An energy-stable variable-step L1 scheme for time-fractional Navier–Stokes equations

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-06-15 DOI:10.1016/j.physd.2024.134264
Ruimin Gao , Dongfang Li , Yaoda Li , Yajun Yin
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Abstract

We propose a structure-preserving scheme and its error analysis for time-fractional Navier–Stokes equations (TFNSEs) with periodic boundary conditions. The equations are first rewritten as an equivalent system by eliminating the pressure explicitly. Then, the spatial and temporal discretization are done by the Fourier spectral method and variable-step L1 scheme, respectively. It is proved that the fully-discrete scheme is energy-stable and divergence-free. The energy is an asymptotically compatible one since it recovers the classical energy when α1. Moreover, optimal error estimates are presented very technically by the obtained boundedness of the numerical solutions and some Sobolev inequalities. To our knowledge, they are the first results of the construction and analysis of structure-preserving schemes for TFNSEs. Several interesting numerical examples are given to confirm the theoretical results at last.

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用于时分数纳维-斯托克斯方程的能量稳定且无发散的变步长 L1 方案
我们针对具有周期性边界条件的时间分数纳维-斯托克斯方程(TFNSE)提出了一种结构保留方案及其误差分析。首先,通过显式消除压力将方程改写为等效系统。然后,分别采用傅立叶谱法和变步长 L1 方案进行空间和时间离散化。研究证明,全离散方案是能量稳定且无发散的。能量是渐进兼容的,因为当 α→1 时,它恢复了经典能量。此外,通过数值解的有界性和一些索波列夫不等式,从技术上提出了最优误差估计。据我们所知,这是构建和分析 TFNSE 结构保留方案的首个成果。我们还给出了几个有趣的数值示例,以最终证实理论结果。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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