A unified IMEX Runge-Kutta approach for hyperbolic systems with multiscale relaxation

2017/01/16 by Sebastiano Boscarino, Lorenzo Pareschi, Boscarino, S. +3 · 3 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1701.04370

openalex publication_date 2017/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we consider the development of Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such systems the scaling depends on an additional parameter which modifies the nature of the asymptotic behavior which can be either hyperbolic or parabolic. Because of the multiple scalings, standard IMEX Runge-Kutta methods for hyperbolic systems with relaxation loose their efficiency and a different approach should be adopted to guarantee asymptotic preservation in stiff regimes. We show that the proposed approach is capable to capture the correct asymptotic limit of the system independently of the scaling used. Several numerical examples confirm our theoretical analysis.

Cited by

• Asymptotic preserving methods for the low mach limit in discrete velocity models approximating kinetic equations
• A structure-preserving semi-implicit four-split scheme for continuum mechanics
• Multi-Order Monte Carlo IMEX hierarchies for uncertainty quantification in multiscale hyperbolic systems

Related

• Implicit-Explicit Runge-Kutta schemes for hyperbolic systems with stiff relaxation and applications
• All-stages-implicit and strong-stability-preserving implicit-explicit Runge-Kutta time discretization schemes for hyperbolic systems with stiff relaxation terms
• Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation
• Uniform accuracy of implicit-explicit Runge-Kutta methods for linear hyperbolic relaxation systems
• Implicit-Explicit multistep methods for hyperbolic systems with\n multiscale relaxation