Monolithic stabilized finite element method for rigid body motions in the incompressible Navier-Stokes flow

2010 ◽  
Vol 19 (5-7) ◽  
pp. 547-573 ◽  
Author(s):  
Stephanie Feghali ◽  
Elie Hachem ◽  
Thierry Coupez
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rigid Body ◽  
Stokes Flow ◽  
Navier Stokes ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Rigid Body Motions ◽  
Element Method

scholarly journals Monolithic stabilized finite element method for rigid body motions in the incompressible Navier-Stokes flow

2010 ◽  
pp. 547-573
Author(s):  
Stephanie Feghali ◽  
Elie Hachem ◽  
Thierry Coupez
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Extra Stress Tensor ◽  
Monolithic Formulation ◽  
Rigid Body Motions

We propose a new immersed volume method for solving rigid body motions in the incompressible Navier-Stokes flow. The used monolithic formulation gives rise to an extra stress tensor in the Navier-Stokes equations coming from the presence of the structure in the fluid. The system is solved using a finite element variational multiscale (VMS) method, which consists in here of a decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. The distinctive feature of the proposed approach resides in the efficient enrichment of the extra constraint. We assess the behaviour and accuracy of the proposed formulation in the simulation of 2D and 3D examples.

scholarly journals An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Aiwen Wang ◽  
Xin Zhao ◽  
Peihua Qin ◽  
Dongxiu Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Mesh Size ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Element Method

We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e.,Q1−P0andP1−P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh sizeH, a large general Stokes equation on the fine mesh with mesh sizeh=O(H)2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph) with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh sizeh. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.

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