(2.70) |

which is commonly termed as relaxation time approximation [14, p.144]. This equation implies that the perturbed distribution function will relax exponentially to the equilibrium function with one time constant when the perturbing field is removed. A discussion on the validity of this approximation is given in [20, p.139].

The equilibrium distribution function is a symmetric function. Since the even weight functions are symmetric in and the odd weight functions are anti-symmetric in , only the even moments of the equilibrium distribution function will be non-zero whereas the odd moments will vanish

(2.71) | ||||

(2.72) |

Applying the relaxation time approximation and inserting the calculated gradients from the previous section into eqns. (2.53) and (2.54) leads to the equation set

where , , , , are the relaxation times for momentum, energy, energy flux density, kurtosis, and kurtosis flux density, respectively.