ABSTRACT This work concerns the development of a gridless method for modeling the inter-particle collisions of a gas. Conventional fixed-grid algorithms are susceptible to grid-mismatch to the physical system, resulting in erroneous solutions. On the contrary, a gridless algorithm can be used to simulate various physical systems without the need to perform grid-mesh optimization. An octree algorithm provides the gridless character to a direct simulation Monte Carlo (DSMC) code by automatically sorting nearest-neighbor gas particles into local clusters. Automatic clustering allows abstraction of the DSMC algorithm from the physical system of the problem in question. This abstraction provides flexibility for domains with complex geometries as well as a decreased code development time for a given physical problem. To evaluate the practicality of this code, the time required to perform the gridless overhead from the octree sort is investigated. This investigation shows that the gridless method can indeed be practical and compete with other DSMC codes. To validate gridless DSMC, results of several benchmark simulations are compared to results from a fixed-grid code. The benchmark simulations include several Couette flows of differing Knudsen number, low-velocity flow past a thin plate, and two hypersonic flows past embedded objects at a Mach number of 10. The results of this comparison to traditional DSMC are favorable. This work is intended to become part of a larger gridless simulation tool for collisional plasmas. Corresponding work includes a gridless field solver using an octree for the evaluation of long range electrostatic forces. We plan to merge the two methods creating a gridless framework for simulating collisional-plasmas.
8 June 2007
30 June 2009
University of Michigan
Naval Research Laboratory
Now at: Air Force Research Laboratory
Collaborator: Andrew Christlieb, Michigan State University
J Comp Phys, Vol 227, pp 8035-8064, 2008.
Low velocity flow
Gas Dynamics Simulation Approaches
Fig. 1.1, G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, 1994.
: Local Knudsen number
: Mean free path
: Local Characteristic length
: N-Body phase-space density
For cm/s and ~10µ m X 10µ m X 1mm resolution,
need ~>> 1 TB of memory!
(and a lifetime to compute the collision integral)
What about a numerical solution of the Boltzmann equation?
: Collision integral
Direct Simulation of gas dynamics using Monte Carlo