A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow

Glowinski, Roland; Pan, Tsorng‐Whay; Hesla, Todd I.; Joseph, Daniel D.; Périaux, Jacques

doi:10.1016/s0045-7825(99)00230-3

Cited by 81 publications

(43 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The numerical simulation of such systems is similarly plagued. If the solid particles are represented by a Lagrangian mesh it is necessary to interpolate their image into the Eulerian mesh, and this is expensive and degrades accuracy [12,26]. Moreover, the absence of a satisfactory theory for the underlying equations undermines the analysis of these algorithms.…”

mentioning

confidence: 99%

An Eulerian Description of Fluids Containing Visco-Elastic Particles

Li¹,

Walkington²

2001

Archive for Rational Mechanics and Analysis

217

203

View full text Add to dashboard Cite

Abstract. Equations governing the flow of fluid containing visco-hyperelastic particles are developed in an Eulerian framework. The novel feature introduced here is to write an evolution equation for the strain. It is envisioned that this will simplify numerical codes which typically compute the strain on Lagrangian meshes moving through Eulerian meshes. Existence results for the flow of linear visco-hyperelastic particles in a Newtonian fluid are established using a Galerkin scheme.

show abstract

mentioning

confidence: 99%

An Eulerian Description of Fluids Containing Visco-Elastic Particles

Li¹,

Walkington²

2001

Archive for Rational Mechanics and Analysis

217

203

View full text Add to dashboard Cite

show abstract

“…As far as the numerical solution of such fluid-solid interaction problems is concerned, several different approaches have been introduced in the literature, based on ALE formulations [7,17,23,24], fictitious domain technique [13], penalty method [20] or Lagrange-Galerkin method [29], but only a few actually received a rigorous analysis of their properties. On this very topic, let us mention the paper of Grandmont et al [15] for proofs of convergence of time decoupling algorithms used to solve an ALE formulation of a one-dimensional fluid-structure interaction problem.…”

Section: S(ζ(t)θ(t))mentioning

confidence: 99%

“…One can easily check (see [13,17,23]) that the strong solution of (1.1)-(1.8) satisfies the following mixed variational formulation: Find (u, ζ, θ, p) verifying (1.7), (1.8), (2.3), and, for almost every t in (0, T ),…”

Section: Weak Formulation Of the Problemmentioning

confidence: 99%

“…Indeed, the method is shown to have an error of O(δt + h 1/2 ), which is suboptimal as a piecewise linear finite element approximation is used. Moreover, this appears somewhat paradoxical since, contrary to "global" methods (like the fictitious domain formulation, the penalty technique or the Lagrange-Galerkin scheme introduced respectively in [13,20,29]), the ALE formulation should allow the scheme to accurately track the motion of the rigid body. This loss in accuracy stems from the fact that the approximate domain at initial time is not based on an exact triangulation of F .…”

Section: Commentsmentioning

confidence: 99%

See 1 more Smart Citation

Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

Legendre¹,

Takahashi²

2008

ESAIM: M2AN

View full text Add to dashboard Cite

show abstract

“…In particular, it was used for modeling unsteady incompressible viscous flow with fixed or moving boundaries [25,21,22,23] and in several applications of wave propagation, such as acoustic scattering problems [15,10,12], electromagnetic scattering problems [17], and musical acoustics [33,29,4]. For both stationary and time-dependent problems the fictitious domain improves the performance of the nu-…”

mentioning

confidence: 99%

A Fictitious Domain Method with Mixed Finite Elements for Elastodynamics

Bécache¹,

Rodríguez²,

Tsogka³

2007

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. We consider in this paper the wave scattering problem by an object with Neumann boundary conditions in an anisotropic elastic body. To obtain an efficient numerical method (permitting the use of regular grids) we follow a fictitious domain approach coupled with a first order velocity stress formulation for elastodynamics. We first observe that the method does not always converge when the Q div 1 − Q 0 finite element is used. In particular, the method converges for some scattering object geometries but not for others. Note that the convergence of the Q div 1 − Q 0 finite element method was shown in [E. Bécache, P. Joly, and C. Tsogka, SIAM J. Numer. Anal., 39 (2002Anal., 39 ( ), pp. 2109Anal., 39 ( -2132 for the elastodynamic problem in the absence of a scattering object (i.e., without the coupling of the mixed finite elements with the fictitious domain method). Therefore we propose here a modification of the Q div 1 − Q 0 element following the approach in [E. Bécache, J. Rodríguez, and C. Tsogka, On the convergence of the fictitious domain method for wave equation problems, Technical report 5802, INRIA, 2006], where the simpler acoustic case was considered. To study the numerical properties of the new element we carry out a dispersion analysis. Several numerical simulations as well as a numerical convergence analysis show that the proposed method provides a good approximate solution.Key words. mixed finite elements, fictitious domain method, elastic waves, convergence AMS subject classifications. 65M60, 65M12, 65M15, 65C20, 74S05 DOI. 10.1137/060655821 1. Introduction. We consider here the scattering of elastic waves by objects or cracks with a homogeneous Neumann boundary condition. This is of interest in several applications such as ultrasonic nondestructive testing, seismic wave propagation, etc. To develop an efficient numerical method we intend to use a fictitious domain approach. Following this approach, we extend artificially the solution to a fictitious domain with a simple shape, typically a rectangle in 2D. Then the boundary condition on the complex geometry is enforced by introducing an auxiliary unknown that leaves only at the boundary of the object. The key point of the method is that the mesh for the unknowns leaving on the enlarged domain can be chosen independently of the geometry of the object. In particular, one can use regular grids or structured meshes which allows for simple and efficient computations.The fictitious domain method was initially introduced for stationary problems [3,30,24,18,20,27], and it was then successfully generalized to time-dependent problems. In particular, it was used for modeling unsteady incompressible viscous flow with fixed or moving boundaries [25,21,22,23] and in several applications of wave propagation, such as acoustic scattering problems [15,10,12], electromagnetic scattering problems [17], and musical acoustics [33,29,4]. For both stationary and time-dependent problems the fictitious domain improves the performance of the nu-

show abstract

A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow

Cited by 81 publications

References 23 publications

An Eulerian Description of Fluids Containing Visco-Elastic Particles

An Eulerian Description of Fluids Containing Visco-Elastic Particles

Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

A Fictitious Domain Method with Mixed Finite Elements for Elastodynamics

Contact Info

Product

Resources

About