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8 June 2007

30 June 2009

Gridless DSMC

Spencer Olson

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.

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Outline

Background

Algorithm Overview

Test Cases

Low velocity flow

Hypersonic flow

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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

Dense

Rarefied

Free-Particle

Limit

Inviscid

Limit

Discrete Particle

Model

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Continuous Solution?

: 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

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Direct Simulation of gas dynamics using Monte Carlo

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Direct Simulation of gas dynamics using Monte Carlo

Grid

Truncate collision integral

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Direct Simulation of gas dynamics using Monte Carlo

Grid

Ansatz: Collisional processes separable from particle motion.

CollideTransport

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Grid Mismatch: Coarse Grid

Grid

Captures only low-density dynamics well

Allows non-probable collisions

Density variations could be due to:

Shockwaves

Nonfree particle systems

Transient processes

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Grid Mismatch: Fine Grid

Grid

Density variations could be due to:

Shockwaves

Nonfree particle systems

Transient processes

Captures only high-density dynamics well

Wastes memory resources

Thermally isolates particles that should be allowed to collide

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Particle Method of Choice: DSMC

Direct Simulation of gas dynamics using Monte Carlo (DSMC)

Algorithm:

Collide

Sort (gridless)

Update/Sample macroscopic gas quantities

Move (integrate)

Apply Boundary Conditions (reflections, absorption,etc.)

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Simple Gridless Case: Binary Sort/Search Algorithm

NOHFMJL

CEG IDKBA

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Binary Sort/Search Algorithm

B

AC

D

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IK

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MO

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NOHFMJ

CEG IDKBA

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Binary Sort/Search Algorithm

B

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CEG IDKBA

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Binary Sort/Search Algorithm

B

AC

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CEG

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Binary Sort/Search Algorithm

B

AC

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J

IK

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MO

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G

Execution time:

Sort:

Search: (averaged over all trees)