DSM 4 - 16 Collision sampling in a cell The ‘primitive’...

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Unformatted text preview: 16 Collision sampling in a cell: The ‘primitive’ scheme i = 1 j = i + 1 P ij = ∆ t σ ij(sim) g ij / V cell α < P ij ) 2 sin( sin ) 2 cos( sin cos cos 1 sin 2 1 cos 2 2 2 1 πα θ = πα θ = θ = θ- = θ α- = θ z y x n n n j = j + 1 i = i + 1 j < N cell Does collision between molecules i and j occur? no yes yes yes no no Go to the next cell Calculation of the collision probability Calculation of velocities after collision Are there other pairs of molecules in the cell? Disadvantage of the primitive scheme: Number of operation ~ N cell 2 In real DSMC simulations, more efficient schemes for collision sampling are used, e.g. the NTC scheme by Bird i < N cell- 1 P( α < P ij ) = P ij 17 X ** = ( r 1 ** , V 1 ** ,…, r N ** , V N ** ) X ** → X n +1 • Implementation of boundary conditions depends on the specifics of the flow problem under consideration. Typically, conditions on flow boundaries is the most specific part of the problem • Examples of boundary conditions – Impermeable boundary (e.g. solid surface): rebound of molecules from the wall – Permeable boundary between the computational domain and the reservoir of molecules (e.g. Earth atmosphere) : free motion of molecules through boundary reproducing inflow/outflow fluxes Stage III. Implementation of boundary conditions Computational domain Reservoir (Earth atmosphere) Flow over a re-entry vehicle in Earth atmosphere 18...
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This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

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DSM 4 - 16 Collision sampling in a cell The ‘primitive’...

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