A Novel Arbitrary Lagrangian–Eulerian Finite Element Method for a Mixed Parabolic Problem in a Moving Domain

2020 ◽  
Vol 85 (1) ◽  
Author(s):  
Rihui Lan ◽  
Pengtao Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parabolic Problem ◽  
Arbitrary Lagrangian Eulerian ◽  
Moving Domain ◽  
Element Method

Semi-Implicit Coupling of CS-FEM and FEM for the Interaction Between a Geometrically Nonlinear Solid and an Incompressible Fluid

2015 ◽  
Vol 12 (05) ◽  
pp. 1550025 ◽  
Author(s):  
Tao He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Fluid ◽  
Computational Cost ◽  
Geometrically Nonlinear ◽  
Arbitrary Lagrangian Eulerian ◽  
Coupling Strategy ◽  
Smoothed Finite Element Method ◽  
Characteristic Based Split ◽  
Element Method

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

NUMERICAL SIMULATION OF FLOW WITH LARGE-AMPLITUDE OSCILLATION OF SOLID BOUNDARIES BY PENALTY FINITE ELEMENT FORMULATIONS

2008 ◽  
Vol 22 (24) ◽  
pp. 4205-4216 ◽  
Author(s):  
W. Q. WANG ◽  
L. X. ZHANG ◽  
Y. YAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Amplitude ◽  
Stokes Equations ◽  
Elastic Beam ◽  
Navier Stokes ◽  
Solid Boundary ◽  
Arbitrary Lagrangian Eulerian ◽  
Eulerian Formulation ◽  
Element Method

A penalty finite element method for the incompressible viscous Navier–Stokes equations is incorporated in an arbitrary Lagrangian–Eulerian formulation to model a flow in the fluid–structure interaction (FSI) with moving meshes. The formulation is derived based on the classical Ritz–Galerkin framework for forming a coupled formulation on the finite element method. In such a way, the pressure-constrained equation is incorporated in the momentum equations of the system with FSI. An improving spring smooth and remeshing technique is used to successively accommodate fluid meshes as the oscillation of a solid boundary in simulation. To demonstrate the performance of the proposed approach, the simulations of the flow with an elastic beam in water, that is oscillating in a large amplitude are presented. The simulations show that the methodology suggested in this paper has a good numerical stability and reliability, and the results are highly agreeable with the published reference.

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