Research

Our work on rarefied gas dynamics is published openly. Preprints are on arXiv; peer-reviewed versions are linked as they appear.

• Wigner–Eckart Factorization of the Polyatomic Boltzmann Collision Operator

  Preprint

  Torsten Keßler, Bas W. T. Gieling, René R. Hiemstra, Michael R. A. Abdelmalik

  Internal energies are invariant under spatial rotations, so the $SO(3)$ reduction survives the Borgnakke–Larsen energy exchange and carries the Wigner–Eckart factorization over to polyatomic gases. The twelve-dimensional collision integral reduces to nine dimensions, split into a sparse geometric tensor and a dense physical one, while preserving the collision invariants and the exchange between translational and internal energy. Validated against the monatomic limit, Landau–Teller relaxation, and transport data for nitrogen, carbon monoxide and hydrogen.

  arXiv:2608.29825 →Read the blog post →

• Analysis of Moment Closures Using φ-Divergences for Rarefied Dynamics with Binary Collisions and Their Galerkin Discretizations

  Preprint

  Michael R. A. Abdelmalik, Irene M. Gamba, Torsten Keßler, Sergej Rjasanow

  Moment closures built on φ-divergences stay well-posed where the classical entropy closure fails. Pairing each divergence with a matching approximate product restores exact entropy dissipation, and an entropy-stable discontinuous Galerkin discretization solves for steady state directly.

  arXiv:2608.03640 →Read the blog post →

• Wigner–Eckart Factorization of the Spectral Boltzmann Collision Operator

  Preprint

  René R. Hiemstra, Torsten Keßler, Michael R. A. Abdelmalik

  Conservation of angular momentum collapses the spectral Boltzmann collision operator into a sparse geometric factor and a small dense physical factor. The factorization is exact and reduces storage by three orders of magnitude at practical resolutions.

  arXiv:2605.28475 →Read the blog post →