2016/12/30 by David Coulette, Emmanuel Franck, Coulette, David +7 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1612.09422
openalex publication_date 2016/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a high order scheme for approximating kinetic equations with stiff relaxation. The objective is to provide efficient methods for solving the underlying system of conservation laws. The construction is based on several ingredients: (i) a high order implicit upwind Discontinuous Galerkin approximation of the kinetic equations with easy-to-solve triangular linear systems; (ii) a second order asymptotic-preserving time integration based on symmetry arguments; (iii) a palindromic composition of the second order method for achieving higher orders in time. The method is then tested at orders 2, 4 and 6. It is asymptotic-preserving with respect to the stiff relaxation and accepts high CFL numbers.