Conveners
Asymptotic Properties of IMEX Runge–Kutta Methods with Application to Stiff Kinetic Equations
- Sebastiano Boscarino (University of Catania)
Description
In this work, we investigate IMEX Runge–Kutta schemes of type I and II applied to stiff kinetic equations, with the goal of capturing the compressible Navier–Stokes limit without resolving the small scales associated with the Knudsen number ε. In particular, we focus on the ES-BGK model, a variant of the classical BGK one, which yields satisfactory transport coefficients at the first-order correction in ε, including the correct Prandtl number at the Navier–Stokes level.
The main objective is to extend the results obtained for IMEX-RK schemes in Boscarino–Pareschi (2017), which were originally developed and analyzed for a specific class of hyperbolic relaxation systems. In that work, an asymptotic expansion up to order O(ε) was carried out for IMEX-RK methods of type I and II. Here, we perform a similar asymptotic analysis in the context of the ES-BGK model.
We analyze the asymptotic behavior of IMEX-RK schemes of type I and II applied to the ES-BGK equations and prove that, for small values of ε, they are able to capture the compressible Navier–Stokes limit without resolving the small parameter ε, thereby yielding consistent limiting numerical schemes for the corresponding compressible Navier–Stokes equations.
