(2.79) |

In this section we assume that the symmetric part is isotropic

(2.80) |

This is a special case of the diffusion approximation [21, p.49] which will be explained in more detail for the MAXWELL distribution in Section 2.3.3.1 on page . By using this assumption the statistical average of the tensor can be written as

(2.81) |

For symmetry reasons all elements outside the trace vanish. For instance, the element

(2.82) |

evaluates to zero because of the integral

Since the distribution function is assumed to be isotropic, the integrals determining the elements of the trace all evaluate to a common value

(2.84) |

The value of can be evaluated by the simple transformation

(2.85) | ||

(2.86) | ||

(2.87) |

Therefore, the statistical averages of the tensors are diagonal with all diagonal elements being equal:

By inserting eqns. (2.88) and (2.89) into eqns. (2.76) to (2.78) one gets

Note that the divergences of the tensors simplify to gradients of scalars.