Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier-Stokes problem

Castillo E.; Codina R.

Abstract

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.

Más información

Título según WOS: Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier-Stokes problem
Título según SCOPUS: Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem
Título de la Revista: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volumen: 349
Editorial: ELSEVIER SCIENCE SA
Fecha de publicación: 2019
Página de inicio: 701
Página final: 721
Idioma: English
DOI:

10.1016/j.cma.2019.02.041

Notas: ISI, SCOPUS