Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation
For computational scientists solving kinetic equations, this method offers an efficient, high-order, and asymptotic-preserving approach that handles stiff relaxation.
The paper presents a high-order numerical scheme for kinetic equations with stiff relaxation, achieving up to 6th order accuracy while preserving asymptotic behavior and allowing high CFL numbers.
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.