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June 2, 2011, 17:17 
maxwellianThermal wall interaction

#1 
Member
Daniel
Join Date: Jul 2010
Location: California
Posts: 39
Rep Power: 8 
could someone explain the final expression for the reflected velocity vector in the diffuse wall interaction model in dsmcFOAM. It looks like it's supposed to be the most probable molecular thermal speed times a random vector, but the most probable molecular thermal speed is (2kT/m)^1/2. Looks like they left out the 2??? Thanks.
00109 U = 00110 sqrt(CloudType::kb*T/mass) 00111 *( 00112 rndGen.GaussNormal()*tw1 00113 + rndGen.GaussNormal()*tw2 00114  sqrt(2.0*log(max(1  rndGen.scalar01(), VSMALL)))*nw 00115 ); 

June 12, 2011, 10:25 

#2 
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Fabian
Join Date: Jan 2010
Posts: 27
Rep Power: 8 
/E: Problem 2 is solved. Multiplication with the inverse of the factor scales a gaussNormaldist exaktly to the Maxwelliandist.
I was also thinking about this these days and I am also not so sure about it, but I have some thoughts, we can discuss over: 1. The first expression equals sqrt(RT), which is the inverse of the factor of the Maxwellian distribution, which I think the name of this model comes from. 2. I THINK there is a try to implement a randomly generated velocity based on the Maxwellian dist. But there are some problems: 2a. The first two expressions based on gaussNormal is a N(0,1)dist with a factor sqrt(RT), but it should be a N(0, sqrt(RT))dist in my opinion. 2b. The last expression is in fact also the gaussNormaldist. This is the formula you can get gaussNormal numbers, BUT there is an pi missing and also the same problem as in 2a (my prof helped me with that). 2c. The same problems took place at the initialisemethod in dsmcCloud.C. Perhaps you can have a look. The only difference is, that there is no thing like the 3rd expression... 3. I have found these formulas in Shen's excellente book "Rarefied gas dynamics: fundamentals, simulations and micro flows" from 2005 beginning on page 135. But to be honest: I didnt get all the points, I think... So perhaps, we could figure out something together... Last edited by gautcho; June 14, 2011 at 09:18. 

Tags 
diffuse, dsmcfoam, maxwellianthermal, wall interaction 
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