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Journal Articles SIAM Journal on Scientific Computing Year : 2023

Invariant-Domain Preserving High-Order Time Stepping: II. IMEX Schemes

Abstract

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 invariantdomain 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 to optimize the time step restrictions induced by the hyperbolic sub-step. 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 a stiff ODE system and a scalar nonlinear conservation equation.
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Dates and versions

hal-03703035 , version 1 (23-06-2022)

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Alexandre Ern, Jean-Luc Guermond. Invariant-Domain Preserving High-Order Time Stepping: II. IMEX Schemes. SIAM Journal on Scientific Computing, 2023, 45 (5), pp.A2511-A2538. ⟨10.1137/22M1505025⟩. ⟨hal-03703035⟩
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