A family of residual‐based stabilized finite element methods for Stokes flows

Oñate, Eugenio; Nadukandi, Prashanth; Idelsohn, Sergio; García, Julio Martínez; Felippa, Carlos A.

doi:10.1002/fld.2468

Cited by 22 publications

(39 citation statements)

References 43 publications

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“…Compared to previous FIC-FEM stabilized formulations of the Navier-Stokes problem [1,17,19,20,21], our method contains a new term on the momentum equation, which introduces an additional non-isotropic dissipation in the direction of the velocity gradients, and a stabilized formulation for the mass equation which is based on a second order FIC balance in space and represents an incompressible Eulerian version of the method presented for quasiincompressible flows in [2].…”

Section: Discussionmentioning

confidence: 99%

“…We follow the approach presented in [22,21] to obtain a stabilized formulation for the mass balance equation given by Eq. (2).…”

Section: Stabilized Mass Balance Equationmentioning

confidence: 99%

“…The expression obtained in this way can be used as the starting point to obtain the weak form of the problem, in place of the original point-wise equation, and results in a variational problem with additional terms that have a stabilizing effect in the numerical solution. The FIC approach has been used in conjunction with the finite element method (FEM) to simulate incompressible flows at a range of Reynolds numbers [19,20,21] in the past. In this paper we present a new FIC-FEM formulation for the incompressible Navier-Stokes equations and explore the possibility of using it to simulate turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

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A FIC-based stabilized finite element formulation for turbulent flows

Cotela-Dalmau

Rossi

Oñate

2017

Computer Methods in Applied Mechanics and Engineering

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We present a new stabilized finite element (FEM) formulation for incompressible flows based on the Finite Increment Calculus (FIC) framework [1]. In comparison to existing FIC approaches for fluids, this formulation involves a new term in the momentum equation, which introduces non-isotropic dissipation in the direction of velocity gradients. We also follow a new approach to the derivation of the stabilized mass equation, inspired by recent developments for quasi-incompressible flows [2]. The presented FIC-FEM formulation is used to simulate turbulent flows, using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation.

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Section: Discussionmentioning

confidence: 99%

“…We follow the approach presented in [22,21] to obtain a stabilized formulation for the mass balance equation given by Eq. (2).…”

Section: Stabilized Mass Balance Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A FIC-based stabilized finite element formulation for turbulent flows

Cotela-Dalmau

Rossi

Oñate

2017

Computer Methods in Applied Mechanics and Engineering

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“…The stabilization procedure is based on the consistent derivation of a residualbased stabilized expression of the mass balance equation using the Finite Calculus (FIC ), also called Finite Increment Calculus method [43,76,92,94,[96][97][98]. The main ideas of this part are taken from [82] where the stabilization technique was derived for homogeneous viscous fluids.…”

Section: Quasi-incompressible Materialsmentioning

confidence: 99%

Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems Using the PFEM

Franci

2017

Springer Theses

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The objective of this work is the derivation and implementation of a unified Finite Element formulation for the solution of fluid and solid mechanics, Fluid-Structure Interaction (FSI) and coupled thermal problems.The unified procedure is based on a stabilized velocity-pressure Lagrangian formulation.Each time step increment is solved using a two-step Gauss-Seidel scheme: first the linear momentum equations are solved for the velocity increments, next the continuity equation is solved for the pressure in the updated configuration.The Particle Finite Element Method (PFEM) is used for the fluid domains, while the Finite Element Method (FEM) is employed for the solid ones. As a consequence, the domain is remeshed only in the parts occupied by the fluid.Linear shape functions are used for both the velocity and the pressure fields. In order to deal with the incompressibility of the materials, the formulation has been stabilized using an updated version of the Finite Calculus (FIC) method. The procedure has been derived for quasi-incompressible Newtonian fluids. In this work, the FIC stabilization procedure has been extended also to the analysis of quasi-incompressible hypoelastic solids.Specific attention has been given to the study of free surface flow problems. In particular, the mass preservation feature of the PFEM-FIC stabilized procedure has been deeply studied with the help of several numerical examples. Furthermore, the conditioning of the problem has been analyzed in detail describing the effect of the bulk modulus on the numerical scheme. A strategy based on the use of a pseudo bulk modulus for improving the conditioning of the linear system is also presented.The unified formulation has been validated by comparing its numerical results to experimental tests and other numerical solutions for fluid and solid mechanics, and FSI problems. The convergence of the scheme has been also analyzed for most of the problems presented.The unified formulation has been coupled with the heat tranfer problem using a staggered scheme. A simple algorithm for simulating phase change problems is also described. The numerical solution of several FSI problems involving the temperature is given.The thermal coupled scheme has been used successfully for the solution of an industrial problem. The objective of study was to analyze the damage of a nuclear power plant pressure vessel induced by a high viscous fluid at high temperature, the corium. The numerical study of this industrial problem has been included in this work.ii ResumenEl objectivo del presente trabajo es la derivación e implementación de una formulación unificada con elementos finitos para la solución de problemas de mecánica de fluidos y de sólidos, interacción fluido-estructura (Fluid-Structure Interaction (FSI)) y con acoplamiento térmico.El método unificado está basado en una formulación Lagrangiana estabilizada y las variables incçognitas son las velocidades y la presión. Cada paso de tiempo se soluciona a través de un esquema de dos pasos de tipo Gauss-Seide...

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“…A mixed FEM with a linear interpolation for the velocities and the pressure was used in both cases. FIC/FEM formulations for Stokes flows were reported in [26,40]. Applications of the FIC/FEM technique to fluid-structure interaction (FSI) problems were reported in [14] (for Eulerian flows) and in [41][42][43][44] (for Lagrangian flows).…”

Section: Applications To the Fic/fem Procedures In Fluid Mechanicsmentioning

confidence: 99%

Finite increment calculus (FIC): a framework for deriving enhanced computational methods in mechanics

Oñate

2016

Adv. Model. and Simul. in Eng. Sci.

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In this paper we present an overview of the possibilities of the finite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical properties for stability and accuracy. The basic concepts of the FIC procedure are presented in its application to problems of advection-diffusion-reaction, fluid mechanics and fluid-structure interaction solved with the finite element method (FEM). Examples of the good features of the FIC/FEM technique for solving some of these problems are given. A brief outline of the possibilities of the FIC/FEM approach for error estimation and mesh adaptivity is given.

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A family of residual‐based stabilized finite element methods for Stokes flows

Cited by 22 publications

References 43 publications

A FIC-based stabilized finite element formulation for turbulent flows

A FIC-based stabilized finite element formulation for turbulent flows

Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems Using the PFEM

Finite increment calculus (FIC): a framework for deriving enhanced computational methods in mechanics

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