## Lagrangian Finite-Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy

Publication: Research - peer-review › Journal article – Annual report year: 2009

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**Lagrangian Finite-Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy.** / Marin, José Manuel Román; Rasmussen, Henrik K.

Publication: Research - peer-review › Journal article – Annual report year: 2009

### Harvard

*Journal of Non-Newtonian Fluid Mechanics*, vol 156, no. 3, pp. 177-188. DOI: 10.1016/j.jnnfm.2008.08.005

### APA

*Journal of Non-Newtonian Fluid Mechanics*,

*156*(3), 177-188. DOI: 10.1016/j.jnnfm.2008.08.005

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*Journal of Non-Newtonian Fluid Mechanics*. 2009, 156(3). 177-188. Available: 10.1016/j.jnnfm.2008.08.005

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### Bibtex

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### RIS

TY - JOUR

T1 - Lagrangian Finite-Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy

AU - Marin,José Manuel Román

AU - Rasmussen,Henrik K.

PY - 2009

Y1 - 2009

N2 - A new finite element scheme for the numerical simulation of three-dimensional time-dependent flow of viscoelastic fluids is presented. The viscoelastic fluids are of the K-BKZ integral type and the method is based on a Lagrangian kinematics description of the fluid flow. The spatial coordinate system attached to the particles is discretized by ten-node quadratic tetrahedral elements using Cartesian coordinates and the pressure by linear interpolation inside these elements. The spatial discretization of the governing equations follows the mixed Galerkin finite element method. The time integral is discretized by a quadratic interpolation in time. The convergence of the method in time and space was demonstrated on the free surface problem of a filament stretched between two plates, considering the axisymmetric case as well as the growth of non-axisymmetric disturbances on the free surface. The scheme converges with respect to discretization of the spatial and time dimensions, both with third order.

AB - A new finite element scheme for the numerical simulation of three-dimensional time-dependent flow of viscoelastic fluids is presented. The viscoelastic fluids are of the K-BKZ integral type and the method is based on a Lagrangian kinematics description of the fluid flow. The spatial coordinate system attached to the particles is discretized by ten-node quadratic tetrahedral elements using Cartesian coordinates and the pressure by linear interpolation inside these elements. The spatial discretization of the governing equations follows the mixed Galerkin finite element method. The time integral is discretized by a quadratic interpolation in time. The convergence of the method in time and space was demonstrated on the free surface problem of a filament stretched between two plates, considering the axisymmetric case as well as the growth of non-axisymmetric disturbances on the free surface. The scheme converges with respect to discretization of the spatial and time dimensions, both with third order.

KW - Three-dimensional

KW - K-BKZ

KW - Viscoelastic

KW - Finite Element

KW - Endplate instability

KW - Lagrangian

U2 - 10.1016/j.jnnfm.2008.08.005

DO - 10.1016/j.jnnfm.2008.08.005

M3 - Journal article

VL - 156

SP - 177

EP - 188

JO - Journal of Non-Newtonian Fluid Mechanics

T2 - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

IS - 3

ER -