2D Coupled LBM-DEM technique method

Hello everybody !!!

I used the 2D coupled DEM-LBM method for simulate the interaction between a fluid flow and grains (grains mving the fluid) in an immersed granular media. I have a technique question. I’d like to have your opinion on the best technique to use to set the parameters of LBM simulation .

First technique :

  • Fixed dimensionless relaxation time " tau " ( 0.5 < tau < 1.5)
  • Fixed lattice grid spacing " dx" (m) (depending on the resolution LBM)
  • Fixed kinematic fluid viscosity (in SI units: m2/s) “nu”
  • Comptute LB timestep " dt_LB " (s) dt_LB = dx * dx * ( tau - 0.5 ) / ( 3 * nu)
  • Compute lattice speed " C" (m/s) : C = dx / dt_LB

Second tehnique :

  • Fixed lattice speed " C" (m/s)
  • Fixed lattice grid spacing " dx" (m) ( depending on the resolution LBM)
  • Fixed kinematic fluid viscosity (in SI units : m2/s) “nu”
  • Comptute LB timestep " dt_LB " (m): dt_LB = dx / C
  • Compute dimensionless relaxation time " tau " ( 0.5 < tau < 1.5) : tau = (3 * nu) / (C * dx) + 0.5

Then I would like to vary the kinematic viscosity of the fluid, for different values ​​of the fluid velocity imposed (Von Neumann Boundary conditon at Inlet U_inlet # 0) . In outlet , i was Imposed dirichlet pressure boundary conditions (rho_out = 1.0).

Thank you for your help

Best regards and be blessed