maxwellianThermal wall interaction
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 );
/E: Problem 2 is solved. Multiplication with the inverse of the factor scales a gaussNormal-dist exaktly to the Maxwellian-dist.
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 gaussNormal-dist. 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 initialise-method 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...
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