2025/12/03 by Domenico Caparello, Caparello, Domenico, Tommaso Tenna +1
Engineering · Mathematics · Physics and Astronomy · #65L04 #65M55 #76P05 #82B40 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2512.03586
openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
In this paper, we propose a high-order domain decomposition method for the ES-BGK model of the Boltzmann equation, which dynamically detects regions of equilibrium and non-equilibrium. Our implementation automatically switches between Euler equations in regions where the fluid is at equilibrium, and the ES-BGK model elsewhere. The main challenge addressed in this work is the development of a coupled strategy between the macroscopic and the kinetic solvers, which preserves the overall temporal order of accuracy of the scheme. A coupled IMEX method is introduced across decomposed subdomains and solvers. This approach is based on a coupled IMEX method and allows high accuracy and computational efficiency. Several numerical simulations in two space dimensions are performed, in order to validate the robustness of our approach and the expected temporal high-order convergence.