A Lagrangian finite element approach for the analysis of fluid–structure interaction problems

Cremonesi, Massimiliano; Frangi, Attilio; Perego, U.

doi:10.1002/nme.2911

Cited by 56 publications

(68 citation statements)

References 36 publications

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“…In a weakly coupled segregated schemes when the transfer of informations through the interface is performed only once for each time step, (for example see [42]), whereas in strongly coupled schemes this operation is performed within a convergence Chapter 1. Introduction 7 loop (as a reference see [34]). Clearly, a weakly coupled scheme has a lower computational cost but it can be used only when the interaction between the solid and the fluid domains is not strong or complex.…”

Section: Algorithms For Fsi Problemsmentioning

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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Section: Algorithms For Fsi Problemsmentioning

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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“…where U and P contain the nodal values of velocity and pressure respectively, M is the mass matrix, K is the matrix of viscoplastic coefficients, D is the discretization of the divergence operator, B is the vector of body forces and boundary tractions (see [3] for the definition of these matrices). K c represents the discretization of the convective term on the slip boundary and K slip is the discretization of the integral slip term.…”

Section: Discretization and Numerical Techniquementioning

confidence: 99%

“…Moreover, an "alpha shape" technique is introduced to identify the free-surfaces and the interacting surfaces between water and landslide. Details on the numerical procedure can be found in [2,3,4,5].…”

Section: Discretization and Numerical Techniquementioning

confidence: 99%

“…The numerical analysis of these events requires capabilities for tracking interfaces and free surfaces undergoing large displacements, and accounting for the mixing of different constituents, for complex constitutive behaviors and for multi-physics processes. In this work, a recently developed Lagrangian finite element approach [3,4,5], formulated in the spirit of the Particle Finite Element Method (PFEM), is here reconsidered and adapted to the specific case of landslide-reservoir interaction. The PFEM was originally developed [5,6,7] for solving problems involving free surfaces fluid flows and fluid-structure interaction.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Lagrangian Pfem Approach to the Numerical Simulation of 3d Large Scale Landslides Impinging in Water Reservoirs

Cremonesi¹,

Ferri²,

Perego³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Landslides are exceptional natural hazards that can generate extensive damage to structures and infrastructures causing a large number of casualties. A particularly critical condition occurs when the landslide impinges in water reservoirs generating high waves. This work proposes a numerical tool to simulate the macroscopic behavior of a propagating landslide. The Particle Finite Element Method (PFEM) is here used and adapted to the specific case of landslide runout. The Lagrangian Navier-Stokes equations of incompressible fluids are used to describe the macroscopic landslide behavior. A rigid-visco-plastic law with a pressure dependent threshold, typical of a non-Newtonian, Bingham-like fluid, is used to characterize the constitutive behavior of the flowing material. Special attention is devoted to the definition of ad-hoc pressure-dependent slip boundary conditions at the interface between the flowing mass and the basal surface to better represent the real landslide-slope interaction. The proposed approach has been validated against numerical benchmarks and small scale experimental tests, showing a good agreement with the physical measurements. Real case scenarios have also been considered. 3D geometries of critical sites, where landslides have occurred, have been reconstructed allowing for the simulation of large scale real landslide runouts. Results are compared with post-event images and measurements, showing the accuracy and the capability of the method. 608

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“…The PFEM was orginally developed to solve problems involving free surfaces fluid flows [9,13,4] and fluid-structure interaction [10,6]. The method is here revisited and applied to the simulation of compressible problems.…”

Section: Numerical Tecniquementioning

confidence: 99%

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

Cremonesi¹,

Frangi²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The numerical solution of compressible fluid flows is of paramount importance in many industrial and engineering applications. Compared to the classical fluid dynamics, the introduction of the fluid compressibility changes the formulation of the problem and consequently its computational treatment.Among the possible numerical solutions of compressible flow problems, the finite element method has always been privileged. However, the standard Eulerian approaches with fixed domain are not particularly suited to represent the strong shock waves and the significant movement of the external boundaries. On the contrary, in problems characterized by evolving surfaces, Lagrangian approaches can be very effective.The governing equations of compressible flow problems are mass, momentum and energy conservation. These equations are discretized in the spirit of the Lagrangian Particle Finite Element Method (PFEM). The strong distortions of the mesh, typical of the Lagrangian approaches, are managed with a continuous remeshing of the computational domain. The nodal unknowns are velocities, density and internal energy. To fully exploit the potential of continuous remeshing, only nodal variables are stored and consequently only linear interpolation are used. In addition, an artificial viscosity has been introduced to stabilize the formation and propagation of shock waves. Finally, explicit time integration of the governing equations enables a highly efficient solution of the discretized problem.The proposed approach has been validated against typical benchmarks of gas dynamics in the presence of strong shock waves. A very good agreement has been shown in all the tests proving the excellent accuracy and versatility of the proposed method.

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A Lagrangian finite element approach for the analysis of fluid–structure interaction problems

Cited by 56 publications

References 36 publications

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

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

A Lagrangian Pfem Approach to the Numerical Simulation of 3d Large Scale Landslides Impinging in Water Reservoirs

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

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