期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 349, 期 -, 页码 701-721出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2019.02.041
关键词
Stabilized finite element methods; Variational multiscale; Dynamic subscales; Term-by-term stabilization
资金
- Chilean Council for Scientific and Technological Research through the project CONICYT-FONDECYT [11160160]
- ICREA Academia Research Program from the Catalan government
In this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for the Navier-Stokes problem that can be viewed as a variational multiscale (VMS) method under some assumptions. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual-based formulations, the introduction of two velocity subscale components. They represent the components of the convective and the pressure gradient terms, respectively, of the momentum equation that cannot be captured by the finite element mesh. A key idea of the proposed method is that the convective subscale is close to a solenoidal field and the pressure gradient subscale is close to a potential field. The method ensures stability in anisotropic space-time discretizations, which is proved using numerical analysis for a linearized problem and demonstrated in classical numerical tests. The work includes a detailed description of the proposed formulation and several numerical examples that serve to justify our claims. (C) 2019 Elsevier B.V. All rights reserved.
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