Unconditional stability for multistep ImEx schemes: Practice

JOURNAL OF COMPUTATIONAL PHYSICS

卷:376

Article

Seibold, Benjamin¹  Shirokoff, David²  Zhou, Dong³ 

[1] Temple Univ, Dept Math, 1801 N Broad St, Philadelphia, PA 19122 USA

[2] New Jersey Inst Technol, Dept Math Sci, University Heights Newar, NJ 07102 USA

[3] Calif State Univ Los Angeles, Dept Math, 5151 State Univ Dr Los Angeles, Los Angeles, CA 90032 USA

关键词: Linear multistep ImEx;    Unconditional stability;    ImEx stability;    High order time stepping;    Semi-implicit backward differentiation;   

DOI  :  10.1016/j.jcp.2018.09.044

来源: Elsevier

【 摘 要 】

This paper focuses on the question of how unconditional stability can be achieved via multistep ImEx schemes, in practice problems where both the implicit and explicit terms are allowed to be stiff. For a class of new ImEx multistep schemes that involve a free parameter, strategies are presented on how to choose the ImEx splitting and the time stepping parameter, so that unconditional stability is achieved under the smallest approximation errors. These strategies are based on recently developed stability concepts, which also provide novel insights into the limitations of existing semi-implicit backward differentiation formulas (SBDF). For instance, the new strategies enable higher order time stepping that is not otherwise possible with SBDF. With specific applications in nonlinear diffusion problems and incompressible channel flows, it is demonstrated how the unconditional stability property can be leveraged to efficiently solve stiff nonlinear or nonlocal problems without the need to solve nonlinear or nonlocal problems implicitly. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free