Unconditional stability for multistep ImEx schemes: Practice
Unconditional stability for multistep ImEx schemes: Practice
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DOI：
10.1016/j.jcp.2018.09.044
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Benjamin Seibold;D. Shirokoff;Dong Zhou
中科院分区：
文献类型：
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作者：
Benjamin Seibold;D. Shirokoff;Dong Zhou
本文重点讨论如何通过多步 ImEx 方案实现无条件稳定性的问题，在实际问题中，隐式项和显式项都允许是刚性的。针对一类涉及自由参数的新型ImEx多步方案，提出了如何选择ImEx分裂和时间步长参数的策略，以便在最小逼近误差下实现无条件稳定性。这些策略基于最近开发的稳定性概念，这也为现有半隐式后向微分公式（SBDF）的局限性提供了新颖的见解。例如，新策略可以实现更高阶的时间步进，而这在 SBDF 中是不可能实现的。通过在非线性扩散问题和不可压缩通道流中的具体应用，证明了如何利用无条件稳定性属性来有效地解决刚性非线性或非局部问题，而无需隐式解决非线性或非局部问题。
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.