Reference for strain rate tensor prefactor in powerLawBGKdynamics

[guojuw]

Dear OLB developers:

From the file “src/dynamics/powerLawBGKdynamics.hh” line 57 and 58:
T pre2 = pow(descriptors::invCs2<T,DESCRIPTOR>()/2.* omega0/rho,2.); // strain rate tensor prefactor
T gamma = sqrt(2.*pre2*PiNeqNormSqr(cell)); // shear rate

I was pretty confused about the determination of shear rate gamma from the strain rate vector pi. Do you have any reference about the prefactor pre2?

From the references you provided at the beginning of the script:
/** \file
* BGK Dynamics with adjusted omega — generic implementation.
* Strain rate similar to “J.Boyd, J. Buick and S.Green: A second-order accurate lattice Boltzmann non-Newtonian flow model”
* Power Law similar to “Huidan Yu, Sharath S. Girimaji, Li-Shi Luo – DNS and LES of decaying isotropic turbulence with and without frame rotation using lattice Boltzmann method”
*/

I cannot see any formulation about this strain rate tensor prefactor.

Regards,
Junwei Guo

[Davide Dapelo]

Dear Junwei,

pre2 is just a multiplicative constant, which is calculated before for the sake of readability. The code lines quoted by Junwei are the implementation of Eqq. 13-14-15 in Boyd et al. (2006). Differences in multiplicative factors are due to different definitions of shear rate(see Eqq 12 and 14 in the cited article: in our code, the 2 factor is not present), different way of reporting the sound velocity (the cited article directly reports its numerical value sqrt(3), while the code adopts a more general notation), and different ways of treating density (in the cited article, everything is divided by density, which is striped out of the equations in this way, while the code keeps it in the passages).

Best wishes,
Davide

[guojuw]

Dear Davide,

Great thanks for your detailed explanation.
I think the paper by Chai et al. (2011) is more clear. The pi in openlb stands for the second order moment of nonequilibrium distribution (the summation part of eq.(18) in Chai et al. (2011)). And your prefactor ‘pre2’ is the square of the prefactor before the summation part of eq.(18). Other formulation in your codes are consistent with eq.(1-4).

Thanks again.
Regards,
Junwei Guo

Chai2011 – Multiple Relaxation Time Lattice Boltzmann Model for Generalized Newtonian Fluid Flows.pdf

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