LBM for blood flow

i am doing simulation of blood flow using LBM. I consider blood as a non-newtonian fluid in rigid wall tube and use careau-yasuda model for viscosity calculation. for viscosity calculation i need tau and in calculation of tau i need shear rate and for shear rate calculation tau is required.simply want to say i have coupled equation, i cant understand what to do.If some-one can help then please tell how can i start??? For my work i am using the referance of paper “Lattice Boltmann simulation of steady non-newtonian blood flow in a 3D generic stenosis case” by Dinan Wang and Jorg Bernsdorf.


e.g. have a look at those articles:

  • Ashrafizaadeh, Bakhshaei. A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations. Computers and Mathematics with Applications (2009)
  • Vikhansky. Lattice-Boltzmann method for yield-stress liquids. J. Non-Newtonian Fluid Mech. 19 (2008)
  • Boyd, Buick. Comparison of Newtonian and non-Newtonian flows in a two-dimensional carotid artery model using the lattice Boltzmann method. Phys. Med. Biol. 52 (2007)
  • Gabbanelli, Drazer, Koplik. Lattice Boltzmann method for non-Newtonian (power-law) fluids. Phys. Rev. E 72 (2005)

You can solve the problem using implicit methods. By the way, you do not need tau for the computation of the shear rate, if you use a FD scheme (which is of course not the LBM spirit).


Hi everyone,
can you tell what should be the density of blood in lattice units??If the viscosity is 0.16Pa s for 40x40 grid and 6000 time step then i calculated the in lattice units its value is 52.910 as nu_lb = (nu_phyx( del_t))/(del_x)^2. I use del_x= 0.00000756 because the physical length pf channel is 0.0062m.I found the value of tau=159.23 as tau=(3xnu_lb/density) +0.5. I used density =1.As the value of tau I found is very large is it fissible???this value of tau i calculated is for viscosity of blood at zero shear rate.

Please read this thread.

hi, working with the non Newtonian fluid in axisymmetric geometry?

first : the relaxation time tau is a function of the viscosity, and the viscosity in the non newtonian fluids is not cst but a function of the velocity gradiants
then you will have a new tau which is a function of velocity gradiants.