The Lagrangian particle method for macroscopic and micro–macro viscoelastic flow computations

Halin, P; Lielens, Grégory; Keunings, Roland; Legat, Vincent

doi:10.1016/s0377-0257(98)00123-2

Cited by 94 publications

(78 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A relative recent and promising approach that does not require closed form constitutive models are so-called micro-macro formulations based on kinetic theories, as first suggested by Laso andÖttinger [161] and Feigl et al [162], and later adopted and improved by Hua and Schieber [163], Bell et al [164], Laso et al [165], Hulsen et al [166],Öttinger et al [167] and Halin et al [168].…”

Section: Discussionmentioning

confidence: 99%

Mixed finite element methods for viscoelastic flow analysis: a review

Baaijens

1998

Journal of Non-Newtonian Fluid Mechanics

272

150

View full text Add to dashboard Cite

The progress made during the past decade in the application of mixed finite element methods to solve viscoelastic flow problems using differential constitutive equations is reviewed. The algorithmic developments are discussed in detail. Starting with the classical mixed formulation, the elastic viscous stress splitting (EVSS) method as well as the related discrete EVSS and the so-called EVSS-G method are discussed among others. Furthermore, stabilization techniques such as the streamline upwind PetrovGalerkin (SUPG) and the discontinuous Galerkin (DG) are reviewed. The performance of the numerical schemes for both smooth and non-smooth benchmark problems is discussed. Finally, the capabilities of viscoelastic flow solvers to predict experimental observations are reviewed.

show abstract

Section: Discussionmentioning

confidence: 99%

Mixed finite element methods for viscoelastic flow analysis: a review

Baaijens

1998

Journal of Non-Newtonian Fluid Mechanics

272

150

View full text Add to dashboard Cite

show abstract

“…138 Nihon Reoroji Gakkaishi Vol.39 2011 eq eq eq eq eq 1 (14) eq eq eq eq eq 1 (15) Here, the notation P eq ( X | Y ) represents the conditional probability of X for given Y. Eq (14) is the equilibrium distribution of a bead index of a slip-spring. Eq (14) can be interpreted as the equilibrium distribution of an ideal gas particle on a one dimensional lattice which has N lattice points.…”

Section: Before Performing Numerical Simulations We Analyticallymentioning

confidence: 99%

Single Chain Slip-Spring Model for Fast Rheology Simulations of Entangled Polymers on GPU

Uneyama

2011

J. Soc. Rheol., Jpn

View full text Add to dashboard Cite

We propose a single chain slip-spring model, which is based on the slip-spring model by Likhtman [A. E. Likhtman, Macromolecules, 38, 6128 (2005)], for fast rheology simulations of entangled polymers on a GPU. We modify the original slip-spring model slightly for efficient calculations on a GPU. Our model is designed to satisfy the detailed balance condition, which enables us to analyze its static or linear response properties easily. We theoretically analyze several statistical properties of the model, such as the linear response, which will be useful to analyze simulation data. We show that our model can reproduce several rheological properties such as the linear viscoelasticity or the viscosity growth qualitatively. We also show that the use of a GPU can improve the performance drastically.

show abstract

“…Along these trajectories the evolution equations reduce to ordinary differential equations. In the first generation Lagrangian Particle Method (LPM) [11] particles are dropped in the flow at the initial time of the simulation, and next these particles are convected by the flow through the whole flow domain. A drawback of LPM is that a large amount of particles is needed in highly graded meshes, resulting in excessive memory and CPU requirements.…”

Section: Methodsmentioning

confidence: 99%

“…At the starting point of a trajectory, the Lagrangian data are initialised by interpolation of the nodal values of a stored finite element field at the corresponding time level. Then the equations are integrated with a predictor-corrector scheme to obtain the values of the Lagrangian data at the fixed particle locations in exactly the same manner as for a forward-tracking Lagrangian particle method [11]. In [8] we have shown that tracking only one time step ∆t backward in time is sufficient for obtaining accurate solutions, provided the initialisation of the Lagrangian data at the start of a particle trajectory is second-order accurate in space.…”

Section: Methodsmentioning

confidence: 99%