Invited Lecture
IMEX multistep method for hyperbolic systems with relaxation
Università degli Studi di Ferrara, Italy
Abstract
In this talk, we consider the development of Implicit-Explicit (IMEX) Multistep time integrators for hyperbolic systems with relaxation. More speci cally, we consider the case in which the transport and the relaxation part of such systems have different time and space scales. The consequence is that the nature of the asymptotic limit can differ, passing from an hyperbolic to a parabolic character. From the computational point of view, this causes many drawbacks that standard time integrators, even implicit ones, are not able to handle: loss of efficiency and loss of capability in describing the limit regime. In this work, we construct highly stable numerical methods which describe all the different regimes with high accuracy in time and space that are able to capture the correct asymptotic limit. Several numerical examples confi rm the consistency and linear stability analysis and show that the proposed methods outperform existing ones.
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