Year: 2026
Type: article
Abstract: We present a deterministic discontinuous Galerkin (DG) finite-element solution of the Boltzmann equation, without moment-closure approximations, under a class of far-from-equilibrium deformations. Specifically, we consider affine flows which reduce the Boltzmann equation to a purely velocity-space problem for the reduced distribution function in a reduced velocity field. We solve the reduced equation using a tensor-product Lagrange DG discretization for four representative flows: simple shear, pressure shear, bi-directional shear, and a vortex flow. Our principal finding is that the velocity distribution is well-approximated by an anisotropic Gaussian throughout the evolution, despite the non-equilibrium conditions. Further, we show the evolution of the covariance tensor of the Gaussian distribution is equal to the inverse of the right Cauchy–Green tensor in the free-streaming limit without collisions. This prediction compares very well with the numerical solution at short times; at longer times, they grow apart, reflecting the influence of particle collisions.
Source: Physics of Fluids
DOI: 10.1063/5.0346853
Authors: Arnab Debnath, Timothy Breitzman, Kaushik Dayal
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7202367915
FWCI:
Cites:
Cited by:
Related to: