AI 中文总结
本研究针对不可压缩流动，提出至多九阶精度的相容分裂隐式-显式多步方法，建立其稳定性理论，证明相关格式可通过参数选取满足可控性要求，数值实验支撑结论。
AI 中文摘要
本研究针对不可压缩Navier-Stokes方程，基于经典的相容分裂技术，提出了高阶解耦隐式-显式线性多步（IELM）方法的简洁统一稳定性理论。借助近期的半生成函数方法与全局离散能量分析，若相关隐式-显式可控性强度大于√2/2（该常数由Stokes压力估计确定），则可建立相容分裂IELM方法关于ℓ^∞(H^1)∩ℓ^2(H^2)范数的无条件稳定性。研究表明，β参数化的GBDF-k（2≤k≤5）格式与γ参数化的SIELM-k（2≤k≤9）格式，可通过选取合适参数满足上述隐式-显式可控性强度要求，从而理论上保持对应相容分裂IELM方法的无条件稳定性。数值实验也被纳入以支撑该理论。
英文摘要
This work presents a concise, unified stability theory of high-order decoupled \lan{implicit-explicit linear multistep (IELM)} methods based on the well-known consistent splitting technique for the incompressible Navier-Stokes equation. With the help of the recent semi-generating function approach and the global discrete energy analysis, one can establish the unconditional stability of a consistent splitting IELM method with respect to the $\ell^{\infty}(H^1)\cap \ell^{2}(H^2)$ norm if the associated implicit-explicit controllability intensity is larger than $\sqrt{2}/2$, a constant determined by the Stokes pressure estimate. It is shown that the $β$-parameterized GBDF-$\rmk$ ($2\le \rmk\le5$) schemes and $γ$-parameterized SIELM-$\rmk$ ($2\le \rmk\le9$) schemes can fulfill this requirement of implicit-explicit controllability intensity by choosing proper parameters so that they can theoretically maintain the unconditional stability of the associated consistent splitting IELM methods. Numerical experiments are also included to support our theory.
Comments22 pages, 30 figures
