User:
LBM equation in the relaxation approximation
Equation 
In the relaxation approximation, it is assumed that the distribution
$\displaystyle\frac{df_i}{dt}=-\displaystyle\frac{f_i-f_i^{eq}}{\tau}$
which has in the discrete approximation the equation
| $f_i(\vec{x}+c\vec{e_i}\delta t,t+\delta t)=f_i(\vec{x},t)+\displaystyle\frac{1}{\tau}(f_i^{eq}(\vec{x},t)-f_i(\vec{x},t))\delta t$ |
where the term of the differences in the distribution functions represents the collisions.
ID:(8489, 0)
Velocidades Microscopicas
Description
Las velocidades microscópicas según las dimensiones son el numero de dimensiones (D1, D2, D3) y el número de puntos (Q3 - para D1, Q9 - para D2, Q15 o Q19 - para D3):
| Modelo | Velocidades | Index |
| 1DQ3 | (0) | i=0 |
| ' | (s) | i=1, 2 |
| 2DQ9 | (0,0) | i=0 |
| ' | (s,0), (0,s) | i=1,...,4 |
| ' | (s,s) | i=5,...,8 |
| 3DQ15 | (0,0,0) | i=0 |
| ' | (s,0,0), (0,s,0), (0,0,s) | i=1,...,6 |
| ' | (s,s,s) | i=7,...,14 |
| 3DQ19 | (0,0,0) | i=0 |
| ' | (s,0,0), (0,s,0), (0,0,s) | i=1,...,6 |
| ' | (s,s,0), (s,0,s), (0,s,s) | i=7,...,18 |
donde los $s$ puede asumir los valores -1 y 1.
ID:(8491, 0)
Distribution in Balance (Gas of Particles)
Equation
The equilibrium distribution can be approximated by a distribution of Maxwell Boltzmann
| $f_i^{eq}=\displaystyle\frac{m}{2\pi kT}e^{-m|c\vec{e}_i-\vec{u}|^2/2kT}$ |
Where
ID:(8490, 0)