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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


 x_i^{1/2} = x_i^{0} + \frac{1}{2} u_i^{0} ~ \Delta t (18.2-3)

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


 \Delta t = \min(\Delta t_{\rm conv}, ~\Delta t_{\rm diff}, ~\Delta t_{\rm mix}) (18.2-4)

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


 x_i^{1} = x_i^{1/2} + \Delta t \left ( u_i^{1/2} - \frac{1}{... ...{i} \sqrt{ \frac{2 \mu_t}{\rho \Delta t {\rm Sc}_t} } \right ) (18.2-5)

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


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Up: 18.2 Composition PDF Transport
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