HIGH-ORDER ASYMPTOTIC-PRESERVING METHODS FOR FULLY NONLINEAR RELAXATION PROBLEMS

被引：43

作者：

Boscarino, Sebastiano ^{[1
]}

Lefloch, Philippe G. ^{[2
,3
]}

Russo, Giovanni ^{[1
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, I-95125 Catania, Italy

[2] Univ Paris 06, Lab Jacques Louis Lions, F-75252 Paris, France

[3] Univ Paris 06, CNRS, F-75252 Paris, France

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2014年 / 36卷 / 02期

关键词：

nonlinear hyperbolic system; hyperbolic-to-parabolic regime; high-order discretization; late-time limit; stiff relaxation; RUNGE-KUTTA SCHEMES; HYPERBOLIC SYSTEMS; CONSERVATION-LAWS; KINETIC-EQUATIONS; NUMERICAL SCHEMES;

D O I：

10.1137/120893136

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic-type which may contain degenerate and/or fully nonlinear diffusion terms. For this class of problems, we develop an implicit-explicit method based on Runge-Kutta discretization in time, and we apply this method to the investigation of several examples of interest in fluid dynamics. Importantly, we impose here a realistic stability condition on the time step and we demonstrate that solutions in the hyperbolic-to-parabolic regime can be computed numerically with high robustness and accuracy, even in the presence of fully nonlinear relaxation.

引用

页码：A377 / A395

页数：19

共 28 条

[21] ASYMPTOTIC-PRESERVING PROJECTIVE INTEGRATION SCHEMES FOR KINETIC EQUATIONS IN THE DIFFUSION LIMIT [J].