
A spatially secondorderaccurate Lagrangian method is used in FLUENT, consisting of two steps. At the first convection step, particles are advanced to a new position
where
=  particle position vector  
=  Favre mean fluidvelocity vector at the particle position  
=  particle time step 
For unsteady flows, the particle time step is the physical time step. For steadystate flows, local time steps are calculated for each cell as
where
=  convection number / (cell fluid velocity)  
=  diffusion number / (cell turbulent diffusivity)  
=  mixing number turbulent time scale  
=  characteristic cell length = where is the problem dimension 
After the first convection step, all other subprocesses, including diffusion and reaction are treated. Finally, the second convection step is calculated as
where
=  mean cell fluid density  
=  mean fluidvelocity vector at the particle position  
=  turbulent viscosity  
Sc  =  turbulent Schmidt number 
=  standardized normal random vector 