Discretization of Boltzmann equation

[Yuji]

Hi all,
I often see that Boltzmann equation(only velocity space is discretised) is discretised by spatial first-order upstream difference scheme and temporal first-order Euler difference scheme that is Lattice boltzmann equation. In my understanding and in brief, high oder schemes(e.g. compact difference schemes) are often used in order to capture high wave number.
Why are not other shceme(except spatial first-order upstream difference scheme and temporal first-order Euler difference scheme) used in Botzmann equation (only velocity space is discretised) ?

[mathias]

Such approaches exists for LBM, see e.g. the once by Domikik Wilde. They are not as local as the stnadward LBM and therefore not as scalable on high perfarmance computers.

[Author]

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