3
with beta=0.1 and beta=1 using the turbulence driving method
A.
Simulation Results
Under no external acceleration, the isothermal MHD
equations applicable to molecular clouds are
Energy Evolution Figure 1 is a plot of the energies as a
function of time for simulations of resolution 512^3 with beta
=0.1 and beta =1 using the turbulence driving method A. For
lines of the same colour, they are kinetic, magnetic and
thermal energies respectively in order of decreasing
magnitude.
Acknowledgement
Numerical Model
Advection Scheme We adopt an isothermal, MPI version of
the efficient TVD MHD code described in the paper [1].
The original serial code consists of about 400 lines. This
is expanded into a few thousand lines in the MPI version
by Matthias Liebendorfer. For more details about the
advection scheme, refer to paper [1].
We thank Weili Liu for creating the pretty image of the fluid.
Literature
[1]
[2]