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G. Kitzler, J. Schöberl:
"A high order discontinuous Galerkin method for the Boltzmann Equation";
Talk: 25th FEM Symposium Chemnitz, TU Chemnitz; 2012-09-24 - 2012-09-26.

A high order discontinuous Galerkin method for the
Boltzmann Equation
Gerhard Kitzler1 Joachim Sch oberl2
The Boltzmann equation is a statistical model for gases. The density distribution
function f(t; x; v) describes the propability to nd a particle at time t near the spatial
position x and which has the velocity close to v. The time evolution of f is given by
the Boltzmann equation. The collision of particles is formulated in terms of the collision
operator Q(f) which is local in x and t. We perform a Petrov-Galerkin method in the
spatial domain
and velocity domain R3. In the v domain the solution is expanded as a
sum over multivariate Lagrange polynomials lj(x) times an appropriate gaussian peak. In
space we discretize by a high order discontinuous Galerkin method with natural upwind

uxes.
Due to this expansion, the Boltzmann transport operator decouples when using Gau -
Hermite integration rules of appropriate order into transport operators for the individual
components.
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