- Do Finite Volume Methods Need a Mesh? (2001)
- In this article, finite volume discretizations of hyperbolic conservation laws are considered, where the usual triangulation is replaced of unity on the computational domain.
- Rigorous Navier-Stokes Limit of the Lattice Boltzmann Equation (2001)
- Here we riqorously investigate the diffusive limit of a velocity-discrete Boltzmann equation which is used in the lattice Boltzmann method to construct approximate solutions of the incompressible Navier-Stokes equation.
- A Hybrid Simulation Method for Radivative Transfer Equations (2001)
- We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role.
- Maximum Entropy Moment Systems and Galilean Invariance (2001)
- In this article, we investigate the maximum entropy moment closure in gas dynamics. We show that the usual choice of polynomial weight functions may lead to hyperbolic systems with an unpleasant state space: equilibrium states are boundary points with possibly singular fluxes. In order to avoid singularities, the necessary arises to find weight functions which growing sub-quadratically at infinity. Unfortunately, this requirement leads to a conflict with Galilean invariance of the moment systems because we can show that rotational and translational invariant, finite dimensional function spaces necessarily consist of polynomials.