## 18.2.2 Particle Convection

A spatially second-order-accurate Lagrangian method is used in FLUENT, consisting of two steps. At the first convection step, particles are advanced to a new position

 (18.2-3)

where

 = particle position vector = Favre mean fluid-velocity vector at the particle position = particle time step

For unsteady flows, the particle time step is the physical time step. For steady-state flows, local time steps are calculated for each cell as

 (18.2-4)

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 sub-processes, including diffusion and reaction are treated. Finally, the second convection step is calculated as

 (18.2-5)

where

 = mean cell fluid density = mean fluid-velocity vector at the particle position = turbulent viscosity Sc = turbulent Schmidt number = standardized normal random vector

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