FIC/FEM Formulation with Matrix Stabilizing Terms for Incompressible Flows at Low and High Reynolds Numbers

Oñate, Eugenio; Valls, Albert Albareda; García, Julio Martínez

doi:10.1007/s00466-006-0060-y

Cited by 47 publications

(53 citation statements)

References 52 publications

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“…This paper extends the work recently presented by Oñate et al [35,36] where an enhanced stabilized FEM for incompressible flows was derived via finite calculus (FIC). The FIC approach is based on expressing the balance laws in mechanics in a domain of finite size.…”

Section: Introductionmentioning

confidence: 75%

Computation of turbulent flows using a finite calculus–finite element formulation

Oñate

Valls

García

2007

Numerical Methods in Fluids

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SUMMARYWe present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented.

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Section: Introductionmentioning

confidence: 75%

Computation of turbulent flows using a finite calculus–finite element formulation

Oñate

Valls

García

2007

Numerical Methods in Fluids

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“…All these mixed schemes are stabilized via the Variational Multi-Scale method (VMS) [21,31,32,33,41], and, specifically, the Orthogonal Subgrid Scales method, in order to gain control of all the variables while circumventing the restrictiveness of the inf-sup compatibility conditions on the choice of the interpolation spaces. Similar mixed approaches have been proposed using alternative stabilization techniques, like SUPG [4,5,29,36] or FIC [41].…”

Section: Introductionmentioning

confidence: 99%

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

et al. 2016

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K: explicit mixed finite elements, stabilization, incompressibility, plasticity, strain softening, strain localization, mesh independence. AbstractThis paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P 1P 1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.

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“…This approach was proved to show better mesh independence properties while providing the formal guarantee of a strain field converging at the same rate as the displacement one, which manifests in enhanced stress/analysis accuracy in both linear and non-linear analyses [8]. Following the ideas in [9,10,11,12,13,14], a stabilization technique is needed to allow the use of the same order of interpolation for the two primary variables of interest. Specifically the Variational Multiscale Method (VMS) is employed in the current work.…”

Section: Introductionmentioning

confidence: 99%

Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

et al. 2015

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Computational mechanics. Although appealing for their simplicity, low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff behaviour when dealing with complex problems. A recent proposal to address such limitations is the adoption of mixed displacement-strain technologies which were shown to satisfactorily address both problems. Unfortunately, although appealing, the use of such element technology puts a large burden on the linear algebra, as the solution of larger linear systems is needed. In this paper, the use of an explicit time integration scheme for the solution of the mixed strain-displacement problem is explored as an alternative. An algorithm is devised to allow the effective time integration of the mixed problem. The developed method retains second order accuracy in time and is competitive in terms of computational cost with the standard irreducible formulation.

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FIC/FEM Formulation with Matrix Stabilizing Terms for Incompressible Flows at Low and High Reynolds Numbers

Cited by 47 publications

References 52 publications

Computation of turbulent flows using a finite calculus–finite element formulation

Computation of turbulent flows using a finite calculus–finite element formulation

Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity

Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

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