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- W2479231665 abstract "The Lagrangian Particle Method (LPM) has been proposed recently (Halin et al., 1998) for the computation of transient viscoelastic flows using either a constitutive equation (macroscopic approach) or a kinetic theory model (micro-macro approach). At the start of the simulation, we drop an ensemble of Lagrangian particles in the flow domain that drift along the fluid trajectories. Each particle acts as a polymer extra-stress calculator. At each time step, the velocity-pressure fields are calculated with a classical finite element method by solving the Navier-Stokes equations slightly modified to account for the polymer stress. To do so, we use the polymer stress values calculated at the previous time step. Next, we track the particles using the new velocity field, and we calculate the polymer stress at each particle location. This is done by solving a macroscopic constitutive equation (e. g. Oldroyd-B, Fene-P, Fene-L (Lielens et al., 1998)) or by simulating polymer dynamics with a kinetic theory model (e. g. the Fene dumbbell theory). In the latter case, each particle contains a large ensemble of dumbbells whose configuration is updated by solving the relevant stochastic differential equation along the fluid trajectories. Finally, the Lagrangian polymer stress field must be mapped onto Eulerian points so as to be accounted for when conservation law equations are solved at the next time step. To this end, we perform a least-squares approximation on an element-by-element basis." @default.
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- W2479231665 date "1998-01-01" @default.
- W2479231665 modified "2023-10-17" @default.
- W2479231665 title "The Adaptive Lagrangian Particle Method (ALPM) Applied to the Startup Flow of Finitely Extensible Dumbbells Between Eccentric Cylinders" @default.
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- W2479231665 doi "https://doi.org/10.1007/978-3-642-51062-5_168" @default.
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