Shanchen two-phase lbm model clarification

Lattice Boltzmann Method LBM: Algorithms
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I am working on both nanofluid enhanced heat transfer and two-phase (nanofluid/oil) flow in porous media using ShanChen LBM model.I have calculated the physical properties of nanofluid via the averaged-volume fraction method and for pore scale analysis, I have capture the fluid-fluid interaction but still have challenges on the following:

  1. what are the parameters to vary when doing grid test analysis in LBM cos I kept getting different Nusselt values at varying lattice sizes despite using different lattices (60x60,80x80,100x100,120x120,140x140,160x160)
  2. After calculating nanofluid viscosity, thermal conductivity, thermal expansion etc via averaged-volume fraction approach, how then is it captured or converted to lattice values for simulation in non-dimensional form?
  3. In using ShanChen LBM model for pore-scale porous media nanofluid/oil flow analysis, how is the liquid-solid (adhesion) added and how can I introduce nanoparticle effect to the flow.
  4. I am using Matlab for coding please.