Simulation of chemical Reaction using LBM

Hi every one

I have a flow containing reacting chemical species can be modelled within LBM.

I have a good background in LBM for fluid flow but no idea about chemical reaction. Who can help me to accomplish this code?

To be specific, here is a simple problem:

  1. A cubic simulation cell Lx=Ly=Lz=L

  2. Periodic boundary conditions along x,y,z

  3. A solid sphere of radius R=L/4 at the center (x=L/2, y=L/2, z=L/2)

  4. A gas enters from the bottom (z=0) with constant velocity: v(x,y, z=0)=v_0 for all x,y

  5. At the entrance (z=0) two spatially separated reacting species also enter the channel. This means:

C_A(x,y,0)=C_1 for x<L/2 for all times t

C_A(x,y,0)=0 for x>L/2 for all times t


C_B(x,y,0)=0 for x<L/2 for all times t

C_B(x,y,0)=C_2 for x>L/2 for all times t

At time t=0 there is no chemical species within the simulation cell. A and B undergo chemical reaction with oneanother with a rate k_AB.

I have purposely left out some important ingredients which are necessary to make the problem statement complete.