2012/10/17 by Sebastiano Boscarino, Philippe G. LeFloch, Boscarino, Sebastiano +3 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical methods for differential equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1210.4761
openalex publication_date 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study solutions to nonlinear hyperbolic systems with fully nonlinear\nrelaxation terms in the limit of, both, infinitely stiff relaxation and\narbitrary late time. In this limit, the dynamics is governed by effective\nsystems of parabolic type, with possibly degenerate and/or fully nonlinear\ndiffusion terms. For this class of problems, we develop here an\nimplicit-explicit method based on Runge-Kutta discretization in time, and we\nuse this method in order to investigate several examples of interest in\ncompressible fluid dynamics. Importantly, we impose here a realistic stability\ncondition on the time-step and we demonstrate that solutions in the\nhyperbolic-to-parabolic regime can be computed numerically with high robustness\nand accuracy, even in presence of fully nonlinear relaxation terms.\n