11.3.1 Particle Convection

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

where

$x_i$	=	particle position vector
$u_i$	=	Favre mean fluid-velocity vector at the particle position
$\Delta t$	=	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

where

$\Delta t_{\rm conv}$	=	convection number $\times$ $\Delta x$ / (cell fluid velocity)
$\Delta t_{\rm diff}$	=	diffusion number $\times$ $(\Delta x)^2$ / (cell turbulent diffusivity)
$\Delta t_{\rm mix}$	=	mixing number $\times$ turbulent time scale
$\Delta x$	=	characteristic cell length = $volume^{1/D}$ where $D$ 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

where

$\rho$	=	mean cell fluid density
$u_i$	=	mean fluid-velocity vector at the particle position
$\mu_t$	=	turbulent viscosity
Sc $_t$	=	turbulent Schmidt number
$\xi_i$	=	standardized normal random vector