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Title: Invariant-Domain Preserving High-Order Time Stepping: II. IMEX Schemes
We consider high-order discretizations of a Cauchy problem where the evolution operator comprises a hyperbolic part and a parabolic part with diffusion and stiff relaxation terms. We propose a technique that makes every implicit-explicit (IMEX) time stepping scheme invariant-domain preserving and mass conservative. Following the ideas introduced in Part I on explicit Runge--Kutta schemes, the IMEX scheme is written in incremental form. At each stage, we first combine a low-order and a high-order hyperbolic update using a limiting operator, then we combine a low-order and a high-order parabolic update using another limiting operator. The proposed technique, which is agnostic to the space discretization, allows one to optimize the time step restrictions induced by the hyperbolic substep. To illustrate the proposed methodology, we derive four novel IMEX methods with optimal efficiency. All the implicit schemes are singly diagonal. One of them is A-stable and the other three are L-stable. The novel IMEX schemes are evaluated numerically on systems of stiff ordinary differential equations and nonlinear conservation equations.  more » « less
Award ID(s):
2110868
PAR ID:
10528788
Author(s) / Creator(s):
;
Publisher / Repository:
SIAM Journal on Scientific Computing
Date Published:
Journal Name:
SIAM Journal on Scientific Computing
Volume:
45
Issue:
5
ISSN:
1064-8275
Page Range / eLocation ID:
A2511 to A2538
Subject(s) / Keyword(s):
ime integration implicit-explicit time integration methods strong stability preserving methods conservation equations hyperbolic systems high-order method
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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