A fictitious domain approach for the simulation of dense suspensions

Gallier, Stany; Lemaire, Élisabeth; Lobry, Laurent; Peters, François

doi:10.1016/j.jcp.2013.09.015

Cited by 57 publications

(59 citation statements)

References 75 publications

(104 reference statements)

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“…This section briefly describes the numerical method used ; more details can be found in a previous paper (Gallier et al 2014). In a fictitious domain method, solid particles are supposed to be filled with a fluid having the same properties as the actual fluid.…”

Section: Dns Simulation : Fictitious Domain Methodsmentioning

confidence: 99%

“…In absence of inertia, hydrodynamic interactions can be defined as (Gallier et al 2014;Yu & Shao 2007)…”

Section: Governing Equationsmentioning

confidence: 99%

“…(2.4)-(2.8) consists in enforcing the rigid body motion inside particles, as well as updating the new forcing term λ n+1 and eventually computing particle velocities. Details are skipped in the frame of this overview and may be found in Gallier et al (2014). Once particle velocities are known, their position can be tracked by solving dX dt = U (2.9)…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…The latter is incorporated as a body-force in the Stokes equations that are subsequently solved using classical flow solvers. More recently, Direct Numerical Simulations (DNS) have emerged as a valuable alternative to the aforementioned SD and FCM methods, such as Lattice-Boltzmann methods (Ladd 1994a,b;Ladd & Verberg 2001) or fictitious domain methods (Glowinski et al 1998(Glowinski et al , 2001Gallier et al 2014;Wachs 2009;Yu & Shao 2007). Because they directly solve the governing equations (Navier-Stokes or Stokes equations) without any further assumptions other than numerical approximations, they are more general and appropriate to deal with inertial flows, arbitrary-shaped particles or non-Newtonian fluid.…”

Section: Introductionmentioning

confidence: 99%

“…The study specifically addresses the role of friction forces between particles. In present work, we make use of a fictitious domain approach as detailed in Gallier et al (2014). Our method explicitly solves long-range hydrodynamics and incorporates a modelling of lubrication interactions as well as DEM (Discrete Element Method)-based contact forces.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Rheology of sheared suspensions of rough frictional particles

et al. 2014

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This paper presents three-dimensional numerical simulations of non-Brownian concentrated suspensions in a Couette flow at zero Reynolds number using a fictitious domain method. Contacts between particles are modelled using a discrete element method (DEM)-like approach, which allows for a more physical description, including roughness and friction. This work emphasizes the effect of friction between particles and its role on rheological properties, especially on normal stress differences. Friction is shown to notably increase viscosity and second normal stress difference $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}|N_2|$ and decrease $|N_1|$, in better agreement with experiments. The hydrodynamic and contact contributions to the overall particle stress are particularly investigated. This shows that the effect of friction is mostly due to the additional contact stress since the hydrodynamic stress remains unaffected by friction. Simulation results are also compared with experiments, such as normal stresses or effective friction coefficient $\mu (I_v)$, and the agreement is improved when friction is accounted for. This suggests that friction is operative in actual suspensions.

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Section: Dns Simulation : Fictitious Domain Methodsmentioning

confidence: 99%

“…In absence of inertia, hydrodynamic interactions can be defined as (Gallier et al 2014;Yu & Shao 2007)…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rheology of sheared suspensions of rough frictional particles

et al. 2014

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A consistent sharp interface fictitious domain method for moving boundary problems with arbitrarily polyhedral mesh

Chai

Wang

et al. 2021

Numerical Methods in Fluids

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A consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain and transport of the body force; the pseudo body force defined at "solid centers" ensures the algorithm consists of the body force between the continuous form and its discretization counterpart; an explicit flux correction on cell faces and resulting mass source is introduced into the continuity equation to lower noncontinuity errors in the velocity correction step. This method is valid for stationary and moving boundary problems with arbitrarily polyhedral mesh.Several numerical tests are carried out to validate the proposed method. A second-order spatial accuracy is found in the flow around a cylinder case, and the spurious force oscillation is well suppressed for the in-line oscillation of a circular cylinder case. The performances on different meshes are tested, and structured mesh yields the best result, polyhedral next, and tetrahedral worst. A serial of tests is further performed on structured mesh to verify the effect of three different features (i.e., storing the body force at the solid centers, flux correction, and whether including the body force in the momentum equation) on the numerical predictions. Numerical results show that, in the in-line oscillation of a circular cylinder, "flux correction" can eliminate the large spikes in the drag coefficient, and "including the body force in the momentum equation" helps suppress the small oscillations. For other tests, "storing the body force at the solid centers" has enormous impacts on the final results of moving boundary problems, "flux correction" has little effects and the necessity of "including the body force in the momentum equation" is case dependent.

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Phase‐field formulation of a fictitious domain method for particulate flows interacting with complex and evolving geometries

Reder

Schneider

Wang

et al. 2021

Numerical Methods in Fluids

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A distributed Lagrange multiplier/fictitious domain method in a phase-field formulation for the simulation of rigid bodies in incompressible fluid flow is presented. The phase-field method yields an implicit representation of geometries and thus rigid body particulate flows within arbitrary geometries can be simulated based on a fixed Cartesian grid. Therefore, a phase-field based collision model is introduced in order to address contact of particles with arbitrary solid structures as boundaries. In addition, grain growth within the boundary geometry can be considered leading to changes in its shape during the simulation. The method is validated on benchmark problems and a convergence study is performed. Multiple numerical experiments are carried out in order to show the methods' capability to simulate problems with differently shaped rigid bodies and particulate flows involving complex boundary geometries like foam structures.

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A fictitious domain approach for the simulation of dense suspensions

Cited by 57 publications

References 75 publications

Rheology of sheared suspensions of rough frictional particles

Rheology of sheared suspensions of rough frictional particles

A consistent sharp interface fictitious domain method for moving boundary problems with arbitrarily polyhedral mesh

Phase‐field formulation of a fictitious domain method for particulate flows interacting with complex and evolving geometries

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