A lattice Boltzmann model for Jeffreys viscoelastic fluid

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Abstract
In this letter, we show that an eleven-velocity two-dimensional lattice Boltzmann model using several relaxation times obeys a Jeffreys viscoelastic constitutive law with full isotropic behavior. The connection between the free parameters of the model and the Jeffreys transport coefficients is made with the help of a modified Chapman-Enskog expansion taking into account large relaxation time effects. Numerical simulation of a pulsed Couette flow is performed leading to an excellent agreement with predictions.