Pure Lagrangian and semi-Lagrangian finite element methods for the numerical solution of Navier–Stokes equations
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Pure Lagrangian and semi-Lagrangian finite element methods for the numerical solution of Navier–Stokes equationsDate
2015-05-26Citation
M. Benítez, A. Bermúdez, Pure Lagrangian and semi-Lagrangian finite element methods for the numerical solution of Navier–Stokes equations, Appl. Numer. Math, 95 (2015) 62-81.
Abstract
[Abstract]: In this paper we propose a unified formulation to introduce Lagrangian and semi-Lagrangian velocity and displacement methods for solving the Navier–Stokes equations. This formulation allows us to state classical and new numerical methods. Several examples are given. We combine them with finite element methods for spatial discretization. In particular, we propose two new second-order characteristics methods in terms of the displacement, one semi-Lagrangian and the other one pure Lagrangian. The pure Lagrangian displacement methods are useful for solving free surface problems and fluid-structure interaction problems because the computational domain is independent of the time and fluid–solid coupling at the interphase is straightforward. However, for moderate to high-Reynolds number flows, they can lead to high distortion in the mesh elements. When this happens it is necessary to remesh and reinitialize the transformation to the identity. In order to assess the performance of the obtained numerical methods, we solve different problems in two space dimensions. In particular, numerical results for a sloshing problem in a rectangular tank and the flow in a driven cavity are presented.
Keywords
Navier–Stokes equations
Characteristics methods
Lagrange–Galerkin methods
Second-order schemes
Pure Lagrangian methods
Characteristics methods
Lagrange–Galerkin methods
Second-order schemes
Pure Lagrangian methods
Description
Accepted manuscript.
Editor version
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© 2015. This manuscript version is made available under the CC-BY-NC-ND
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ISSN
0168-9274
1873-5460 (e-ISSN)
1873-5460 (e-ISSN)