[sparta-users] some questions about SPARTA's method and work on discretization errors

[Jacob S. <jsc...@pp...>]

Dear SPARTA users,

I'm trying to understand better the relationships between the various
discretizations (N_c, delta-x, delta-x) and their effects on properties
such as viscosity and thermal conductivity. I have a few questions about
the applicability of the result by Rader et al [1] in their Equation (23).
I hope these questions are not inappropriate for this mailing list.

1) Just making sure: is sampling in SPARTA equivalent to 'standard' DSMC,
MCS, as explained in [1] ?

2) Just making sure: is SPARTA's algorithm DSMC94 as in [2]?

3) If I understand correctly, Rader et al's Equation (23) expresses
discretization errors for thermal conductivity when sampled using the MSCS
scheme, using a hard-sphere gas. Though Figure 6 in the paper seems to
imply it could be extended to use with MCS schemes as well?

4) Has anyone undertaken a study similar to [1] for viscosity coefficients,
such as with Couette flow?
5) ... for a VHS or VSS gas, rather than a hard sphere gas? I admit my
ignorance of the methods of the Chapman-Enskog procedure; would it be
reasonable to expect similar discretization errors?

I understand of course the exact coefficients of the terms in Equation (23)
only strictly apply to the specific scenario of Fourier heat flow with
certain temperature differences, wall separations, etc. Also, as a PhD
student especially, the answer to most of these might be 'go do some
convergence studies yourself'. I would appreciate any insight to make sure
I'm not spending *too* much time reproducing existing literature.

Best,
Jacob Schwartz

[1] Rader, D. J., M. A. Gallis, J. R. Torczynski, and W. Wagner. “Direct
Simulation Monte Carlo Convergence Behavior of the Hard-Sphere-Gas Thermal
Conductivity for Fourier Heat Flow.” *Physics of Fluids* 18, no. 7 (July
2006): 077102. https://doi.org/10.1063/1.2213640.

[2] Direct Simulation Monte Carlo: The Quest for Speed, M. A. Gallis, J. R.
Torczynski, S. J. Plimpton, D. J. Rader, T. Koehler, 29th Intl Symposium on
Rarefied Gas Dynamics in Xi'an, China, AIP Conf Proc, 1628, 27 (2014)

-- 
Jacob Schwartz
PhD Candidate, Princeton Program in Plasma Physics
S206, Princeton Plasma Physics Laboratory
609-243-2659 <%28609%29%20243-2659>