Hi Guys, how to comments the numerical accuracy of the transport properties which are computed by Lattice Boltzmann method, such as the effective diffusivity. I find the effective diffusivity is highly impacted by the selected relaxation time of the LB- SRT model at D3Q7 velocity space though they can be validated well in simple structures. Whether existence of any theoretical error analyses as like the LB-BGK model for the momentum equation, which shows the best choice of the relaxation time is 1.0 to recover the no-slip boundary conditions. Thank you! Wish all good days.
I did not find any theoretical assessment of the error for computing average transport parameters with LBM. The usual heuristic procedure, like in any numerical analysis, is to compare against some known analytical solution or against direct numerical simulation. I found it useful to perform sensitivity analysis of the relaxation parameter to determine a range where the sensitivity coefficient is low. Then the value of the sensitivity coefficient can be used to assess the relative error.
I usually choose 1 for the relaxation time, and the relaxation time suggested by Prof. Moran Wang ranges from 0.5 to 2. A paper also compares the error between SRT and MRT for diffusion coefficient: A comparative study on the lattice Boltzmann models for predicting effective diffusivity of porous media.