Modeling and numerical approximation of two-phase incompressible flows by a phase-field approach
Modeling and numerical approximation of two-phase incompressible flows by a phase-field approach
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DOI：
10.1142/9789814360906_0003
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Jie Shen;J. Shen
中科院分区：
文献类型：
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作者：
Jie Shen;J. Shen
我们在本文中提出了一种关于如何为 Allen-Cahn 或 Cahn-Hilliard Navier-Stokes 系统设计简单、高效和能量稳定的时间离散方案的统一方法，该系统对具有匹配或不匹配密度的两相不可压缩流进行建模。特别强调设计方案只需要在每个时间步求解线性系统，同时满足模拟连续能量定律的离散能量定律。我们以弱公式构建时间离散化方案，以便它们可以与任何一致的伽辽金型空间离散化方案（例如有限元方法和谱/谱元方法）一起使用。
We present in this note a unified approach on how to design simple, efficient and energy stable time discretization schemes for the Allen-Cahn or Cahn-Hilliard Navier-Stokes system which models twophase incompressible flows with matching or non-matching density. Special emphasis is placed on designing schemes which only require solving linear systems at each time step while satisfy discrete energy laws that mimic the continuous energy laws. We construct the time discretization schemes in weak formulations so that they can be used with any consistent Galerkin type spacial discretization schemes such as finite element methods and spectral/spectral-element methods.